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//home/cluster1/data/bu01/1121861/html/mydownloads/praat.exe
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YYݞ $D$$%(vd ܞ uD$ ݆ ݆ Euݞ ݖ V YVYVY1@]^[SVD$ p V YVYV1Y@^[SVD$ p V YVUYV1Y@^[SVUt$ ~ l$$^u1j hwd V F hwd hwd v " v > Yu7݃ ܃ PP vd $hwd v d j v Y F 9tUV YY 1 hwd P YY $ L$D$ D$(vd $Eu D$ $D$݃ %(vd $u$D$ $ S+ YSYSAY1@]^[SVUt$ ~ l$$^u1j hwd V F hVwd hwd v v Yuj v q Y F 9tUV YY 1 hwd P ݃ ܃ YY vd $ L$D$ $\$u D$ $D$݃ $Eu$D$ $ S+ YSYSY1@]^[SVUt$ ~ l$$^u1j hwd Ve F hVwd hwd v v Yuj v > Y F 9tUVd YY 1 hwd P ܃ YY $ L$D$ $\$u D$ $D$݃ $Eu $D$ $ ݃ ݃ Euݛ ݓ S+ YSYSY1@]^[SVUt$ ~ l$$^u1j hxd V) F hVwd hwd v a v } Yuj v Y F 9tUV( YY 1 hwd PX ܃ YY $ L$D$ $\$u D$ $D$݃ $Eu $D$ $ ݃ ݃ Euݛ ݓ S+ YS\YSY1@]^[ËD$HpX݁ ܁ PP vd $h'xd * 1@ËD$HpX h'xd 1@ËD$HpX h'xd 1@ËD$HpX݁ ܡ PP $h'xd 1@S\$݃ ܣ $j > YD$ ud uf݃ D$ݛ ݃ (vd ܛ Euݓ ݃ $ݛ ݃ %(vd ܛ ulݓ d݃ D$ݛ ݃ %(vd ܛ uݓ ݃ $$ݛ ݃ (vd ܛ Euݓ S( Y[ËD$H݁ ܡ PP 0vd $Q 1@ËD$H݁ ܡ PP ud $Q 1@D$L$݁ u EAt݁ 8vd #݁ u$ 8vd PP $Q2 Q' YËD$H݁ ܡ8 ݙ ݁ (vd ܙ Euݑ ݁ ܡ8 ݙ ݁ (vd ܙ Euݑ ݁ ܁ PP vd $Q 1@ËD$H݁ ܁8 ݙ ݁ %(vd ܙ uݑ ݁ ܁8 ݙ ݁ %(vd ܙ uݑ ݁ ܁ PP vd $Q[ 1@ËD$H݁ ܡ8 ݙ ݁ (vd ܙ Euݑ ݁ ܁ PP vd $Q 1@ËD$H݁ ܁8 ݙ ݁ %(vd ܙ uݑ ݁ ܁ PP vd $Q 1@ËD$H݁ ܡ8 ݙ ݁ (vd ܙ Euݑ ݁ ܁ PP vd $Q2 1@ËD$H݁ ܁8 ݙ ݁ %(vd ܙ uݑ ݁ ܁ PP vd $Q 1@SVU\$ { l$$suFj h0xd S C hwd hwd s hwd hwd s s YuH hwd s hwd s j s ( Y C 9tUSN YY 1 hwd P~ YYݞ L$D$ D$(vd ܞ EuD$ hwd s . YYݞ $D$$%(vd ܞ uD$ V YVYV{YVY1@]^[SVt$݆ ܦ 5@vd ݆ ݞ ݆ ݞ V YV#YVYVRY^[SVt$݆ ܦ 5Hvd $j Y݆ $$ݞ ݆ (vd ܞ Euݖ ݆ $ݞ ݆ %(vd ܞ uݖ V YVtYViYVY^[SU\$ S+ YSYSYSHY][SVt$݆ ݆ EuBݖ V YVYVYVY^[SVUD$t$(PD$PD$ PD$ Pt$4g ݆ ݆ D$H$$5ud ܦ D@$ ݆ ݞ ݆ (vd ܞ Euݞ ݆ ݞ ݆ %(vd ܞ uݞ V YV Y =ud u 1E y tu9tq y 4 y Y4 y B y Y l Y4 y YEdtك]^[S \$(D$ D$ j D$Ph D$$Ph D$$PjOD$(Ph t$HU (D$+D$PD$PD$+D$ PD$$P 5 D$koD$ f D$koD$f $$PP $5ud 5ud D$D$PP $5ud 5ud 躮 $$$PP $5ud 5ud D$D$PP $5ud 5ud 3 $ | Yj D$ PjOD$Ph s T D$ud D$ [ud 1SVWUt$ 1Aȃ< y u4 y y =y u Y 1@, y t9t=ud t0 ݅ ݆ Et݆ ܝ uJEuݖ ݅ ݆ uݞ V YV8 V> YV!Y Ͽ ݆ ܝ Yt݆ ܝ E 1E y 9 ݆ ܛ uݑ ݆ ܛ Eu y ݐ 4 y Y4 y n y Y YEdl41@94 y u$ y y V Y վ Y tVHY]_^[맋D$j pj 1@ËD$j pj m 1@ËD$j pj 1@ËD$j pj 1@h5xd 1Y@SU wd \$ ShU,YhiG j h;xd hJxd S j j hOxd hJxd S՝ j haxd SN hatG j hgxd haxd S諝 hatG h h~xd haxd S莝 h-tG jhxd haxd St htG j hxd haxd SZ htG j hxd haxd S@ j hxd S蹜 S+ YhiG h pLhxd S h~yG j hxd hxd S hzG jAhxd hxd S՜ hG jIhxd hxd S軜 hG jOhxd hxd S衜 hG jNhxd hxd S臜 huG jhyd hxd Sm hvG jhyd hxd SS j j h(yd hxd S< hiG h h3yd hxd S hjG j h:yd hxd S hkG j hByd hxd S hlG h @ hOyd hxd SΛ hlG jh[yd hxd S贛 j hwd S- hmG j hmyd hwd S芛 hnG j hwyd hwd Sp hnG h hyd hwd SS hnG j hyd hwd S9 h0oG j hyd hwd S hpG j hyd hwd S hqG j hyd hwd S hqG h h zd hwd SΚ hrG j h;zd hwd S贚 hvG jhWzd hwd S蚚 hUwG jhfzd hwd S耚 hwG h @ hszd hwd Sc hwG h hzd hwd SF hRxG h @ hzd hwd S) hRxG h hzd hwd S hxG h hzd hwd S hyG h h{d hwd Sҙ hւG j h5xd h {d S踙 ][SVUt$1Ej j h%{d vW j j h jj\ Ph jh jh jjvSV 8j j h \ PjOjj jjjh Sh h-{d K 8Vh |G jP= j j h W\ "PjOjj jjUh Sh h1{d K 8Vh{G jP= j j h \ "PjOjj jjUh Sh h4{d jK 8Vhj{G jPK= j j h [ "PjOjj jjUh Sh h8{d !K 8Vht|G jP= j h5wh jh h 5wh jh a[ PE"jOjjjTh jh Pjwjjvjh Sh h<{d J h j jPh [ @PjOjj jjjh Sh hF{d tJ 8VhG h G< j P \ j j hL{d SCU xh t2 1j kZ Pj jjUh jh jh jjv TT 8 D xh YtUj j hX{d SQ j jj@jh j2jOjh jh jjv S 8 D YSxD Y]^[SUl$ ]$5ji S YYuh hwd h]{d C K CK ݅ ݅ t ܕ Euݝ ݅ ܝ tܝ Eu ݅ ܝ u0 ݅ ݅ uݝ ݅ ݅ Euݝ ݅ ݅ uݝ ݅ ݅ Euݝ U Y][SD$$D$ \$Eu \$$ T$ $j YYjj Ѣ t$ t$ h{d 5ud 5ud t$ t$ 輦 jj 萢 t$t$h{d 5ud 5ud t$t$ { j j O t$ t$ h{d 5ud 5ud t$ t$ : j j t$t$h{d 5ud 5ud t$t$ 5 Y[UM ESVuWLL$@MD$DEL$(D$,15ud 5ud 5ud 5ud . $} $ ݆ ݆ d$$ ED$$|$$ tT$\$|$$ t\$T$E ݆ Eu݆ uE 5ud 5ud 5ud 5ud PP $PP $V> $E \$ E \$uEAuoE d$PP $t YY\$8E d$PP $t YY|$$ \$0t(D$L$ D$ L$ D$8\$0u EM EM D$ $݆ ݆ E[ ݆ Et݆ uE 5ud 5ud 5ud 5ud PP $PP$V> $ D$(PD$DP L ݆ D$@uT$@݆ D$@EuT$@D$@e PP $ U PP $6s vd YYEu1C ~K Yg } u M E $D$݆ ݆ E ݆ Et݆ uE 5ud 5ud 5ud 5ud PP $PP$V $t$Dt$Dt$ t$ VD$@ $Eu $D$@ D$@$5ud 5ud 5ud 5ud PP $PP$V $q D$DL$@D$ D$(L$PD$DP 7J ݆ D$@t݆ D$@EuT$@D$@\$D@ t$ t$ t$ t$ VD$ $Eu $D$ D$$D@t65ud 5ud 5ud 5ud PP $PP$V $D$@ $Eu $D$@ D$@$D@ 5ud 5ud 5ud 5ud PP $PP$V $t$Dt$Dt$ t$ V H Y{D$@ $Eu D$ $ L$@D$DD$DL$@ $D$ 4} u\EM ى 1@/[$6̍e_^[]ËT$D$ L$ ݂ ݂ Euݚ ݒ 1@ËT$D$ L$ ݂ ݂ Euݚ ݒ 1@S\$ $$PP $5$vd 5 vd D$D$PP $5ud 5ud ͚ $5ud 5ud 5ud 5ud 豝 ([USV$D$u] PD$PD$ PD$ P 7 V-Yj 9 YY ݆ ܞ ܖ EA 5ud 5ud PP$5ud 5ud PP$ $tZE ܞ uJE ܞ u:EAt25ud 5ud u$u 5ud 5ud u$u s $ Y 1 Yt$ t$ t$ t$ t$,t$,t$,t$, , E$M $ E ]uv tmE ܞ EuE ܞ uM E$ E$M V YV)YVcY 1@e^[]t$$t$$t$$t$$t$$t$$t$$t$$D$$ _ $t$$t$$t$$t$$t$$t$$t$$t$$D$$ 荽 $SU'j x l$ uPYU 'j YE1iG E,G E0IG E4G EDG EHG eh EL{d EP{d ET{d EX{d E\{d E`{d Ed{d ElG EpjG Et7G ExxG E|G Dž TG Dž iG Dž wG Dž xG Dž yG Dž zG Dž {G Dž G Dž G ][ËD$ tP耽YUSVu] 1W { D$D$PP $5ud 5ud D$$D$$PP $5ud 5ud 蛙 $D$PD$PCPCP A D$ vd E ȉD$D$\$Ey ȉD$D$PP $5$vd 5 vd D$$D$$PP $5ud 5ud ӕ $5ud 5ud 5ud 5ud 跘 $D$PD$PCPCP ] ݆ $u$݆ $Eu$ t$t$t$t$V SpÃt V> Y D$D$PP $5ud 5ud D$$D$$PP $5ud 5ud Ŕ $tVQYM V胺YA 1ۉ$ܜ E $ܜ D$ܜ E D$ܜ $ \ C f L 2 V>WlCe_^[]SL$D$ @ PQS|YY[ËL$ = T$u QRE= u QRYYSUT$\$ B J BJ Rt$5ud 5ud j j t$(SE u1 ݃ ܃ vd ݛ @ Yuh hwd h{d 谴 蕦 Y j & YYj S ShG jE ' ShG jj ' Sho~G h ' Sh|G h ' Sh|G j> q' S+ Y 諵t j Sj h ǃ ud ud 8 < 1@][SVt$ V YV贵YV詷YVY^[SD$P Y[t$脷YSV1ۋt$ C tK j j F C94 y u$ y y V Y Y^[hud h |d YYhud h$|d YYhud h?|d YYhud hZ|d YYSUl$ \$x$ $ $ D$ PWX 5 vd 5vd P $\$dP \ YYD$d\$dj C ݃ YY$ $ D$lPP $$ $ PP$ $Uj ӎ u(5 vd 5vd Ӕ ܬ$ ݜ$ $P$ $ S l][S\$j ~ ݃ YYt$t$݃ Pvd Xvd PP $t$$t$$PP$ $5vd 5vd t$ t$ ݃ ܃ PP vd $ 2' j YYjj t$t$t$t$ t$ 譑 [SU|$ L$lD$p$ $ L$tD$x݄$ ܤ$ PP $ `vd d$d ݄$ ܤ$ D$dPP $ Γ `vd 1݄$ ܜ$ ݄$ ܜ$ Eu j Ʈ ݅ YY$ $ PP$$ $ ݅ Pvd Xvd PP $ $5vd 5vd $ $ ݅ ܅ PP vd $ h% |$d t=t݄$ ܄$ vd H5dvd 5`vd ܬ$ %t%5dvd 5`vd ԑ ܄$ \$t$ $ $ D$ PtT $P 藂 YY\$d5vd 5vd $ $ 5vd 5vd > ݅ D$tPP $ q$ j / YYjj $Pt$|t$|t$|t$| 趆 |][S\$j YYt$t$ t$$t$$ 8 $jj | t$t$t$t$ t$ h [S\$j U YYj x6 YYt$t$ t$ t$ $j 36 YY[hl}d 1 1Y@SUh}d l$ UXS,YhVG j hz}d h}d Ul{ ][ËD$$ t"P t$ t$ t$ t$ QƯ SUd x l$ uPYU d YE,eG ElG Dž }d Dž }d Dž }d Dž }d Dž I@ Dž Y@ Dž }d Dž }d Dž }d Dž }d Dž ~d Dž ~d Dž ,~d ][Ã5h}d _ Y$t!t$t$t$t$t$P: u$P 1Y$SVUl$} \$uu1j hd UB E hd hd u u Yu&F$p4p0hd u j u YP;] tSU- YYu?1>^$hd V: YYhd u R YYPP $S贼 VWYV褁 Y1@]^[SVUl$} \$u j hd Uw E hd hd u hd hd u hd hd u hd hd u p h d hd u [ hd hd u t j h&d u v u P Yu)F$p4p0hd u j u Y ;] tSU YY 1 ^$hd V YYh&d u s YYPhd u YYPP $hd u YYPP $hd u YYPP $hd u YYPP $hd u YYPP $hd u YYPP $S/ 8VYV Y1@]^[ËD$H݁ ݁ D@u h4d jj PP$q$, h4d j PP $PP$q$: PP $ 1@SUD$ h]$h:d U YY 5D~d 5@~d 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YYPhHn 5|/} YYPh;n 5|/} YYPt$ t$ 5D Nf v 2X1@e[]US,=/} ]u7hnn j hqR hn 5@ P /} PY5/} Yuu 5/} y YYG ; /} t S5/} 虗 YY) 1* h2n 5/} Ý YY\$t D$PD$PD$(PD$ P5D A D$PD$PD$(PD$ PD$ $$ Pn $\$EtD$ \$u!t$$t$$t$ t$ hn ]v hn 5/} 譝 YYPhRn 5/} f YYPhHn 5/} S YYPh;n 5/} @ YYPt$ t$ 5D f wV1@e[]US,=/} ]u7hnn j h,R hn 5@ 蕄 /} P Y5/} = Yuu 5/} 辕 YYG ; /} t S5/} ޕ YY) 1* h2n 5/} YY\$ D$PD$PD$(PD$ P5D @ D$PD$PD$(PD$ P8D$ $$ Pn $\$EtD$ \$u!t$$t$$t$ t$ hn \v hn 5/} YYPhRn 5/} 諛 YYPhHn 5/} 蘛 YYPh;n 5/} 腛 YYPt$ t$ 5D fg T1@e[]S\$hn h2n S蒃 jh;n SĄ jhHn S贄 jhRn S褄 hcn hÎn Sc hÎn hn S蟄 [US4=/} ]u7h2n j hWR h`n 5@ j /} PPY5/} Yuu 5/} 蓓 YY ; /} t S5/} 賓 YY 1 h2n 5/} ݙ YY\$ D$(PD$PD$ PD$,P5D = D$(PD$PD$ PD$,P D$($$ Pn \$$d$PP $5\n 5Xn \$Et/D$(D$PP $5\n 5Xn \$uQt$,t$,5\n 5Xn PP $t$ t$ 5\n 5Xn PP $hn |Yt hn 5/} c YYPhRn 5/} YYPhHn 5/} YYPh;n 5/} YYPt$ t$ 5D g q -R1@e[]US4=/} ]u7h2n j hvR hn 5@ K /} P1Y5/} Yuu 5/} t YY ; /} t S5/} 蔑 YY 1 h2n 5/} 辗 YY\$o D$(PD$PD$ PD$,P5D ; D$(PD$PD$ PD$,PD$($$ Pn \$$d$PP $5\n 5Xn \$Et/D$(D$PP $5\n 5Xn \$uQt$,t$,5\n 5Xn PP $t$ t$ 5\n 5Xn l PP $hn ]Wtk hn 5/} D YYPhRn 5/} YYPhHn 5/} YYPh;n 5/} ז YYPt$ t$ 5D g R P1@e[]US4=/} ]u7h2n j hR hn 5@ ,~ /} PY5/} ԁ Yuu 5/} U YY ; /} t S5/} u YY 1 h2n 5/} 蟕 YY\$P D$ PD$ PD$0PD$ P5D 9w D$ PD$ PD$0PD$ PD$($$ Pn \$$d$PP $5\n 5Xn \$Et/D$(D$PP $5\n 5Xn \$uQt$,t$,5\n 5Xn n PP $t$ t$ 5\n 5Xn M PP $hn >UtL hn 5/} % YYPhRn 5/} ޔ YYPhHn 5/} ˔ YYPh;n 5/} 踔 YYPt$ t$ 5D h 3 M1@e[]US4=/} ]u7h2n j hR hۛn 5@ | /} PY5/} Yuu 5/} 6 YY ; /} t S5/} V YY 1 h2n 5/} 耓 YY\$1 D$ PD$ PD$0PD$ P5D 7X D$ PD$ PD$0PD$ PD$($$ Pn \$$d$PP $5\n 5Xn \$Et/D$(D$PP $5\n 5Xn y \$uQt$,t$,5\n 5Xn O PP $t$ t$ 5\n 5Xn . PP $hn St- hn 5/} YYPhRn 5/} 迒 YYPhHn 5/} 謒 YYPh;n 5/} 虒 YYPt$ t$ 5D h K1@e[]S=/} \$u@j j hR hn 5@ y /} h7n h<n Pyz 5/} } Yut$5/} YY ; /} t S5/} 2 YY 1 5n 5D z1YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D -1$5D 1Yhn 5/} YYPP $5D Q6 $5D 3Yt$t$hJn ~N J1@[S=/} \$u@j j hR hPn 5@ x /} hn h{n P6y 5/} O| Yut$5/} ω YY ; /} t S5/} YY 1 5n 5D 70YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D /$5D 0Yhn 5/} 輏 YYPP $5D 5 $5D P2Yt$t$hn ;M II1@[S=/} \$u@j j hY S hn 5@ pw /} h7n h<n Pw 5/} { Yut$5/} 茈 YY ; /} t S5/} 謈 YY 1 5n 5D .YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D .$5D H/Yhn 5/} y YYPP $5D 3 $5D 1Yt$t$hJn K H1@[S=/} \$u@j j hS hn 5@ -v /} hn h{n Pv 5/} y Yut$5/} I YY ; /} t S5/} i YY 1 5n 5D -YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D d-$5D .Yhn 5/} 6 YYPP $5D W3 $5D /Yt$t$hn J F1@[S=/} \$u@j j hS hn 5@ t /} h n hn Pv 5/} x Yut$5/} YY ; /} t S5/} & YY 1 5.} 5D #,YY5n 5D [,YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D ,$5D ,Yhn 5/} 腌 YYP5D X"YY $5D y.Yt$t$hJn dI rE1@[S=/} \$u@j j h0S hn 5@ s /} h n hn Pu 5/} 5w Yut$5/} 资 YY ; /} t S5/} Մ YY 1 5.} 5D *YY5n 5D +YY5n 5n 5n 5n 5n 5n 5.} 5.} 5D *$5D ^+Yhn 5/} 4 YYP5D !YYPP $5D 0 $5D -Yt$t$hn H D1@[SU=/} \$uqj j hS h0n 5@ 4r /} jh[n PKt hin Ua YYhnn Ua YYh n hn 5/} s 5/} u Yut$5/} YY ; /} t S5/} ? 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U )ƅ} #? }}1BD$,9}tPh0s h;/s 7b _ E 9ȉD$|L$D$~ ~ & ~ @$E +~ @D$E 9$}$L$0~ R ~ h,-s QC~ PD$P#< ~ ; SЋD ։ ~ ~ D ?$ E +~ @$+~ D$~ @t$4t$0 ~ ~ PD$<Qh,-s RD$ PD$ Ph}/s : ~ S$~ ~ ։D~ D$9~ 1 ]_^[SVWUl$8E D$ |$,t$0@)D$4D$H\$@ jjh4-s h4-s VWh/s h\0s h0-s i ,~ ,~ $1ɣ8~ 8~ D$D8 <~ } D$H]D$} D$H G}1B9U } D$H .|$}D$ D$DL$9}=<~ u D$H D$H t ؉$Ph\0s h;/s _ =<~ 9|ɉ ~ uC ?# h ~ %0~ @~ =,~ 9 ,~ $$ jjh4-s h4-s VWh/s h\0s h8-s 5h $D$$;D$D$0~ ; ~ }v4~ ,~ @~ D$D ;@~ }U=4~ $ jjh4-s h4-s VWh/s h\0s h<-s ,~ g $D$$;D$D$ ~ ,~ ; ~ ; ~ 0~ ; ~ ~ +0~ $,~ D$~ } ~ +~ @;,~ D$|,~ (~ +~ @D$h$~ SD$D ~ QUD$ @~ D$DPh(~ D$(P,~ (~ ; +~ @D$h4~ SD$D ~ QUD$ @~ D$DPh(~ D$(Ph,0s h70s R: $+~ @D$+~ +(~ @D$C (~ A~ (~ h4~ QUD$~ D$@Ph4~ SUD$(@~ D$PPh(~ D$(PD$8Ph,0s h70s h/s h}/s ! <D$~ |$ }1 ~ ; $1 ~ ; $V ~ ~ ; ~ Y+~ @D$+~ @$h$~ SD$D ~ QUD$ @~ D$DPD$PD$,P @~ 1]_^[SVWUD$0l$$t$,L$<|$(\$ D$ d$ +t$ ! U } #? }}1BD$09}t ؉$Ph0s h;/s [ M 9|D$ H~ t$D$ D~ ~ +H~ D~ $E L$4D~ ʍ + H~ D~ Rt$4Q+ H~ D~ + H~ D~ QD$Pw5 +H~ D~ E +H~ D~ ƋD P~ T~ +H~ D~ E +H~ D~ D ?$ E +H~ D~ H$+H~ D~ D$t$8t$4t$D$@ D~ Qt$@E +H~ D~ PD$ PD$ Ph/s 3 +H~ D~ ӡT~ P~ $U +H~ D~ ։D D~ =D~ u1]_^[SVWU<D$dL$$ȉD$D$d$D$)D$`D$pȉL$0D$ D$ d$ D$ )D$lD$xȉL$4D$D$d$D$)D$t$ l$P|$|$ # D$\D$X 9|ȣ~ D$TD$ $ l$D$ jh+s D$PD$PD$"Pt jjh} h} t$lt$lD$*Ph0s h,s a $~ h0s U0t YY~ h/s U t ~ 1=~ YYu =~ ~ h0s Us YY~ h/s Us YY~ h0s t$Xs YY~ h/s t$Xs ~ 1=~ YYu =~ ~ h0s t$Xs YY~ h/s t$Xls ~ Ԃ~ 1>Y~ =~ Yu#=~ u=~ u=~ u =~ u=~ u=~ u =~ t=~ t=~ t D$X}}D$\}k}1EՋD$d9(}OD$p | =~ t 9}/D$x | =~ t9|=~ t;~ }; $ >} =~ $ D$X$ D$\ $ 9T ~ D$X ;~ r =~ > D$\(jjh+s h+s Pt$lh/s h\0s h+s W_ $D$8܂~ D$\(jjh+s h+s PPh/s h/s h+s _ $L- IȉD$,D$8;D$,D$,܂~ =~ u =~ tQD$8D$\(jjh+s PPPh/s hx0s h+s ^ $M IȉD$,D$8;D$,D$,܂~ ܂~ ;~ ~ ~ ܂~ D$\ ;~ D$8~ 9Ԃ~ Q J =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s ] $裄~ D$8D$\(jjh+s PPt$lh/s h0s h+s ] $D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s x] $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s &] $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$\ЉD$8D$\D$XJʉL$,D$89~T$,܂~ D$\D$X I;~ L$8~ 9£Ԃ~ ! {! =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s 5\ $裄~ D$8D$\(jjh+s PPt$lh/s h0s h+s [ $D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s [ $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s \[ $ʼn IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh/s hx0s h+s [ $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$\ЉD$8D$\D$XJʉL$,D$89~T$,܂~ D$\D$X I;~ L$8~ 9£Ԃ~ g ` =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s Z $裄~ D$8D$\(jjh+s PPt$lh/s h0s h+s Y $D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s Y $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s AY $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$\У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s tX $裄~ D$8D$\(jjh+s PPt$lh/s h0s h+s :X $D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s W $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s W $ʼn IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh/s hx0s h+s MW $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$\ У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s |V $裄~ D$8D$\(jjh+s PPt$lh/s h0s h+s BV $D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s U $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s U $ʼn IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh/s hx0s h+s UU $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$\У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s T $裄~ D$8jjh+s t$ht$ht$lh/s h0s h+s KT $L$XL$\D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s S $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s S $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$\У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ ^ ܂~ T =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s R $裄~ D$8jjh+s t$ht$ht$lh/s h0s h+s R $L$XL$\D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s HR $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s Q $ʼn IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh/s hx0s h+s Q $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$\ У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ ^ ܂~ T =~ =~ D$\(jjh+s h+s Pt$lh/s h\0s h+s P $裄~ D$8jjh+s t$ht$ht$lh/s h0s h+s P $L$XL$\D$,D$8;D$,D$,D$8~ D$\(jjh+s h+s PPh/s h/s h+s HP $L- IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh0s hx0s h+s O $ʼn IȉD$,D$8;D$,D$,D$8~ D$\(jjh+s PPPh/s hx0s h+s O $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$\У܂~ D$\D$X I;~ L$8~ Ԃ~ 9܂~ _ ܂~ U D$\(jjh+s h+s Pt$lh/s h/s h+s N $L$X Iȣ܂~ =~ u =~ tV܂~ D$8D$\(jjh+s PPt$lh0s hx0s h+s N $ʼn IȉD$,D$8;D$,D$,܂~ =~ t^܂~ D$8jjh+s t$ht$ht$lh0s hx0s h+s 5N $L$XL$\ IȉD$,D$8;D$,D$,܂~ =~ uV܂~ D$8D$\(jjh+s PPPh/s hx0s h+s M $M IȉD$,D$8;D$,D$,܂~ ܂~ ;~ ~~ ܂~ D$\D$X I;~ L$8~ 9£Ԃ~ ] V ȍ~ D$\ ;~ { =~ = D$X(jjh+s h+s t$lPh/s hF0s h+s M $D$8܂~ D$X(jjh+s h+s PPh/s h/s h+s L $L- IȉD$,D$8;D$,D$,܂~ =~ u =~ tND$8D$X(jjh+s PPPh0s hx0s h+s bL $ʼn IȉD$,D$8;D$,D$,܂~ ܂~ ;~ ~ ~ ܂~ D$X ;~ D$8~ 9Ԃ~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s K $裄~ D$8D$X(jjh+s Pt$lPh/s h0s h+s pK $D$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s #K $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s J $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$XЉD$8D$XD$\JʉL$,D$89~T$,܂~ D$XD$\ I;~ L$8~ 9£Ԃ~ * # =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s I $裄~ D$8D$X(jjh+s Pt$lPh/s h0s h+s I $D$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s VI $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s I $M IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh0s hx0s h+s H $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$XЉD$8D$XD$\JʉL$,D$89~T$,܂~ D$XD$\ I;~ L$8~ 9£Ԃ~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s G $裄~ D$8D$X(jjh+s Pt$lPh/s h0s h+s G $D$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s ;G $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s F $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$XУ܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s F $裄~ D$8D$X(jjh+s Pt$lPh/s h0s h+s E $D$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s E $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s @E $M IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh0s hx0s h+s D $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$X У܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s !D $裄~ D$8D$X(jjh+s Pt$lPh/s h0s h+s C $D$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s C $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s HC $M IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh0s hx0s h+s B $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$XУ܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s *B $裄~ D$8jjh+s t$dt$lt$ph/s h0s h+s A $L$\L$XD$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s A $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s IA $M IȉD$,D$8;D$,~T$,;~ ~ ~ D$XУ܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s y@ $裄~ D$8jjh+s t$dt$lt$ph/s h0s h+s ?@ $L$\L$XD$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s ? $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s ? $M IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh0s hx0s h+s G? $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$X У܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ܂~ =~ =~ D$X(jjh+s h+s t$lPh/s hF0s h+s y> $裄~ D$8jjh+s t$dt$lt$ph/s h0s h+s ?> $L$\L$XD$,D$8;D$,D$,D$8~ D$X(jjh+s h+s PPh/s h/s h+s = $L- IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh/s hx0s h+s = $M IȉD$,D$8;D$,D$,D$8~ D$X(jjh+s PPPh0s hx0s h+s G= $ʼn IȉD$,D$8;D$,~T$,;~ ~ ~ D$XУ܂~ D$XD$\ I;~ L$8~ Ԃ~ 9܂~ ~܂~ ܂~ D$X(jjh+s h+s t$lPh/s h/s h+s < $L$\ Iȣ܂~ =~ u =~ tV܂~ D$8D$X(jjh+s Pt$lPh/s hx0s h+s 5< $ʼn IȉD$,D$8;D$,D$,܂~ =~ t^܂~ D$8jjh+s t$dt$lt$ph/s hx0s h+s ; $L$\L$X IȉD$,D$8;D$,D$,܂~ =~ uV܂~ D$8D$X(jjh+s PPPh0s hx0s h+s r; $M IȉD$,D$8;D$,D$,܂~ ܂~ ;~ ~~ ܂~ D$XD$\ I;~ L$8~ 9£Ԃ~ ܂~ ܂~ ;Ԃ~ }=~ ut ؉D$8Ph0s h;/s 1 v~ =~ i~ D$X8 t D$\8 u>N~ G ?' ?~ h/s B:Y ~ h/s 1:YPP $ 5~ YY ~ 5~ Ȃ~ D$`D$(D$D$(h ~ t$ht$0t$ht$hh0s `~ %X~ `~ @,s Eu<`~ ~ u&X~ hh~ t$ht$0t$ht$hh~ 7`~ Ȃ~ Eu@X~ hh~ t$ht$0t$ht$hhȂ~ h`~ h} h} h0s 0@ (D$\D$X 9= ;~ 8 =~ 6 l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$t D$\ HD$8D$\ HD$,t$dD$(D$dPh} h} D$<PD$LPh0/s F ~ D$\ @~ D$\ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ QW$ $ U$ $ N,%p~ =~ u =~ t^+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$tt$xt$|h/s 諯 (D$\ p~ D$\ ~ ~ GSQ ~ h+s h ~ h+s h ~ t$|t$DQ$ h} h} hp~ $ h2/s 腌<=~ x t$xD$xD$ Pt$lt$4, =~ =~ ;~ D$8~~ D$\9 ~ ~ D$8D$dD$\AL$,D$89~l$,D$dыD$\9| ~ D$dj~ D$8D$dD$\AL$,D$89~L$,D$\(Ջ9|D$d ~ D$\)ș ~ D$\ Ђ~ D$\ Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tG ~ hЂ~ Qt$lUt$lt$ph2/s D$\ HD$8D$\ HD$,G ~ AhЂ~ Qh} h} D$<PD$LPh0/s vC +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$tt$xt$x $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Q$ $ s,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h0s (D$\ ~ ~ GSQ ~ h+s h ~ hЂ~ Q ~ h+s h ~ Q$ h} $ h} $ h2/s 躈< ~ D$\ Ă~ D$X D$8~ D$,x~ D$X +x~ @;~ |~ |~ G Ă~ h~ Q ~ h} hЂ~ Qt$xD$<x~ D$xPh(,s t$|$ h|~ h/s h/s 4t$dD$(x~ D$dPG Ă~ h~ Qt$lh|~ hn/s D$,x~ |$, }1 x~ ;L$81 x~ ;L$8s ~ D$\ @~ D$\ ~ ~ )@D$,l$`l$hh~ D$0PGQ ~ Q ~ QW$ $ U$ $ ر,+~ @D$,hh~ D$0PG ~ Q ~ Qt$tUt$tt$xt$xh0s Q (D$\ ~ ~ GSQh+s h ~ t$t! =~ =~ ;~ D$,~~ D$\9 ~ ~ D$,D$dD$\AL$8D$,9~l$8D$dыD$\9| ~ D$dj~ D$,D$dD$\AL$8D$,9~L$8D$\(Ջ9|D$d ~ D$\)ș ~ D$\ Ђ~ D$\ Ђ~ A l~ ~ )@D$,l$`l$hh~ D$0PGQ l~ Qt$tUt$tt$t D$tD$0D$D$0t$xt$4t$lUt$lt$ph2/s " D$\ HD$,D$\ HD$8t$xD$8D$xPh} h} D$HPD$@Ph0/s = +~ @D$,hh~ D$0PG ~ Q l~ Qt$tUt$tt$xt$x褺 $l~ ~ D$\ ~ ~ ~ )@D$,hh~ D$0PGQ ~ Q ~ Q ~ Q$ $ t$P$ $ 莮G, ~ hЂ~ Q$ t$<t$lt$ph0/s ɨ +~ @D$,hh~ D$0PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h0s ǥ (+~ @D$,hh~ D$0PG ~ Q ~ Q$ t$Dt$tt$xt$|h/s q (D$\ ~ ~ GSQ ~ h+s h ~ hЂ~ Q ~ $ t$LQ$ h} $ $ $ h2/s H< ~ D$\ Ă~ D$X D$,~ D$8x~ D$X +x~ @;~ |~ |~ G Ă~ h~ Q ~ h} hЂ~ Qt$xD$<x~ D$xPh(,s t$|$ h|~ h/s h/s 44t$dD$(x~ D$dPG Ă~ h~ Qt$lh|~ hn/s 衦 D$8x~ |$8 }1 x~ ;L$,1 x~ ;L$,^m l~ D$\ @~ +~ @D$8D$`D$(D$D$(hh~ D$<PG ~ QWt$tt$<t$tt$tw l$tl$t$xUt$lt$4t$lt$ph2/s ԥ D$\ HD$8D$\ HD$,t$xD$8D$xPh} h} D$<PD$LPh0/s =9 +~ @D$8hh~ D$<PG ~ Q l~ Qt$tt$<t$tt$xt$xS $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ U$ $ @,+~ @D$8hh~ D$<PG ~ Q ~ t$pt$8Q$ Ut$|$ $ h/s hr/s h0s q 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$tt$xt$|h/s K (D$\ ~ ~ GSQh+s h ~ t$tt$<$ M! =~ m =~ ~ ;~ D$8~~ D$\9 ~ D$\D$d~ 9|Ђ~ Ђ~ D$\ Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tPG ~ hЂ~ Qt$lUt$lt$ph2/s 詢 D$\ HD$8D$\ HD$,G ~ AhЂ~ Qh} h} D$<PD$LPh0/s 6 +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$tt$xt$x) $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Q$ $ ,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h0s z (D$\ ~ ~ GSQ ~ h+s h ~ hЂ~ Q ~ h+s h ~ Q$ h} $ h} $ h2/s T{<t$pD$pD$ P ~ Gh} hЂ~ Qt$xU> l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$t薻 D$lD$0D$ D$0t$pt$4t$lUt$lt$lh0/s +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Dt$tt$xt$x豰 $l~ ~ D$\ ~ ~ ~ HD$8D$\ HD$,t$dD$(D$dPh} h} D$<PD$LPh0/s 2 +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ U$ $ N,+~ @D$8hh~ D$<PG ~ Q ~ t$|t$@Qt$|Ut$|$ $ h/s hr/s h0s 肽 8D$\ ~ ~ GSQh+s h ~ $ t$D =~ ;~ D$8~~ D$\ 9/ Ă~ D$dD$\ ,-~ 9| D$\~ D$dA ~ =,-~ 9|~ ыD$\A ~ ~ D$\A ~ Ђ~ D$\ Ђ~ ~ l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tjG Ă~ h~ Qt$lUt$lt$ph2/s Ü D$\ HD$8D$\ HD$,G Ă~ Ah~ Qh} h} D$<PD$LPh0/s *0 +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$tt$xt$xC $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Q$ $ 'G, ~ hЂ~ Q Ă~ h~ Qt$lt$ph2/s \ +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$tt$xt$|h0s Z (+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h/s (D$\ ~ ~ GSQ Ă~ h+s h ~ h~ Q ~ hЂ~ Q ~ Q$ h} $ $ $ h2/s t<t$pD$pD$ PG Ă~ h} h~ Qt$xUh(,s t$|$ $ h/s h/s ! 4 ~ Gt$dUhЂ~ Q l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tϴ D$lD$4D$ D$4t$pt$8t$lUt$lt$lh0/s $ +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Ht$tt$xt$x $l~ ~ D$\ ~ ~ ~ HD$8D$\ HD$,t$dD$(D$dPh} h} D$<PD$LPh0/s , +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ U$ $ 臝,+~ @D$8hh~ D$<PG ~ Q ~ t$|t$DQt$|Ut$|$ $ h/s hr/s h0s 軶 8+~ @D$8hh~ D$<PG ~ Q ~ Qt$tUt$tt$xt$|h/s 蘔 (D$\ ~ ~ GSQh+s h ~ $ t$Ht$| =~ ] ;~ D$8~~ D$\9 Ă~ D$\D$d~ 9|~ ~ D$\ ~ A l~ ~ )@D$8D$`D$(D$D$(hh~ D$<PGQ l~ Qt$tt$<t$tt$t蟱G Ă~ h~ Qt$lt$4t$lt$ph2/s D$\ HD$8D$\ HD$,G Ă~ Ah~ Qh} h} D$<PD$LPh0/s \) +~ @D$8hh~ D$<PG ~ Q l~ Qt$tt$<t$tt$xt$xr $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Q$ $ V,l$tl$G Ă~ t$xUh~ Qt$lt$ph2/s 菔 +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$tt$xt$|h0s 荑 (+~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$tt$xt$|h/s : (D$\ ~ ~ GSQ Ă~ h+s h ~ h~ Q ~ $ UQ$ h} $ $ $ h2/s n<t$pD$pD$ P Ă~ Gh} h~ Qt$xt$@h(,s t$|W= l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tJ D$lD$(D$ D$(t$pt$,t$lUt$lt$lh0/s 蟒 +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$<t$tt$xt$xe $D$tD$0D$D$0t$xt$4t$lUt$lt$ph2/s D$\ HD$8D$\ HD$,t$xD$8D$xPh} h} D$<PD$LPh0/s % l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ t$P$ $ Ӗ,+~ @D$8hh~ D$<PG ~ Q ~ t$|t$8Q$ t$Lt$|$ $ h/s hr/s h0s 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ t$Dt$tt$xt$|h/s ؍ (D$\ ~ ~ GSQh+s h ~ $ t$<$ t$L =~ +W =~ + D$\L$8 D$,;D$,~T$,;~ T$8~ D$\9[ ~ D$\D$d~ 9|Ђ~ Ђ~ D$\ Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$t辪 D$lD$0D$ D$0t$pt$4t$lUt$lt$lh0/s G ~ hЂ~ Qt$lUt$lt$ph2/s D$\ HD$8D$\ HD$,G ~ AhЂ~ Qh} h} D$<PD$LPh0/s L" +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Dt$tt$tt$x_ $l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Q$ $ C,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h0s 谊 (D$\ ~ ~ GSQ ~ h+s h ~ hЂ~ Q ~ h+s h ~ Q$ h} $ h} $ h2/s gG< ~ t$dUh} hЂ~ Q$ t$Hh(,s t$|$ $ h/s h/s 4t$pt$4y= l~ D$\ @~ +~ @D$8D$`D$0D$D$0hh~ D$<PG ~ QWt$tt$Dt$tt$t蒧 l$ll$ t$pUt$lt$<t$lt$lh0/s +~ @D$8hh~ D$<PG ~ Q l~ Q$ Ut$tt$tt$x踜 $l~ ~ D$\ ~ ~ ~ HD$8D$\ HD$,t$dD$(D$dPh} h} D$<PD$LPh0/s +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ t$P$ $ R,+~ @D$8hh~ D$<PG ~ Q ~ t$|UQt$|t$Lt$|$ $ h/s hr/s h0s 膩 8D$\ ~ ~ GSQh+s h ~ $ U ~ h+s h ~ Q$ h} $ h} =~ D$\L$8 D$,;D$,~T$,;~ T$8~ D$\ 9 Ă~ D$dD$\ ,-~ 9| D$\~ D$dA ~ =,-~ 9|~ ыD$\A ~ ~ D$\A ~ Ђ~ D$\ Ђ~ ~ l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$t+ D$lD$$D$ D$$t$pt$(t$lUt$lt$lh0/s 耈 +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$8t$tt$tt$xF G$ Ă~ h~ Qt$lUt$lt$ph2/s D$\ HD$8D$\ HD$,G Ă~ Ah~ Qh} h} D$<PD$LPh0/s h l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Q$ $ 谌G, ~ hЂ~ Q Ă~ h~ Qt$lt$ph2/s +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$tt$xt$|h0s (+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$tt$xt$|h/s 臃 (D$\ ~ ~ GSQ Ă~ h+s h ~ h~ Q ~ hЂ~ Q ~ Q$ h} $ $ $ h2/s X`G< Ă~ t$dUh} h~ Q$ t$<h(,s t$|$ $ h/s h/s 4t$pt$(t$lUt$lt$lhn/s 7 ~ Gt$dUhЂ~ Qt$lt$pD l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$t0 D$lD$(D$ D$(t$pt$,t$lUt$lt$lh0/s 腄 +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$<t$tt$tt$xK $l~ ~ D$\ ~ ~ ~ HD$8D$\ HD$,t$dD$(D$dPh} h} D$<PD$LPh0/s y +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ U$ $ ,+~ @D$8hh~ D$<PG ~ Q ~ t$|t$8Qt$|Ut$|$ $ h/s hr/s h0s 8+~ @D$8hh~ D$<PG ~ Q ~ Qt$tUt$tt$xt$|h/s (D$\ ~ ~ GSQh+s h ~ $ t$<t$|U@ =~ RI D$\L$8 D$,;D$,~T$,;~ T$8~ D$\9 Ă~ D$\D$d~ 9|~ ~ D$\ ~ A l~ ~ )@D$8D$`D$(D$D$(hh~ D$<PGQ l~ Qt$tt$<t$tt$t D$lD$ D$ D$ t$pt$$t$lt$4t$lt$lh0/s 9 +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$4t$tt$tt$x G$ Ă~ h~ Qt$lt$4t$lt$ph2/s 跀 D$\ HD$8D$\ HD$,G Ă~ Ah~ Qh} h} D$<PD$LPh0/s l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Q$ $ f,l$tl$G Ă~ t$xUh~ Qt$lt$ph2/s +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$tt$xt$|h0s | (+~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$tt$xt$|h/s J| (D$\ ~ ~ GSQ Ă~ h+s h ~ h~ Q ~ $ UQ$ h} $ $ $ h2/s $YG< Ă~ t$dt$,h} h~ Q$ t$8h(,s t$|$ $ h/s h/s u4t$pt$$t$lt$4 / l~ D$\ @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$t, D$lD$ D$ D$ t$pt$$t$lUt$lt$lh0/s } +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$4t$tt$tt$xG $D$tD$(D$D$(t$xt$,t$lUt$lt$ph2/s | D$\ HD$8D$\ HD$,t$xD$8D$xPh} h} D$<PD$LPh0/s g l~ ~ D$\ ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ t$H$ $ 赁,+~ @D$8hh~ D$<PG ~ Q ~ t$|t$0Q$ t$Dt$|$ $ h/s hr/s h0s 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ t$<t$tt$xt$|h/s x (D$\ ~ ~ GSQh+s h ~ $ t$4$ t$D ~ Q$ h} $ $ ~ D$\ @~ D$\ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ QW$ $ t$H$ $ ,=~ l$ll$ t$pUt$lt$4t$lt$lh0/s 9z =~ t D$\ ~ =~ t D$X ~ +~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$th~ t$xh0s w (=~ t}l$tl$t$xUt$lt$4t$lt$ph2/s y +~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$tt$xt$|h/s v (=~ tS+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$tt$xt$xh0s 5v (=~ tS+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$tt$xt$|h/s u ( ~ D$\ ~ =~ u =~ t D$X ~ =~ t%~ =~ u =~ t D$\ p~ =~ t%p~ =~ uK=~ uBG ~ SQh+s h ~ $ $ D$0P$ $ D$4PG=~ ue=~ t\G ~ SQh+s h ~ $ $ D$0Pt$|t$D ~ GQ$ h} h~ hp~ ZG ~ SQh+s h ~ t$tt$<$ $ D$4P ~ GQ$ h} h~ hp~ $ 9 ; ~ 9 =~ K l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$t虄 D$X HD$8D$X HD$,t$dD$(@D$dPh} h} D$<PD$LPh2/s ~ D$X @~ D$X ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ QW$ $ Ut$|$ <{,=~ u =~ tS+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$pt$tt$xh0s r ( ~ D$X ~ %~ =~ u =~ t D$X ~ G ~ SQ ~ h+s h ~ t$tt$<h+s h ~ Q$ h} h~ h} $ h2/s [O<=~ ; t$pD$pD$ Pt$lt$4, =~ ; =~ . ;~ D$8~~ D$X9 ~ ~ D$8D$dD$\D$XL$,D$89~l$,D$dыD$X9|~ D$\ |~ D$d ~ D$8D$dD$\D$XL$,D$89~T$,D$X9| D$d ~ D$\ |~ D$X' ~ D$X()ș |~ D$X Ђ~ D$X Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$t G ~ hЂ~ Qt$lUt$ht$lh0/s r D$X HD$8D$X HD$,G ~ Ђ~ hЂ~ Qh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$pt$xt$xv $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Qt$|$ w,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh/s n (D$X ~ ~ GSQ ~ h+s h ~ h+s h ~ hЂ~ Q ~ Q$ h} h} $ $ h2/s eK< ~ D$X Ă~ D$\ D$8|~ D$,x~ D$\ +x~ @;|~ ||~ ~ G Ă~ h~ Qh} t$px~ D$4 ~ @D$pPGhЂ~ Qh(,s t$xh~ $ h/s h/s M4t$dx~ D$( Ă~ @D$dPGh~ Qh~ t$lhn/s o D$,x~ |$, }1 x~ ;L$81 x~ ;L$8v6 ~ D$X @~ D$X ~ ~ )@D$,l$`l$hh~ D$0PGQ ~ Q ~ QW$ $ U$ $ ~t,+~ @D$,hh~ D$0PG ~ Q ~ Qt$tUt$pt$xt$xh/s k (D$X ~ ~ GSQ ~ h+s h ~ h+s h ~ t$|UQ$ h} h} $ &5 =~ * =~ ;~ D$,~~ D$X9E ~ ~ D$,D$dD$\D$XL$8D$,9~l$8D$dыD$X9|~ D$\ |~ D$d ~ D$,D$dD$\D$XL$8D$,9~T$8D$X9| D$d ~ D$\ |~ D$X' ~ D$X()ș |~ D$X Ђ~ D$X Ђ~ A l~ ~ )@D$,l$`l$hh~ D$0PGQ l~ Qt$tUt$tt$tz D$lD$(D$ D$(t$pt$,t$lUt$ht$lh0/s pl D$X HD$,D$X HD$8t$pD$4@D$pPh} h} D$HPD$@Ph2/s +~ @D$,hh~ D$0PG ~ Q l~ Qt$tUt$pt$xt$xp $l~ ~ D$X ~ ~ ~ )@D$,hh~ D$0PGQ ~ Q ~ Q ~ Q$ $ t$Ht$|$ pG, ~ hЂ~ Qt$xt$4t$ht$lh2/s k +~ @D$,hh~ D$0PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh/s h (+~ @D$,hh~ D$0PG ~ Q ~ Q$ t$<t$pt$tt$xh0s g (D$X ~ ~ GSQ ~ h+s h ~ $ t$<hЂ~ Q ~ Q$ h} $ $ $ h2/s D< ~ D$X Ă~ D$\ D$,|~ D$8x~ D$\ +x~ @;|~ ||~ ~ G Ă~ h~ Qh} t$px~ D$4 ~ @D$pPGhЂ~ Qh(,s t$xh~ $ h/s h/s 4t$dx~ D$( Ă~ @D$dPGh~ Qh~ t$lhn/s h D$8x~ |$8 }1 x~ ;L$,1 x~ ;L$,/ l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tyv D$lD$ D$ D$ t$pt$$t$lUt$ht$lh0/s &h D$X HD$8D$X HD$,t$pD$4@D$pPh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$pt$xt$xhl $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ t$@t$|$ l,+~ @D$8hh~ D$<PG ~ Q ~ t$pUQ$ t$<t$x$ $ h0s h0/s h/s ƅ 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ t$4t$pt$tt$xh0s c (D$X ~ ~ GSQh+s h ~ $ t$4t$|U!! =~ : =~ . ;~ D$8~~ D$X9 ~ D$XD$d~ 9|Ђ~ Ђ~ D$X Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tMsG ~ hЂ~ Qt$lUt$ht$lh0/s d D$X HD$8D$X HD$,G ~ Ђ~ hЂ~ Qh} h} D$<PD$LPh2/s ` +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$pt$xt$x9i $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Qt$|$ `i,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh/s ` (D$X ~ ~ GSQ ~ h+s h ~ h+s h ~ hЂ~ Q ~ Q$ h} h} $ $ h2/s =<t$xD$xD$ P ~ Gh} t$pUhЂ~ Qh(,s t$x l~ D$X @~ +~ @D$8D$`D$4D$D$4hh~ D$<PG ~ QWt$tt$Ht$tt$t}p l$tl$t$xUt$lt$@t$lt$lh2/s 2b +~ @D$8hh~ D$<PG ~ Q l~ Q$ Ut$pt$xt$xf $l~ ~ D$X ~ ~ ~ HD$8D$X HD$,t$dD$(@D$dPh} h} D$<PD$LPh2/s ) +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ t$Tt$|$ f,+~ @D$8hh~ D$<PG ~ Q ~ $ UQt$|t$P =~ ;~ D$8~~ D$X 91 Ă~ D$dD$X ,-~ 9| D$X~ D$dA ~ =,-~ 9|~ ыD$XA ~ ~ D$XA ~ Ђ~ D$X Ђ~ ~ l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tmG Ă~ h~ Qt$lUt$ht$lh0/s h_ D$X HD$8D$X HD$,G Ă~ ~ h~ Qh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q l~ Qt$tUt$pt$xt$xc $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Qt$|$ cG, ~ hЂ~ Q Ă~ h~ Qt$ht$lh0/s ] +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$pt$tt$xh/s Z (+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh0s Z (D$X ~ ~ GSQ ~ h+s h ~ hЂ~ Q Ă~ h~ Q ~ Q$ h} $ $ $ h2/s r7<t$xD$xD$ PG Ă~ h} t$pUh~ Qh(,s t$x$ $ h/s h/s 4 ~ Gt$dUhЂ~ Q l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tj D$tD$ D$D$ t$xt$$t$lUt$lt$lh2/s [ +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$4t$pt$xt$xM` $l~ ~ D$X ~ ~ ~ HD$8D$X HD$,t$dD$(@D$dPh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ Ut$|$ -`,+~ @D$8hh~ D$<PG ~ Q ~ $ t$0Qt$|Ut$x$ $ h0s h0/s h/s ^y 8+~ @D$8hh~ D$<PG ~ Q ~ Qt$tUt$pt$tt$xh0s ;W (D$X ~ ~ GSQh+s h ~ t$tU$ t$< =~ ;~ D$8~~ D$X9 Ă~ D$XD$d~ 9|~ ~ D$X ~ A l~ ~ )@D$8D$`D$ D$D$ hh~ D$<PGQ l~ Qt$tt$4t$tt$tfG Ă~ h~ Qt$lt$,t$ht$lh0/s X D$X HD$8D$X HD$,G Ă~ ~ h~ Qh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q l~ Qt$tt$4t$pt$xt$x\ $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Qt$|$ \,l$ll$ G Ă~ t$pUh~ Qt$ht$lh0/s 3W +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$pt$tt$xh/s 1T (+~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$pt$tt$xh0s S (D$X ~ ~ GSQ Ă~ h+s h ~ $ Uh~ Q ~ Q$ h} $ $ $ h2/s 0<t$xD$xD$ P Ă~ Gh} t$pt$0h~ Qh(,s t$x$ $ h/s h/s 4 l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tvc D$tD$ D$D$ t$xt$$t$lUt$lt$lh2/s #U +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$4t$pt$xt$xY $D$lD$4D$ D$4t$pt$8t$lUt$ht$lh0/s T D$X HD$8D$X HD$,t$pD$4@D$pPh} h} D$<PD$LPh2/s l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ t$Tt$|$ ZY,+~ @D$8hh~ D$<PG ~ Q ~ $ t$0Q$ t$Pt$x$ $ h0s h0/s h/s r 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ t$Ht$pt$tt$xh0s \P (D$X ~ ~ GSQh+s h ~ $ t$H$ t$< =~ =~ / D$XL$8 D$,;D$,~T$,;~ T$8~ D$X9f ~ D$XD$d~ 9|Ђ~ Ђ~ D$X Ђ~ A l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$t_ D$tD$4D$D$4t$xt$8t$lUt$lt$lh2/s Q G ~ hЂ~ Qt$lUt$ht$lh0/s iQ D$X HD$8D$X HD$,G ~ Ђ~ hЂ~ Qh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Ht$pt$xt$|U $l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q ~ $ hЂ~ Qt$|$ U,+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh/s 2M (D$X ~ ~ GSQ ~ h+s h ~ h+s h ~ hЂ~ Q ~ Q$ h} h} $ $ h2/s *G< ~ t$dUh} $ t$DhЂ~ Qh(,s t$x$ $ h/s h/s `4t$xt$8t$lUt$l_ l~ D$X @~ +~ @D$8D$`D$4D$D$4hh~ D$<PG ~ QWt$tt$Ht$tt$t\ l$tl$t$xUt$lt$@t$lt$lh2/s hN +~ @D$8hh~ D$<PG ~ Q l~ Q$ Ut$pt$xt$|R $l~ ~ D$X ~ ~ ~ HD$8D$X HD$,t$dD$(@D$dPh} h} D$<PD$LPh2/s _ +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ t$Tt$|$ R,+~ @D$8hh~ D$<PG ~ Q ~ $ UQt$|t$Pt$x$ $ h0s h0/s h/s k 8D$X ~ ~ GSQ ~ h+s h ~ h+s h ~ $ UQ$ h} h} =~ D$XL$8 D$,;D$,~T$,;~ T$8~ D$X 9 Ă~ D$dD$X ,-~ 9| D$X~ D$dA ~ =,-~ 9|~ ыD$XA ~ ~ D$XA ~ Ђ~ D$X Ђ~ ~ l~ ~ )@D$8l$`l$hh~ D$<PGQ l~ Qt$tUt$tt$tSY D$tD$4D$D$4t$xt$8t$lUt$lt$lh2/s K +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Ht$pt$xt$|O G$ Ă~ h~ Qt$lUt$ht$lh0/s J D$X HD$8D$X HD$,G Ă~ ~ h~ Qh} h} D$<PD$LPh2/s l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Qt$|$ .OG, ~ hЂ~ Q Ă~ h~ Qt$ht$lh0/s cI +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$pt$tt$xh/s aF (+~ @D$8hh~ D$<PG ~ Q ~ Q ~ hЂ~ Qt$pt$tt$xh0s F (D$X ~ ~ GSQ ~ h+s h ~ hЂ~ Q Ă~ h~ Q ~ Q$ h} $ $ $ h2/s "G< Ă~ t$dUh} $ t$Dh~ Qh(,s t$x$ $ h/s h/s *4t$xt$8t$lUt$lt$lhn/s G ~ Gt$dUhЂ~ Qt$ht$l6 l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tVU D$tD$0D$D$0t$xt$4t$lUt$lt$lh2/s G +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$Dt$pt$xt$|K $l~ ~ D$X ~ ~ ~ HD$8D$X HD$,t$dD$(@D$dPh} h} D$<PD$LPh2/s +~ @D$8hh~ D$<PG ~ Q ~ Q ~ Q ~ Q$ $ Ut$|$ iK,+~ @D$8hh~ D$<PG ~ Q ~ $ t$@Qt$|Ut$x$ $ h0s h0/s h/s d 8+~ @D$8hh~ D$<PG ~ Q ~ Qt$tUt$pt$tt$xh0s wB (D$X ~ ~ GSQh+s h ~ t$tU$ t$L ~ Q$ h} $ $ $ =~ D$XL$8 D$,;D$,~T$,;~ T$8~ D$X9 Ă~ D$XD$d~ 9|~ ~ D$X ~ A l~ ~ )@D$8D$`D$0D$D$0hh~ D$<PGQ l~ Qt$tt$Dt$tt$tQ D$tD$$D$D$$t$xt$(t$lt$<t$lt$lh2/s C +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$8t$pt$xt$|H G$ Ă~ h~ Qt$lt$<t$ht$lh0/s C D$X HD$8D$X HD$,G Ă~ ~ h~ Qh} h} D$<PD$LPh2/s j l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q Ă~ $ h~ Qt$|$ G,l$ll$ G Ă~ t$pUh~ Qt$ht$lh0/s A +~ @D$8hh~ D$<PG ~ Q ~ Q Ă~ h~ Qt$pt$tt$xh/s > (+~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$pt$tt$xh0s > (D$X ~ ~ GSQ Ă~ h+s h ~ $ Uh~ Q ~ Q$ h} $ $ $ h2/s sG< Ă~ t$dt$4h} $ t$4h~ Qh(,s t$x$ $ h/s h/s ij4t$xt$(t$lt$<t$lt$lhn/s L@ B l~ D$X @~ +~ @D$8l$`l$hh~ D$<PG ~ QWt$tUt$tt$tN D$tD$$D$D$$t$xt$(t$lUt$lt$lh2/s ? +~ @D$8hh~ D$<PG ~ Q l~ Q$ t$8t$pt$xt$|AD $D$lD$D$ D$t$pt$t$lUt$ht$lh0/s 8? D$X HD$8D$X HD$,t$pD$4@D$pPh} h} D$<PD$LPh2/s l~ ~ D$X ~ ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ Q ~ Q$ $ t$4t$|$ C,+~ @D$8hh~ D$<PG ~ Q ~ $ t$4Q$ t$0t$x$ $ h0s h0/s h/s ] 8+~ @D$8hh~ D$<PG ~ Q ~ Q$ t$(t$pt$tt$xh0s : (D$X ~ ~ GSQ ~ h+s h ~ $ t$($ t$@Q$ h} $ $ $ h2/s ~ D$X @~ D$X ~ ~ )@D$8hh~ D$<PGQ ~ Q ~ QW$ $ t$H$ $ /B,=~ t}l$ll$ t$pUt$lt$4t$ht$lh0/s k< +~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$tt$tt$xh0s r9 (=~ l$tl$t$xUt$lt$4t$lt$lh2/s ; =~ t D$\ t~ =~ t D$X t~ +~ @D$8hh~ D$<PG ~ Q ~ Q$ Ut$pt$xht~ h/s 8 (=~ tS+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$tt$tt$xh0s c8 (=~ tS+~ @D$8hh~ D$<PG ~ Q ~ Qt$tt$<t$pt$xt$xh/s 8 ( ~ D$X ~ =~ u =~ t D$X ~ =~ t%~ =~ u =~ t D$\ p~ =~ t%p~ =~ uK=~ uBG ~ SQh+s h ~ $ $ D$0P$ $ D$4PG=~ uq=~ thG ~ SQh+s h ~ $ $ D$0Pt$|t$D ~ GQ$ h} h~ hp~ $ h0/s fG ~ SQh+s h ~ t$tt$<$ $ D$4P ~ GQ$ h} h~ hp~ $ h0/s <; =~ ~J~ HD$8x~ %-x~ ~ ljLD Dx~ x~ ;D$8=~ }?~ Hx~ %-x~ ~ ljLD D x~ =x~ =X~ T `~ Ȃ~ Eu9hh~ h~ t$ph+s h~ h`~ hȂ~ h} h} h0s $ (; tV`~ Ȃ~ EuC~ HD$8Ghh~ h~ Ph+s D$HPh`~ hȂ~ h} h} h0s (`~ ~ u9hh~ h~ t$ph+s h~ h`~ h~ h} h} h0s z (; tY`~ ~ uC~ HD$8Ghh~ h~ Ph+s D$HPh`~ h~ h} h} h0s (܂~ 1<]_^[SVWU$D$\L$D$d$D$)D$XD$dL$ D$ d$ D$ )D$`D$tL$D$d$D$)D$pD$|L$D$d$D$)D$x$ L$D$d$D$)$ |$P$ $ $ h2/s t$< YY~ hp/s t$@ YY~ h0s t$D YY~ # =~ u h/s t$< YYu 7 =~ u h/s t$@n YYu =~ u h/s t$DF YYu D$D} D$HɉL$} D$Lɉ $} }1AыD$\9} <$}1A $D$d9}dD$t | =~ t 9}DD$| |=~ t ;$}#$ |=~ t ;D$}tPh0s h;/s ° Vt$`D$`D$ Pt$Tt$Th1s <W ~ Vt$hD$hD$Pt$Tt$\h1s W ~ h1s 7Y ~ h1s & ~ ~ ~ YEu ~ ~ ~ ~ D$ D$HL$ D$D 9ȉ$$L$ ~ h~ ~ ~ Eu~ ~ D$HD$L 9ȉ$$$ D$D$D$D$xD$D$D$D$pD$D$D$D$`D$D$ D$D$XD$ D$D$ S ~ x~ D$LAFQVU$ t$ $ t$,$ t$<t$|Whx~ hh~ $ t$P$ t$`$ $ $ $ $ $ `Sh~ V$ t$$ t$($ t$8$ $ hx~ hh~ $ t$L$ t$\$ W$ $ $ $ $ $ dh@-s Vh@-s t$tt$XzD$TD$D +9| d~ L$ ~ ~ p~ ~ TD~ ~ ~ @~ N~ TD~ ~ ~ ~ Eu~ p~ ~ ~ ~ ~ 9 ~ ~p~ ;~ tQ ~ p~ TDTD~ ~ ~ TD~ p~ D ~ D~ D$ 9~ 1$]_^[SVWU<D$lL$0ȉD$$D$$d$$D$tȋl$h+l$$L$D$D$d$$ ȋ|$p+|$L$D$D$d$D$)$ $ ȉL$D$ D$ d$ D$ )$ $ L$ D$ d$ D$ )$ t$|$ h2/s t$Tk YY܃~ hp/s t$XV YY~ h0s t$\A ~ YY~ $ =܃~ u#h/s t$T YYu$ =~ u&h/s t$X YYu$ [ =~ u&h/s t$\ YYu$ , D$\ɉL$4}$ D$`}$ D$dɉL$ }$ |$4}1AL$4D$l9}$ }1AыD$t9}$ $ |=܃~ t;D$4}$ T$ | =~ t9}$ *$ |=~ t;D$ } $ $ t ؉$Ph 1s h;/s ک D$d 1ɉ$ $ d A; $~ Ѓ~ D$|$ D$ $ $ $ $ $ t$0t$|t$|? 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YYX~ &5X~ HD$%X~ =`,s $uuD$PD$ P A\~ X~ F~ 1ɉD$ p~ A9~ `~ PX~ &5X~ HD$%X~ =`,s $uuD$PD$ P@\~ X~ Fe_^1[]USVW(E L$$Au)ƋE(L$y]$E)8 hn/s u=> YYd E D$ \$ |$ ~ 0 E ~ \D@u3~ 1GL$D$ ˃d $ G9~=~ T$$B~ D ։ ~ ~ D ?$ h0s u = YY E +~ @D$~ HD$ E ~ Dࡐ~ \$h-s D$@Ph~ h-s D$4@~ Pu D$<~ PD$,PD$<PD$,Ph/s ~ HD$E +~ @D$ E ~ Dࡐ~ \$h-s D$@Ph~ u D$4@~ Pu ~ D$<@PD$,PD$<PD$,Ph/s #,T$$~ B~ ~ ։D~ HD$h-s ~ D$@Pu(t$,D$Ph0s h/s h0s f=~ E L$TDA ~ ˉD~ ~ ;D$ E ~ E ~ \D@u>E D$ ~ L$~ NjT$ ˃d $ G9~=~ ~ E;r h0s u K; YY T$$EB~ +8E8D ~ ~ E+ED ?$ EE+ ~ L$ +~ D$E ~ D\$h-s D$@~ @Ph~ h-s ~ D$4@Pu ~ @D$<@PD$,PD$(PD$0Ph/s !,ET$$B~ +E EE+~ T$$~ D ։ ~ ~ EE+ ~ L$$ ~ D ?$ E +~ D$ EE+ ~ L$E ~ D\$D$$~ h-s L$A ~ AQ @h~ u Qu PD$,PD$(PD$0Ph/s E,E+~ T$$~ ~ ~ ։DE +~ D$ h-s D$@~ @Pu(~ @D$~ @PD$ Ph0s h/s h0s c =~ E L$TDA ~ ˉD ~ =~ e_^1[]USVW =-s u] %-s h/s %Y ؒ~ h0s %Y ~ ht/s %Y\$pht/s %YPP $ YY\$(ؒ~ PP5~ $c YYt$(|$VfD$VfL$V 5,s l$VfD$VD$d\$(L$(L$dl$VPD$tP8 Ȓ~ 5Ȓ~ YY В~ E D@u E@ ?E f & E8E@ $D$ $D@u)E` E F ?& E @ C5 $D$ ~ ~ E @ ~ Ē~ t$t$ YY\$p5Ē~ 5~ YY\$(D$p\$(Eu L$pD$tL$(D$,L$D$ D$ L$D$ ~ ~ В~ d Ȓ~ ̒~ L$X $D$\D$L$ ~ D$ Ē~ 1L$8D$< В~ Ԓ~ L$hD$lD$L$XG\$D$8L$X\$8t$ t$ % YY\$t$<t$< YY\$HD$\$HEu L$D$L$HD$LD$4L$0D$0\$htD$8L$0D$4D$ ~ ~ L$D$L$pD$tL$8D$< ~ L$Ē~ D$ L$pD$tPP ~ ~ ȉ=~ $ YYD$3ED$831@ |$d В~ @9~ D$ Ȓ~ z EAn В~ Ԓ~ L$H $D$LD$L$ ~ D$$Ē~ 1L$@D$D Ȓ~ ̒~ L$xD$|D$ L$HG\$ D$@L$H\$@t$$t$$ YY\$t$Dt$D YY\$0D$\$0Eu L$D$ L$0D$4D$L$D$\$xEt@tD$@L$D$D$ ~ ~ L$D$ L$pD$tL$@D$D ~ L$ Ē~ D$$L$pD$tPP ~ ~ ȉ=~ $ YYD$ 3ED$@31@ |$d Ȓ~ @9~~ @D$~ $$L$pD$tPP $ YY$3E~ 3 E p0U EYY\$(p0B YY1\$(Et.E @,s u Ev s 1e_^[]USVW0E ȉL$,D$D$d$u ] +\$}D@# h0/s u2 YY E H w$\ \$h-s u$h~ h-s Wu Sh-s uu h/s ,\$ u Sh-s u$h-s W ɋE1-`,s ~ D$,D ~ \A9~ ~ # G @~ D~ @~ ~ G O H~ L~ H~ E ~ ~ OH~ ~ L$,L@~ L~ ~ l\~ ~ l\~ 9~ ~\" G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ E ~ ~ oH~ ~ L$,L@~ LP~ L~ ~ l\~ ~ l\~ ~ l\~ 9~ ~s! G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ E ~ ~ H~ ~ L$,L@~ LP~ LX~ L ~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ 9~ eD G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ E ~ ~ H~ ~ L$,L@~ LP~ LX~ L `~ L(~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ 9~ E G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ E ~ ~ H~ ~ L$,L@~ LP~ LX~ L `~ L(h~ L0~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ ~ l0\0~ 9~ %) G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ E (~ ~ H~ ~ L$,L@~ LP~ LX~ L `~ L(h~ L0p~ L8~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ ~ l0\0~ (~ l8\8~ 9~ = G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ x~ E 0~ ~ H~ ~ L$,L@~ LP~ LX~ L `~ L(h~ L0p~ L8x~ L@~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ ~ l0\0~ (~ l8\8~ 0~ l@\@~ 9~ G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ x~ 0~ GDO@ ~ ~ ~ E 8~ ~ / H~ ~ L$,L@~ LP~ LX~ L `~ L(h~ L0p~ L8x~ L@~ LH~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ ~ l0\0~ (~ l8\8~ 0~ l@\@~ 8~ lH\H~ 9~ G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ x~ 0~ GDO@ ~ ~ ~ 8~ GLOH ~ ~ ~ E ~ ~ O H~ ~ L$,L@~ LP~ LX~ L `~ L(h~ L0p~ L8x~ L@~ LH~ LP~ ~ l\~ ~ l\~ ~ l\~ ~ l \ ~ ~ l(\(~ ~ l0\0~ (~ l8\8~ 0~ l@\@~ 8~ lH\H~ ~ lP\P~ 9~ E H w$\ \$h-s u$h~ h-s Wu Sh-s uu h/s ,\$ u Sh-s Wh-s u$D$8Puu $ ɋE 1-`,s ~ D$, ~ B9~~ D G @~ D~ @~ T$, ~ G O H~ L~ H~ E ~ ~ ^5~ H~ @~ D$, D$,~ ~ , ~ ~ 5~ , ~ 9 ~ ~ G @~ D~ @~ T$,R ~ G O H~ L~ H~ ~ GO P~ T~ P~ E t$, ~ ~ =~ H~ @~ D$, P~ D$,~ ~ , ~ =~ ~ , ~ ~ =~ , ~ 9 ~ mp G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ E X~ ~ L$ t$,T$,L$,~ R =~ H~ @~ D$, P~ X~ D$,~ ~ , ~ =~ ~ , ~ =~ ~ , ~ ~ =~ , ~ D$ 9~ @ G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ E `~ ~ L$ D$,ƉD$d$~ 4v =~ H~ D$ @~ D$, P~ X~ `~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ , ~ =~ ~ , ~ ~ =~ , ~ D$ 9~ ? G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ E h~ ~ L$D$,Ɖ ID$d$D$d$~ 4v =~ H~ D$ @~ D$, P~ D$X~ `~ h~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ , ~ =~ ~ D$, ~ =~ ~ , ~ ~ =~ , ~ D$9~ ! G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ E p~ (~ L$D$,ljD$d$ƉD$ d$ I )~ 4vD$C =~ H~ D$ @~ D$, P~ D$ X~ `~ h~ D$p~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ , ~ =~ ~ D$ , ~ =~ ~ , ~ =~ ~ , ~ (~ D$=~ , ~ D$9~ G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ E x~ 0~ L$D$,ljD$d$ƉD$ d$ )D$ IɉD$ d$ ~ 4vt =~ H~ D$ @~ D$, P~ D$ X~ `~ h~ D$p~ D$ x~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ , ~ =~ ~ D$ , ~ =~ ~ , ~ =~ ~ , ~ =~ (~ D$, ~ 0~ D$ =~ , ~ D$9~ | G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ x~ 0~ GDO@ ~ ~ E ~ 8~ L$D$,ʉD$Qd$D$D$,D$ Ɖ )d$ D$ȍR҉D$d$~ 4 =~ H~ D$ @~ D$, D$P~ D$ X~ `~ h~ D$p~ D$x~ ~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ D$, ~ =~ ~ D$ , ~ =~ ~ , ~ =~ ~ , ~ =~ (~ D$, ~ =~ 0~ D$, ~ 8~ =~ , ~ D$9~ K G @~ D~ @~ ~ G O H~ L~ H~ ~ GO P~ T~ P~ ~ G O X~ \~ X~ ~ G$O `~ d~ `~ ~ G,O( h~ l~ h~ ~ G4O0 p~ t~ p~ (~ G<O8 x~ |~ x~ 0~ GDO@ ~ ~ ~ 8~ GLOH ~ ~ E ~ ~ L$D$,ʉD$Qd$D$D$,ʉD$ d$ D$L$, )ȋt$,D$ ȍ4v D$d$~ =~ H~ D$ @~ D$, D$P~ D$ X~ D$`~ h~ D$ p~ D$x~ ~ ~ D$,~ ~ , ~ =~ ~ D$, ~ =~ ~ D$, ~ =~ ~ D$ , ~ =~ ~ D$, ~ =~ ~ , ~ =~ (~ D$ , ~ =~ 0~ D$, ~ =~ 8~ , ~ ~ =~ , ~ D$9~ 1e_^[]SVWUD$,l$0|$4t$8\$<p0详 ~ YYuu 蜦 ~ YYw7芦 ȓ~ ~ ȓ~ YYu ~ ~ ȓ~ ̓~ L$D$D$L$ ~ ~ ~ ȓ~ Eu ~ ~ ȓ~ ̓~ $D$D$ $\$ ~ ~ D@ f & $D@y $ ~ Eu$~ $ ~ u$~ $ ~ Eu $D$ ~ ē~ ȉL$D$ PP`,s $^ YYL$ ~ $ D$4$`,s Г~ $d$4$ ؓ~ ~ 4$PP ~ ؓ~ ~ $ YY\$Г~ PP~ $Υ YYD$\$,s t$ ~ D$ ~ $5~ $5~ ~ ~ D@u&D$ $5~ ē~ ~ C D$4$`,s Г~ $d$4$ ؓ~ Г~ ~ $ؓ~ ~ PP`,s $ YY\$$PP`,s $ YYD$ $4$ ~ D$ ~ ~ ~ =~ 1]_^[SVWUl$DE D$t$@@\$H|$8# )h0s t$(b YYt % ~ h0/s t$(B YYt ~ h2/s t$( YYt ~ h*1s t$( YYt ~ ght/s t$( YYt ~ Gh0s t$( YYt ~ 'h,1s t$( YYt ~ ~ = ~ u 2 D$0D@u } D$<ɉL$ | = ~ u9u= ~ u9T$ t = ~ }1A9M = ~ D$(Jɉ $| 19$~ T$ D$,JɉL$ |"19T$ ~ wD$ 9$tC= ~ u $A9M |+= ~ u L$ A9M |= ~ u $L$ A9M }tPh.1s h;/s D$<8 ? u h/s d 0~ Y50~ (~ D$0@ ~ $~ D$4@ ~ ~ ~ 0~ ~ ~ 5(~ @~ 5~ 5~ v YY $5 ~ 5~ ` YY1 $EtJ ~ D@t84~ 0~ 8~ <~ %~ ~ ~ ~ $~ 5$~ 5 ~ YY $5D~ 5@~ ܟ YY1 $Et5,~ (~ 8~ <~ %~ D~ @~ ~ ~ ~ 5 ~ 8~ ~ = ~ uQD$<~ 21ۋ~ CT$/ 8~ C9~ ~ ~ 9 ~ ~ = ~ uVD$<~ 7~ \$~ 8~ E9~-~ ~ 9~ ~ = ~ u_D$<~ @9 ~ } ~ 1 ~ E\$ 8~ E9~-~ ~ 9~ ~W = ~ u^D$<~ ? ~ A9|1 ~ E\$ 8~ E9~-~ ~ 9~ ~ = ~ D$( @ ~ D$< @~ D$< $~ ~ 1D$ : ~ )9 ~ }L$ 1ۉCT$ 8~ C9~ ~ E;,$~W = ~ u~D$, ~ D$, @ ~ D$< $~ 1 ~ 3 ~ )1CT$ 8~ C9~ ~ E;,$~ = ~ D$(D$, ~ D$( @~ D$(D$,A ~ D$(D$,AD$< ~ L$ ~ |e ~ 1$L ~ ~ ))9 ~ } $; ~ ~ T$ 8~ C9~ ~ E;l$ ~-~ =~ H1]_^[SVWUL$4D$@l$ )D$0\$(h2/s U YYt|D$$ $L~ W-L~ D$ M 9|H~ L~ T$ D$0<Ћ H~ C34ωDH~ 9-H~ ~L~ $9L~ ~ h0/s UG YYtzD$$D$ 9щ $|$L~ KD$ L~ @H~ -L~ l$ D$0< H~ C34ωDH~ 9H~ ~L~ $9L~ ~jD$$ $L~ JD$ H~ -L~ l$ D$0< H~ C34ωDH~ 9H~ ~L~ $9L~ ~D$$D$ (9|H~ *D$,H\$C H~ D$0؋D$0LH~ 9-H~ ~1]_^[SVWU |$4D$Dt$8\$@ }-D$D D$D ؉$Ph51s h;/s J q i uv6舙 YY Q uAFhp~ hh~ Pt$HVt~ p~ Fl~ h~ NF %t~ %p~ H$P~ P~ DPP$ P~ YY\$D$L$LD p~ L$ P~ t~ D$ D$<tt軘 YY\$p~ \$Eu L$D$ L$D$L$D$ L$D$ p~ t~ P~ P~ ;$M/ttT YY\$D$ L$LD p~ D@uh`~ VWh<1s H $P~ 8p~ P~ Dp~ Eu p~ P~ P~ ;$~h1s ,Y ~ ha/s x~ ~ YPP5x~ $袘 YYh+s Sh+s VW X~ mH$Ch+s Ph+s t$HD$PHH$HD$h`~ D$PSh+s D$PhX~ hp~ h} h} h0s |(H$P~ P~ D\P~ P~ ;$~ߋd d t$DSW D$D8 ul$P~ #P~ tt藗 YP~ Y\P~ P~ ;$~h`~ WVh+s Whp~ hX~ h} h} h0s (1 ]_^[SVWUt$4|$0& h1s Y P~ ha/s s H~ P~ 0,s YX~ h~ D$, }5+s h>1s h;/s u= @,s 75+s h>1s h;/s G @,s tG @,s u Eu ؔ~ GOG GG_ GG h~ r ,s ~ G5~ O~ ~ u8EAt0~ 5~ PP`,s $蠕 `,s YY ~ A~ PP~ $v YY $5~ 5~ ` YY $ $~ $O ~ ~ G ~ 5~ O_~ ~ GGOOG G_(j d8 d8 G O ~ ~ %Ĕ~ %~ %̔~ %Ȕ~ %ܔ~ %ؔ~ %~ %~ D$,I~ 0 ~ D @,s u~ ؉&~ @,s u'~ ؉5+s h>1s h;/s ؔ~ ؔ~ ~ ~ ~ ~ D~ Eu~ ~ ~ ~ u ~ Ȕ~ EuȔ~ ڡ~ Eu Ȕ~ ~ 9 ~ D$,D @,s u+ ؉5+s h>1s h;/s w ؔ~ ËD$, ؔ~ ~ D~ Eu ~ Ȕ~ EuȔ~ Ȕ~ ~ D@uxD$,~ #~ ~ LDLD~ 9 ~ ~h ~ Wt$4h<1s A D$,ҡܔ~ ؔ~ LD ؔ~ ~ ~ ~ D@u D$, d d 1Y 1jjh ,s h+s h+s h+s h/s h>1s h,s 4 $u5jjh ,s h+s h+s h+s h/s h>1s h ,s $É ~ D$, ~ V~ d d ~ TL~ TLd d ~ TLTL-~ =~ }$~ D$, ,~ D$d$D$ p,s \ ,~ @`~ -,~ (~ (~ LD ~ ~ (~ `~ +(~ LTTL ~ ~ TL (~ TL~ ~ Lԋ (~ TЉTL ~ ~ TЉLԃ(~ 9-(~ \%0~ ~ ,~ $$$D$ d$ 0~ ZD$NjLDT$ ؔ~ ܔ~ ى(~ m(~ Dh~ ؔ~ u)(~ d d (~ lD-ؔ~ ܔ~ ؔ~ á(~ =ؔ~ L ؔ~ -(~ 9 (~ }0~ L D$ ~ ~ 0~ NjD ؔ~ ܔ~ (~ 0~ ? (~ ؔ~ D (~ )\(~ Dh~ ؔ~ uH(~ d d ܔ~ -ؔ~ lDd d (~ ,NjD-ؔ~ ܔ~ D١(~ H~ u?H~ u+ ~ (~ ~ L\ؔ~ ~ \ؔ~ t(~ ؔ~ ~ D~ u ~ (~ 9(~ ܔ~ L$+ 0~ ؔ~ TD + 0~ DT~ Ĕ~ (~ 9~ (~ D~ Eu ~ (~ 9 (~ ~1@+0~ 0~ ~ =~ "~ % ~ $~ D$,L$ D$ 4~ =,~ % ~ %~ ,~ D$,;u% ~ %~ ,~ D ~ ~ @,s u %~ %~ ,~ ;$~ ~)tt YY $D$ $ ~ ~ %~ %~ ,~ DT~ ~ ~ Ĕ~ (~ # (~ D @,s E @ ~ ,s ~ uoEAtg~ (~ D~ u ~ ~ (~ D~ Eu ~ ~ (~ DD~ Eu ~ ~ (~ D~ u ~ -(~ =(~ (~ (~ $~ ~ ~ TD5~ 5~ 9 YY $5~ 5~ # ,s YY $ $~ $$ $ $Eu d$ d$ $D$L$D$D$ ~ %0~ ,~ +$~ @ ) ~ 8~ $~ ;,~ h~ h~ h~ h ~ h~ h~ h~ h~ h0~ Wh,~ h$~ 1@+0~ 00~ J ,~ +$~ 6 h~ -,~ ~ \/t#h~ ,~ ~ \ $~ HД~ $~ LT~ Ĕ~ LT~ ~ $~ TL@~ D~ ,~ (~ ? (~ h~ L\th~ ~ \ug~ (~ \(~ Д~ %Ĕ~ %~ (~ TD~ ~ (~ TD @~ D~ ~ (~ ~ Eu ~ ~ (~ D~ u ~ @~ (~ D@~ u @~ (~ 9 (~ ~ ,~ ~ LDD~ @~ L/D/Д~ @$~ 8~ 9 8~ 7 = 4~ D$ 94~ D$,~ $~ ~ LDLD~ 9 ~ ~h ~ Wt$4h<1s 6 D$,%~ %~ ~ ~ ~ D ~ ~ =~ }܋D$,ҡ~ ~ DD$,ҡ~ ~ LD ~ D$, \D$,ɉD$D$~ \~ D$, ~ 0,s \ 1j]_^[SVWU|$0t$4\$@~ h1s Y Е~ ha/s ȕ~ Е~ 0,s Yؕ~ ~ D$, 9} 1 9tuD$8D$,ĕ~ $A9 ĕ~ D ~ \u/D$8~ (D- ĕ~ )ĕ~ L\t D$8 D\R~ ĕ~ \ưu!ĕ~ ~ LƠ\θ ĕ~ D\Eu* ~ ĕ~ LDĉLDĕ~ \ĕ~ DD~ ĕ~ D ,s ~ D5~ L~ ~ u6EAt.~ 5~ PP`,s $i `,s YY ~ ?~ PP~ $A YY $5~ 5~ + YY $ $~ $ĕ~ |L ~ ĕ~ ~ DD ~ D5~ L\ĕ~ ~ ~ LDġĕ~ D\ĕ~ D\sD$< @,s Et@t ;~ $DL p,s \ $~ D$, $$$$$ ~ ~ LD ~ ~ -~ ~ +~ LTTL ~ ~ TL ~ TL~ ~ -~ LTTL ~ ~ TL ~ TL~ ~ -~ LԋTЉTL ~ ~ TЉLԋ ~ TL~ ~ L܋-~ T؉TL ~ ~ T؉L܃~ $9~ D$,/)ȃFD$8ыTLTLD$8D$, )ȋ)ʋLDLD~ D$8D~ u ~ D$8(D$,DDtDu\D$8(D$,))DDtDu\D$H D$,D$8DEtEuڋD$HD$<` D$< D$8 DDưt~ )DD$< @,s t0uȕ~ D$H hp~ h~ h~ h~ h~ h~ hx~ t$Xh~ t$\VWt$\ 4t$Xh~ h~ h~ h~ hx~ t$Th~ t$XVWt$X9 0D$,+D$TD$P D$<@L$D$D$ @,s ux~ @,s E D$ @,s x~ @,s EuxD$8/M+(C L$D$ D$~ ؕ~ \EuD5~ 5~ x| ؕ~ YYL$Eu d d D$<` D$< D$ @,s urD$L =p~ |ux~ @,s Eu2~ D$< Е~ ,s -`,s ~ p~ m~ ,s ~ p~ OD$\$D@t%~ %~ *h~ h~ h~ h~ hx~ t$Pt$PVWt$P (D$,+D$TD$P %~ %~ ~ u"D$D ~ D$D ~ #( ~ D$D~ %~ + ~ ~ C124]_^[SVWU|$@ @,s l$4t$LT$T\$\uEAtD$X ` D$0D$8D$0 ~ $D$<; $k D@tD$PD@| ~ tt5{ ~ YY\$tt { YYL$ $D$ $ ~ ~ ~ tŴtŰz ~ YY\$ttz YYL$\$D$L$ ~ ~ ~ DD ~ D@J D$D D$PD@s D$H % ~ ,s 8~ @,s Eu!8~ \$EuD$58~ L$$D$ ~ & 0~ 0~ @,s EuN0~ $Eu>$50~ $. ,s Eu ~ %~ %~ $Eu $$ ~ $D$ ~ Eu4~ ~ ~ u ~ ~ ,s ~ Eu ~ ,s ~ D@uK (~ %~ % ~ ~ DDEl ~ ~ D$8ɡ ~ )ȣ ~ LD ~ ~ D$P@ (~ ,~ ~ DDE ~ ~ DŠDŰE ~ ~ ~ ~ D$,~ ~ D$8I ~ ~ ~ D@ ~ ~ ~ ~ ~ DDEB ~ ~ ~ ~ ~ ~ ~ Eu~ ~ 0,s ~ t),s ~ t-~ 9 ~ 0 ~ ,s ~ ,s ' D@O ,s D$8 ~ ɡ ~ )ȣ ~ LD ~ ~ ~ LȋD̉ ~ ~ B (~ ,~ ~ DŸ ~ E ~ D ~ Eu 5~ D$0`,s 5~ ~ D$,+, ~ DŐt̀D$, ~ ~ ~ ~ ID$8 ~ ~ ~ D@ ~ ~ ~ ~ ~ DDE ~ ~ ~ ~ ~ ~ ~ Eu~ ~ 0,s ~ t),s ~ t-~ 9 ~ 0 ~ ,s ~ ~ ,s x 5~ 5 ~ t -`,s YY (~ ~ `,s ~ u %~ ,s ~ ~ ,u~ O?~ Zd;~ ?%~ ~ ~ $@9 D$D D$PD@n D$H D@X D$D ,s ~ ~ DDET ~ ~ ~ ~ ~ ~ D@ D$8D$,ID$0 У~ ~ ~ ~ ~ ~ DDE ~ ~ ~ ~ ~ ~ ~ Eu~ ~ 0,s ~ t-~ 9 ~ \~ PP ,s $tr ~ YYD$D`,s 8 ~ D$H ,s % ~ 8~ @,s E ~ ~ 8~ uU~ ~ 58~ ~ ,s ~ -`,s ~ ~ Eu# ~ ~ ,s -`,s ~ ~ Eu ~ @ ,s D$D ~ D$PD@u ,s ~ $9 D$H D@s ~ D ,s \O D$H ,s ~ ~ DDEtw ~ ~ ~ ~ ~ ~ D@ D$8D$,ID$0 У~ h~ DDEu 1 ~ ~ ~ ~ ~ ~ 0,s ~ t-~ 9 ~ }~ PP ,s $o ~ YYD$H`,s 8 ~ ~ LŰDŴL$D$ PQo ~ YY $tŤtŠo ~ YY $\$DD$d$% ~ 8~ @,s E ~ ~ 8~ uO~ ~ 58~ ~ ,s ~ -`,s ~ ~ Eu?9~ ~ ,s -`,s ~ ~ Eu ~ h ,s ~ R9~N%~ %~ ًD$X ~ ~ D$XH1 >}Uă]_^[SVWU|$D$/ )Ht$ \$$T$(L$< D$ (-X~ lD -@~ D~ X~ D# P~ T~ -P~ *BX~ DD$,D$@8 D$ 8 D$(X~ X~ P~ D\=X~ t H~ P~ H~ # P~ P~ uP~ X~ H~ L\X~ D @~ u@~ @~ X~ 9-X~ K D$(X~ X~ P~ D\=X~ Dt H~ P~ H~ # P~ P~ uP~ X~ H~ L\X~ D @~ u@~ @~ X~ 9-X~ JT~ -P~ )AjD$0:8D$0hD$(D$ +(-X~ H\~ D\\~ D-X~ tL\X~ t\~ LD$8#D$8 uJD$,*(D$,HX~ D$ X~ H\~ D$8 DX~ \\~ X~ DtL\D$8 \~ X~ tLD$4#D$4 uf ] D$ 8 D$(X~ X~ P~ D\P~ @,s E =X~ Dt \X~ P~ t # P~ P~ uP~ @~ X~ D@~ u @~ X~ 9-X~ 6 D$(X~ X~ P~ D\P~ @,s [ =X~ DtL\X~ P~ tL# P~ P~ uP~ @~ X~ D@~ u @~ X~ 9-X~ 4T~ -P~ )AjD$0:8D$0hD$(D$ +(-X~ H\~ D\ @,s T \~ D-X~ tL\X~ t\~ LD$8#D$8 uJD$,*(D$,HX~ D$ X~ H\~ D$8 DX~ \D$8 @,s \~ X~ DtL\D$8 \~ X~ tLD$4#D$4 uD$4X~ @LD D$D$ +D~ @~ LD1]_^[SVWUD$D$+Iɋl$ |$$t$0\$41 ha/s ~ YD$D$ x~ ȋLD `~ d~ x~ LD p~ t~ GD$ 8 t D$D$ x~ @ x~ p~ DTD@u:x~ d d T Dp~ t~ G%d~ %`~ x~ D ~ u?~ u+ h~ x~ h~ L\p~ h~ x~ D\p~ tL p~ p~ up~ `~ x~ D`~ u `~ x~ 9 x~ o D$D$ x~ @ x~ p~ DTD@u:x~ d d TD p~ t~ G%d~ %`~ x~ D~ u?~ u+ h~ x~ h~ L\p~ h~ x~ D\p~ tL p~ p~ up~ `~ x~ D`~ u `~ x~ 9 x~ t~ p~ D$8D$8HOD$,D$,HD$D$ + x~ H~ D$8 Dx~ TD@u>x~ d d ~ LD CC G%d~ %`~ ~ D~ uD~ u0 h~ ~ h~ Lx~ \D$8 h~ +~ Dx~ \D$8 t衈~ Lu D$(OD$(Hx~ D$ x~ H~ Dx~ TD@u>x~ d d ~ LD FFG%d~ %`~ ~ D~ u@~ u, h~ ~ h~ Lx~ \ h~ %~ Dx~ \t衈~ L u x~ FLD D$D$ +d~ `~ LD1]_^[SVWUD$<\$8A|$ l$$t$, $%~ )h0/s t$ S YYu#hr/s t$ ? YYu~ hp/s W YYu.h0s W YYu ht/s W YYu ~ ohn/s U YYu ht/s U YYu ~ AD$(} ~ +> } ~ }1AD$<9} ~ =~ t 5~ hE1s h;/s D$(8 > u h0/s t$ 1 YYF hp/s W YY} hn/s U YY+ D$(8O~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ ~ $~ ӋlT -~ ~ ~ ~ ~ ~ ~ \~ ~ ~ ~ ~ ~ 9 ~ o~ 9=~ y ht/s U YYd D$( H~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ ~ $~ ӋlT -~ ~ ~ ~ ~ ~ ~ \~ ~ ~ ~ ~ ~ 9~ n ~ =~ < h0s W YY: hn/s Uu YY D$(8~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ l ~ $~ Ӌ,ʋT-~ ~ ~ L~ ~ ~ ~ L~ ~ \~ 9~ ~~ 9=~ ht/s UV YY D$( ~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ l ~ $~ Ӌ,ʋT-~ ~ ~ L~ ~ ~ ~ L~ ~ \~ 9~ ~ ~ =~ ht/s W; YY hn/s U& YY D$(8O~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ v~ $~ Ë,ЋD-~ ~ ~ D$( ~ ~ ~ ~ D$( ~ ~ ~ 9 ~ ~~ 9=~ ht/s U YY D$( H~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ ~ v~ $~ Ë,ЋD-~ ~ ~ D$( ~ ~ ~ ~ D$( ~ ~ ~ 9 ~ ~ ~ =~ hr/s t$ Ӿ YYp hp/s W达 YYn hn/s U詾 YY* D$D$~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ D$( ~ ~ B ~ $ $j-~ <Ӌ4l5~ -~ -~ ~ 4 ~ ~ ~ -~ 4 ~ ~ ~ 9~ ~~ D$9~ ht/s Uj YY H~ ~ D$0LD ~ ~ D$4LD ~ ~ ~ D@u ~ D@ D$( ~ ~ B ~ $ $j-~ <Ӌ4l5~ -~ -~ ~ 4 ~ ~ ~ -~ 4 ~ ~ ~ 9~ ~ ~ =~ h0s W; 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$1 ~ ; $ؙ~ D$H1 ]_^[SVWUD$4|$0t$Dl$@& C)jjh8.s t$8t$8t$8h/s h0s h4.s s $~ D$(}1A~ 1ɣ~ D$<~ } D$$ ~ ɉL$}mD$(|;T$~UD$, |9~?|$}D$ D$4L$9} }1B9U }= ~ ut ؉D$ Ph0s h;/s j = ~ D$(8 D$<@ ?D$< ~ % ~ D$( ~ =~ ~ D$,; d$ jjh8.s Pt$8t$8h/s h0s h<.s rr $$D$ ;$~ $D$, ~ ;}{D$( ~ ~ ~ E ;~ }Y=~ D$ jjh8.s ~ t$8t$8t$8h/s h0s h@.s q $$D$ ;$$~ ~ ;~ D$, 9~ 9 ~ + ~ Iș=~ ~ D$, ~ D$ ~ $D$ ;$} $ ~ D$( D$ A;D$ ~ I $D$ D$%1EӋ4$ ׃d $ E9~-ܙ~ A;L$~Չ ~ %~ ~ D$(;}kD$$ )ȉD$ D$( )ȉ$D$, )ȉD$A h~ t$@L$@~ @Rt$@PD$PD$PD$(P$ =~ J ~ ؉D$ ~ @ܙ~ ~ $D$, +ܙ~ @D$$;D$|D$~ ܙ~ D$(; D$$ +ܙ~ @$h~ t$@D$@ ܙ~ QCܙ~ t$@Ph~ D$Ph,0s h70s C$D$$ +ܙ~ @$D$( +ܙ~ +~ @D$h~ D$@ ~ AQܙ~ ~ t$<ܙ~ PCܙ~ h~ t$Pt$LPh~ D$(PD$(Ph,0s h70s h/s h}/s <+<D$$ +ܙ~ @$h~ t$@D$@ ܙ~ QCܙ~ t$@Ph~ h~ D$ Pdܙ~ ~ H $ܙ~ ;$~ FHD$$ ~ D$&1FӋl$ ׃d $ F9~5~ A;L$~ԉ ~ D$ ܙ~ |$ }1=ܙ~ 1=ܙ~ ~ D$<1]_^[SVWUD$8L$ȉD$D$d$D$)D$4l$,\$H# D$D1Ƀ8 ,~ h2/s U( YY ~ uh0/s U YYu aD$0}O}1AD$89}7D$0$ HD$}1AL$D$D9}=,~ u; = ~ tDD$0 H$D$0 HD$D$0 HD$ jjhH.s D$PD$$PD$Ph/s hl1s BD$0 H$D$0 HD$D$0 HD$ jjhH.s D$PD$$PD$Ph/s h0s hD.s l $$~ D$0$ HD$}1AL$$~ (~ (~ D$@t ؉$Ph|1s h;/s 4c =,~ D$0 uD$@@ ?D$@ = ~ d H$~ ~ H~ 5~ FD$~ t$D$D$&D$4 ~ <ًڋTωT~ ~ ;D$~ϋD$0L$D$4d D$4$ ~ ~ ;$nD$0 H$~ (D$0L$D$4 ~ d D$4$ ~ ~ ;$~D$0L$AD$4D ?D$4$ D$0 H$D$0 HD$D$0 HD$ h ~ t$Ht$Ht$Ht$HD$HD$PD$$PD$0PD$ P52 ~ u-~ l$D$4d D$4d D$0 $~ @~ 5~ Nt$&D$4 ~ <ًڋTωT~ ~ ;$~ ~ =~ }D$4L$D ?D$4L$d D$0 $ D$4L$ȃd $ C9~D$0 ~ ~WH$D$0 HD$D$0 HD$ h ~ t$Ht$Ht$Ht$HD$$D$HPD$$PD$0PD$ P3$(~ D$@1]_^[SVWUD$4 $t$0A)ƋD$@L$A\$H)D$<l$(|$,# h0/s t$ i{ YY0~ h/s t$$T{ YX~ =0~ YtD$$ E T~ =0~ u hr/s t$ { YYu =X~ u h0s t$$z YYupD$$}^} }P|;T~ ~:=T~ }1BT~ D$49}}1AD$@9}tPh1s h;/s ^ D$$8 } u =0~ t =X~ t=0~ u&=X~ t 8~ <~ @~ 8~ <~ @~ =0~ tE P~ H~ D$$ L~ D~ 8~ <~ =@~ 4~ =0~ t D$$ +4~ @L~ 4~ D~ E +4~ @P~ 4~ H~ $B4~ D ։ `~ d~ D ?$ t$Dt$DH~ D$ 4~ D~ D$DPD$DQhL.s RhP~ hL~ t$<6$$B4~ d~ `~ ։D=4~ } 19 4~ 19 4~ 1]_^[SVWU,D$\L$(ȉD$D$d$D$)D$XD$hL$$ȉD$D$d$D$)D$d\$t|$Lt$Pl$l# h0s t$Dx YY~ h0/s t$Hx YYh~ h/s t$Lw ~ YYD$p1Ƀ8 ~ =h~ t ~ ~ ~ =~ u h/s t$Dw YYu / =h~ u hr/s t$Hyw YYu =~ u h0s t$LQw YYu ? } > } D$T8 } D$TD$ 9 ~ } ~ =~ L$ t =~ }1B~ D$\9|=~ u}1AD$\9}E}1AD$h9}+=~ }1A ~ D$p9}=~ u; =~ =h~ taD$D$D$HD$D$ D$ jhX.s D$PD$ PD$Pjv HD$ HD$ jjhT.s D$,PVD$0P_D$D$D$HD$D$ D$ jhX.s D$PD$ PD$P v HD$ HD$ jjhT.s D$,PD$,PWD$"Phf0s =h~ tkD$D$D$HD$D$ D$ jhX.s D$PD$ PD$Pu HD$ HD$ jjhT.s D$,PVD$0PD$"Ph0s iD$D$D$HD$D$ D$ jhX.s D$PD$ PD$P'u HD$ HD$ jjhT.s D$,PD$,PWD$"Ph0s hP.s $b $x~ =~ }1A ~ x~ ~ ~ ] t ؉D$ Phq0s h;/s X u =~ h E ?e S > uI =~ ~ D$T;|3hl~ t$tUt$tD$tD$$Pt$tt$tD$tD$4Pt$tVW =~ =h~ t%B|~ ~ p~ t~ "|~ H~ p~ t~ ~ HD$ hl~ t$tUt$tt~ D$4p~ D$tPt$tt$tD$DD$tPD$<Ph~ h|~ t$tt$tp * =~ t ~ T~ N ~ D$T;~Ahl~ t$tUt$tD$tD$$Pt$tt$tD$tD$4Pt$tVWh~ t$t =~ =h~ t%H|~ ~ p~ t~ #|~ H~ p~ t~ ~ HD$ hl~ t$tUt$tt~ D$4p~ D$tPt$tt$tD$D@D$tPD$<Ph~ h|~ h~ t$t9 4~ ] 1,]_^[SVWUD$4 $t$0A)ƋD$@L$A\$H)D$<l$(|$,# h0/s t$ jq YY~ h/s t$$Uq YȚ~ =~ YtD$$ E Ě~ =~ u hr/s t$ q YYu =Ț~ u h0s t$$p YYudD$$}R} }D|;Ě~ ~.}1BD$49}}1AD$@9}tPh1s h;/s T D$$8 } u =~ t =Ț~ u=~ u&=Ț~ u ~ ~ ~ ~ ~ ~ =~ tE ~ ~ D$$ ~ ~ ~ ~ =~ ~ =~ t D$$ +~ @~ ~ ~ E +~ @~ ~ ~ $B~ D ։ К~ Ԛ~ D ?$ t$Dt$D~ D$ ~ ~ D$DPD$DQt$DRh~ h~ t$<,$$B~ Ԛ~ К~ ։D=~ } 19 ~ 19 ~ 1]_^[SVWU(D$TL$ȉD$D$d$D$)D$PD$`L$ ȉD$$D$$d$$D$$)D$\\$ll$D|$Ht$L# h0/s t$@(n YYؚ~ h/s t$Dn YYD$h1Ƀ8 $ =ؚ~ t E E =ؚ~ u hr/s t$@m YYu = u h0s t$Dm YYu M }~? }q|; ~[}1BD$T9}C}1AD$`9}+= }1A D$h9}=$ u; D$<D$D$@D$ $ D$ jhd.s D$PD$PD$"Pm jjh`.s VWUD$*Ph0s h\.s .Z $@~@ = }1A D$dtPh0s h;/s P =$ } t ? t> uD$d@ ?D$d r = ; ( D$h ;( = $ D$ D$<D$D$@D$ jhd.s D$PD$PD$" Pk jjh`.s VWUD$*Ph0s hd.s X $} ( ; | 9 |?h t$ht$hD$hD$0Pt$ht$hD$hD$0PVWUt$ht$h&03 =ؚ~ t = u=ؚ~ u!= u -Hș= A أ =ؚ~ t E = t T N D$$ ܚ~ 9 D$ +ܚ~ @9D$ }D$ +ܚ~ @D$ hh.s h~ D$` ܚ~ Qt$`D$$@ܚ~ D$`Ph D$4PhM0s h70s *$=ؚ~ tE +ܚ~ @ ܚ~ +ܚ~ @ ܚ~ h t$ht$h D$, D$hPhh.s h~ t$lD$0@ܚ~ D$lPh h h hM0s h70s h t$t<D$$ܚ~ |$$ } 19 ܚ~ 19 ܚ~ D$d1(]_^[SVWU(D$TL$ȉD$D$d$D$)D$PD$`L$ ȉD$$D$$d$$D$$)D$\\$ll$D|$Ht$L# h0/s t$@ h YY, h/s t$D h l YYD$h1Ƀ8 x =, t E d d E h =, u hr/s t$@g YYu =l u h0s t$Dg YYu M } ? }}|;d ~g=d }1Bd D$T9}C}1AD$`9}+=h }1A h D$h9}=x u; D$<D$D$@D$ $ D$ jht.s D$PD$PD$"Pg jjhp.s VWUD$*Phf0s hl.s T $@~@ X =h }1A h t t D$dtPhf0s h;/s J =x } t ? t> uD$d@ ?D$d X 8 h p =X X ; h X | D$h ;| =p $ D$ D$<D$D$@D$ jht.s D$PD$PD$" X Pe jjhp.s VWUD$*Phf0s ht.s R $} 8 h | X ;8 | 9X |?h< t$ht$hD$hD$0Pt$ht$hD$hD$0PVWUt$ht$h0 =, t =l t=, u!=l t@ D X -Hș=X X A @ D X أH =, t` T E \ P H D$$@ D 0 8 X D$ +0 @9D$ }D$ L d +0 @D$ hx.s h8 D$` 0 Qt$`D$$@0 D$`PhL D$4Ph,0s h70s $$=, tE +0 @\ 0 P +0 @` 0 T hp t$ht$hT D$,P D$hPhx.s h8 t$lD$0@0 D$lPhL h` h\ h,0s h70s t$tt$t <D$$0 |$$ } 19 0 19 0 t D$d1(]_^[SVWUD$< $\$8A)ËD$HL$ D$ d$ D$ )D$Dl$P|$0t$4e h0/s t$(9b YY h/s t$,$b Y = YtD$, = u hr/s t$(a YYu M = u h0s t$,a YYu E hD$,} E U? } E G|; ~ E 0}1AD$<9} E }1BD$H9}E E tPh1s h;/s E D$,8 ? u = t = t= u&= t = t D$, D$ - D$DD$D$ D$ = tD$, + + + $ ËD + $ D ?$ t$Lt$Lt$ D$L Qt$LD$ Ph h t$D $ + $ ӉDD$ |$ } 19- 19- 1]_^[UESVW L$A]})ËEu h2/s W_ YY uh0/s W^ YYuE)} E }1AE9} E E tPh1s h;/s 3C D$ = v R |$G HD$ D$= h+s @Ph+s PD$,P,8, @,s u EAm 5 5 YY D ; HD$ + D$ @D$ uQ@h.s h+s L$AQuPh.s D$8PD$@Ph/s D,+ D$ 5 @\$uD$ PD$PD$(P_ D$9 z N |$G HD$ D$ = uPuPD$,P6, @,s u EAt D 5 5 YY D9 + D$ HD$D$ Oh+s Q @h.s uQuPh.s D$8PD$@Ph/s C,+ D$ 5 \$h+s D$@ @PD$PD$(P] D$9 Ee_^1[]SVWU$D$LL$ȉD$ D$ d$ D$ )D$HD$Tl$<|$@t$D\$P h/s t$<<[ YYt % Ghp/s t$< [ YYt 'h(1s t$<Z YYt = } D$T=M } D$T *D$L |= ~}1A9} D$T D$T t ؉$Ph1s h;/s ? E u/= z D$HL$D ?D$HL$d X h0s Gؠ Yh/s sG Y5 5 5 YY5,s 5 5 5 YY = u&t$LD$LD$ Ph.s h UUh#1s U E ) % p E H E 9p @ =p ~p d d p ; $p H H tt YY\$D$L$ \$D@ H t4 YY\$ t$ t$ H YY\$ tt~ YY\$t$t$ YYL$ \$ؠ L$\$uH d d H H ;$.E H p D H @p ;D +D @$ D D1PD9PD$Ph(1s h % h D@Ph E +D @$G D t$TUQh.s D$Ph hh h h h0s K( +D $F D t$TUQh.s D$Ph h +D @$G D t$TUQh.s D$Ph hh h h h0s K( +D $F D t$TUQh.s D$Ph hh h h h0s J(D tt" YY\$tt YY\$u D ;D % D ; Ht $D H uH DPP$ YY H t4z H YY\$ttb YY\$ L$L$ tH H ;$~ H H ; } d d D LD P T H ;D D A9O = OʡD L0h` h hР hȠ RQL8Q_D $ LDd U D ` LDt$LD D$@D$LPCM I D Q D Qh.s Uht/s hp/s hr/s 茌$1 OʡD L0hР hȠ RQL8QCD ̠ Ƞ LDԠ D Р DD d d D ; D D ,s %P h.s h0 0 "YY X h0 hX S 0 D Y|H D%P Y 0 d ?%` $ ?% %T %P H D $ 8 8 ` L ( LhX h` h h( h0 H H98 t8 \ X ։D8 %P 0 ,s D%0 ` X ` X P 0 P X % 0 = ~.$ 8 LD` E 8 \ 8 8 ;$= ~dH +D @ t$LD D$@D$LPCM I D Q D Qh Uht/s hp/s hr/s 蠉$D D%P \D 4 0 LDD T P LDD D ; % D ; @x $D H vH DPP$p YY H ttT H YY\$tt< YY\$ L$ L$ t H H ;$} H H ; ~ d d D LD P T H ;D D H9H K = OD ʍL0h` h hР hȠ RQL8Q9H $ LDd U H ` LD t$LD HD$@D$LPCM I H Q H Qh.s Uhn/s hp/s hr/s e$.OD ʍL0hР hȠ RQL8Q D ̠ Ƞ LDԠ D Р LDD d d D ; D D ,s D%P h.s h0 0 YY X h0 hX M 0 D Y|H D%P Y 0 d ?%` $ ?% %T %P D H $H 8 $ 8 ` L ( LhX h` h h( h0 8 ;H t¡\ X LD8 D%P 0 ,s %0 ` X ` X P 0 P \ X % 0 = ~58 $ LDU 8 d ` LD8 8 ;$= ~dD +H @ t$LH D$@D$LPCM I H Q H Qh Uhn/s hp/s hr/s v$D D%P \ 4 0 LD D T P LD D D ; = + @$G t$TUQh.s D$Phh h h h h0s ?( + $F t$TUQh.s D$Phh h = + @$G t$TUQh.s D$Phh h h h h0s ?( + $F t$TUQh.s D$Phh h h h h0s >( ; E H$8 !8 \D@tD$T 8 8 ;$~7 = ut$TWUh(1s 訒 $| | H8 @ LD P T | M < << D P u < @ TDP T < 9 < ~@ ;8 tm8 @ LDLD8 T P LDh.s @ D$@D$LPh.s 8 D$ @D$TPU'L| | ;$1$]_^[SVWU|$(D$4t$,\$0 }*D$4D$4 ؉$Ph1s h;/s - h0s 5 Yh/s ء 5 Y5 5 5 < YY5,s 5 5 5ء YY ) %T %P % ` ` ; ~ d d H$` t4| YY\$ t$t$ YY\$ ttQ YY\$t$t$^ YYL$ \$tt" YY\$ L$\$ u d d ;$U ` С @` ; + @$ DPD1PD$Ph(1s X %p X E p + @$F t$4WQh.s D$Ph hX h h h0s ~:( + $C t$4WQh.s D$Ph X p + @$F t$4WQh.s D$Ph hX h h h0s 9( + $C t$4WQh.s D$Ph hX h h h0s 9( H$ D\ ;$~ߡ tt YY\$ tt YY\$ uС ; ; tq H$ R D PP $2 YY\$tt YY\$ ء L$\$ t ;$~ ; } d d LD ( , ; - E9 tt FYY ȡ h h Q hȡ Q LD ։D d d m ; R tt ȡ %( ȡ ,s YYh.s hP P YY 8 hP h8 sB P YY=ȡ -( P ?% %D %@ D%P 0 ( I$ ( TDh l ( h 8 9 t@ 8 á ( 58 h 58 @ 4 0 x | TDH L @ x H %P 0 H %0 x D@t0 5 h ( ;$@ ( \P 0 \E , ( LD ; @$ S DLPP $N YY\$ tt6 YY\$ء L$ \$t ;$} ; ~ d d LD ( , ; - M9 tt FYY ȡ h h Q hȡ Qܩ LD LD d d m ; m tt ȡ D%( ȡ ,s YYh.s hP P YY 8 hP h8 > P YY=ȡ -( P ?% %D %@ D%P 0 ( H$ ) LD h l ( h 8 ; t@ 8 \ ( 58 h 58 @ 4 0 x | ƋD H L @ x H %P 0 H %0 x \ D@t0 5 h ( ;$@ ( \P 0 \P , ( LD ; =p uN +С @$F С t$4WQh.s D$PhX h h h h0s 0(=p uN +С @$F С t$4WQh.s D$PhX h h h h0s r0( ; H$ ! \D@tD$4 ;$~t$4VWh(1s W1]_^[UESVW 8|$D$d$D$)Eu ](hp/s u`; YY h0/s u L; E$YY1Ƀ8 \ # = uh/s u; YYu t= uh2/s u : YYuPE}?}1AыE9}$эLI}1AE$9}=\ u; uQjjh.s h.s h.s uu h1s h.s ( $ HE$}1Aȉ$$ X tPh1s h;/s 1 =\ $ E uF ?& uEEL TE E HF @& = ED ?Ed ha/s 'Y 0 h1s ' ` 0 5` Y P 5P 8 5T 5P m YY5< 58 T YY}|$VuWuu h0s %( @,s Eu( u( # Eu ( 5 =( u*SuWuuh h.s h h u ,( E @@ E D E$ )@H Fh hH Q @ QVu uWuu (E $$D D|$fD$fL$ l$ $ $fD$ = l$u F SQu uoF}|$ D h hH Q @ QuWuu F @ SQ uWQu uu =( u9uE H 5 \$h.s u D$Ph 8X e_^1[]SVWUD$8 $t$4l$HȉD$ D$ d$ +t$ |$0\$@e h2/s t$06 YY uh0/s t$06 YYuM &} E }1AD$89}E E tPh1s h;/s = Hx D$ t$D$ x A $hp h.s APx Phx x A $x =x ʋD,։lD p D@ AD ?$ h.s t$Hhh h.s Pt$Lt$(hp hx t$P(;(h.s x @D$@Ph.s t$Phx p ,s h.s x @t$Hh.s D$ @Ph hx # x @t$8t$h.s t$Ph.s D$@Ph.s hx t$L Bx x $B$LDx ։DL l=x D$<,D$<L-x D$D t p TD$DL x =x $L TD$<D$<H D$D$x x D$+x D$9L$}L$hp h.s x D$PD$ @x @PD$P$Bx -x DD$ D D$D$ DD$D p рD@ D ?d +x D$h.s D$H x BQhh h.s Pt$Lx @D$x @Php D$4Pt$P8(+x D$h.s D$@x x @Ph.s D$PQD$$P p ,s +x D$h.s D$H x Qh.s D$ @x @Ph D$(Po+x D$t$8x @D$ x x @Ph.s D$PQh.s D$@x @Ph.s D$0Pt$L<?x $ $TDA x TD -x LD$<TD$<L-x D$D t p TD$DLx D$9x S $@ËLƋD$<TD$<L1]_^[SVWUD$88t$4|$D$d$D$P+t$l$<\$@ h2/s t$00 YYD$L1Ƀ8 = u h0/s t$00 YYu D$PND$0} D$P 8}1AD$89} D$P D$L8}= u D$P D$P8 uPjjh.s h.s h.s t$Dt$Dh1s h.s $D$0 D$HD$P t ؉$Ph1s h;/s b = D$0 uD$H@ ?D$H = D$0; ȉ$jjh.s h.s h.s t$Dt$Dh1s h.s $9$~$L$0 9ЉT$ У D$L ; }y|$ $~1@ jjh.s h.s h.s t$Dt$Dh1s h.s Q $; } D$0 D$ = D$0L$ + Iș= )L$ D$ @$ D$ \$ D$0 + @t$ D$D$D$D$ HD$h t$Lt$LSt$Ht$$h D$0Pt$LŃ$ HD$ t$8t$h.s @h t$Xt$LPh.s h D$8Ph/s t$XA 0HD$ ; TLG TL ƋDLD ;D$~D$ |$ }1 ; $1 ; $h t$HSUt$Ht$ h D$0 L$)D$ $ Z D$0 + @D$h t$LD$L PDPG t$HPh D$0Pt$L6$D$0 + + @D$ t$8 A Ph.s h D$XQG t$L Ph.s h D$8Ph/s t$X5? 0HD$ ; TLG TL ƋDLD ;D$~$ <$ }1ɋD$9 1ɋD$9 xD$0 + @$h D$H PDPD)PG t$HPD$Pt$H D$H1]_^[UE,SVWLL$A)M(E4L$ A]0)ËELL$<ȉD$0D$0d$0D$0)EHETȉL$4D$ D$ d$ D$ )EPE\ȉL$@D$8D$8d$8D$8)EX} u$h(1s u* YY $$ $uh2/s u) YY$$ h(1s u ) YY $$ $uhp/s u ) YY$$$ h(1s u) YY d$ D$uh0s ue) YYD$D$ Eh = u'= u h/s u.) YYu Eha = u*=$ u!h/s u ( YYuEh . = u*= u!h/s u( YYuEh Eɉ $}Eh EɉL$}Eh D$,}Eh <$}1B$E,9}Eh |$}1BT$E49} Eh iEL|= t; $} Eh FET|=$ t;L$} Eh "E\|= t;L$,} Eh Eh tPh1s h;/s - = t(uLMHL$4Qh.s h uuh#1s k# = t(uTMPL$ Qh.s h uuh#1s :# = t$u\MXL$<Qh.s h WWh#1s # % 8 & 1Ƀ= D$,D$,Ȣ ' D$DȢ @̢ E %ܢ %آ % % % % Ȣ E;,+Ȣ T$E(Ȣ ЋD آ ܢ E ̢ E;,+̢ T$E(̢ ЋD +Ȣ D$ Ȣ ËD +̢ D$ ̢ ËD = tWE Ȣ E;,+̢ T$E(Ȣ ЋD +̢ D$ Ȣ UE ̢ E;,+Ȣ T$E(̢ ЋD +Ȣ D$ ̢ ËD hX h@ hp hP hh hH h h h h h hآ h E ̢ E4;C+@D$hh hH u,ȋ Ȣ M(Qu, ̢ M(QV$ +AL$ Ȣ hp hP u4P̢ u4PV$E E 9|L$+Ȣ hX h@ h.s D$ @E(Ph.s ̢ D$$@E(PD$0P $+ Ȣ hX h@ h.s D$@Ph.s ̢ D$ @PV# = tQE Ȣ E;&+̢ T$E(Ȣ d E($ +̢ D$ Ȣ OE ̢ E;&+Ȣ T$E(̢ d E($ +Ȣ D$ ̢ d $ = tWE ̢ E;CȢ hh hH h.s D$H@EHPh.s D$P@EHPu" =$ tChp hP h.s Ȣ D$@@EPPh.s ̢ D$H@EPPuy" = tI+Ȣ hX h@ h.s D$L@EXPh.s ̢ D$T@EXPW'" ̢ ̢ ;D$DȢ D$,9Ȣ = %, %( D$DEE +L$L$D;L$}D$$Ȣ +Ȣ @D$Dh.s u`u,E + Ȣ L$ Ȣ M(QD$TP+Ȣ @D$Dh.s JE`Qu4)Ȣ D$Ȣ PD$TP+Ȣ @D$Dh0 h.s AE`Qh.s u`D$XP)( 0 Eu( 0 ( Ȣ $9Ȣ E< ڋE8 u$ $5, 5( ۷ YY1 $Et@u!8 =8 (Eh E 1ɋ#E@D ?E@d EDd EDd A9~؉ Ȣ D$DEE +T$L$D9}D$D$ Ȣ +Ȣ T$E Ȣ E( Љ $L$آ ܢ + Ȣ L$ Ȣ ˋL آ D@ 5آ Т @,s um+Ȣ @D$Du4+Ȣ D$Ȣ Ph /s D$PP[ =$ t'h.s Ȣ D$8@EPPh /s u+ 5Ԣ 5Т E YY\$ Ȣ h` E@PEDPh.s D$0PSE Ȣ E@DED\u`+Ȣ @D$DE E@Ȣ t\$ u,E + Ȣ L$ Ȣ M(QD$(PD$PPb +Ȣ @D$DE EDȢ t\$ u4+Ȣ D$Ȣ PD$(PD$PP 9E Ȣ E@d E@d E Ȣ EDD ?EDd +Ȣ @D$D+u,Ȣ E L$ Ȣ M(Qu4D$Ȣ PD$TPȢ D$ 9Ȣ 4E E @Ȣ $E@d E@d EDD ?EDd B9~؉Ȣ E 9}5@Ȣ !E@d E@d EDd EDd B9~ۉȢ 8 Ede_^1[]SVWU \$0t$,+l$D$d$D$4+t$|$( h2/s t$$ YY h/s t$( Y = Yu h0/s t$$o YYu D$4Q= u h2/s t$(I YYu D$4 (} D$4 }1@9} D$4 D$4 t ؉$Ph1s h;/s | = $|$ = t E 4 % HD$ h/s @PSWD$Pt$8h/s h0s 9E HD$ h/s @Ph D$P ;$K = t E 4 % 9 + $E h/s @P @S @PD$Pt$8h/s h0s OD + $E h/s @Ph D$ P = %1 ]_^[SVWU,l$PE D$ t$LD$$D$$d$$+t$$\$T|$H# h2/s t$D YY h/s t$H Y = Yuh0/s t$D YYu F= u h2/s t$H YYu!}}1A9M }t ؉D$ Ph1s h;/s = t4D$ D$ @ D@ ;L$ ~ۃ# D$@$D$DD$D$ D$ jh/s D$PD$ PD$P jjh/s h/s h/s WD$"Ph1s h /s $ ~ 9 | SUD$,PWt$Tt$Tu = U D$ D$D$$t$D$ D$(+ @9D$(}D$( HD$(U D$ @PUt$$h/s h D$@Pt$`h/s h0s h}/s 5, HD$(U D$ @PUD$(@ Ph /s h D$@Pt$`h/s h0s h/s J,SUD$$@ Ph t$Th0s LD$ |$ }1 ;L$ 1 ;L$ Hș= A D$$\$$ 4 D$ + @D$(D$ ;D$(}L$( ȋ9 + )BT$ UT$ B RUT$( Rh/s h D$8Pt$`h/s h0s h}/s w3,+ + @D$ D$ @ U QUPh /s h D$8Pt$`h/s h0s h/s dH,SUD$$@ Ph t$Th0s D$$ |$$ }1= 1= 1,]_^[SL$T$ 2\$ u EA 2 D@j 5 E D@' 5 u EA u EA ; u1@ 5 Ĥ Ȥ ̤ Ф %Ԥ D@tBĤ Ĥ D@t,Ȥ Ȥ D@t̤ ̤ D@u11[SVW|$H L$$t$(\$0w$8\ t$4jt$$h a Z |UzP a |z = ~ 1ɢ A<St<Dt1ɉ 1 A<Ct<Zt1Ʌɉ u = jjh h jjh h jjh h to jjh1s h ( jjh1s h jjh1s h ( jjh1s h jjh1s h jjh1s h u jjh1s h s jjh2s h U jjh 2s h 2 ujjh1s jjh2s h uTjjh1s h = t jjh2s h = _= tdjjh2s h uJjjh1s h y 2 jjh2s h [ jjh2s = jjh 2s h " <G jjh 2s h 1 jjh"2s h jjh%2s h jjh(2s h jjh+2s h } jjh.2s h _ jjh12s h A M x <M@ jjh 2s h R jjh"2s h 4 jjh%2s h jjh(2s h jjh+2s h jjh.2s h jjh12s h b n = jjh42s h 2 <G jjh 2s h A jjh"2s h # jjh%2s h jjh(2s h jjh+2s h jjh.2s h o jjh12s h Q ] <MP jjh 2s h & b jjh"2s h D jjh%2s h & jjh(2s h jjh+2s h jjh.2s h jjh12s h r ~ jjh72s h O u;jjh1s h 5 A = t ;@c$ ;@Y jjh:2s h uIjjh1s h = t >@ >@ jjh.2s h u jjh2s h } 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Q ? ??? Q ?{Gz?{Gz?{Gz33333sU@ @`@P\s{RAAT} %%doing phonetics by computer version 4.4 www.praat.org Copyright \co 1992-2005 by Paul Boersma and David Weenink PostScript phonetic font: \co 2005 Fukui Rei & Rafael Laboissi\e`re GNU Scientific Library: \co 1996-2001 Gerard Jungman & Brian Gough Praat Articulatory synthesis Create a default Articulation articulation Name Edit Art 0.0 Cannot edit an Art from batch. Create Artword... Create an empty Artword hallo 1.0 Duration (seconds) Duration Draw one Artword tier Muscle Garnish Cannot edit an Artword from batch. Get one Artword target Time (seconds) Time %.16g Artword Set one Artword target Target value (0-1) 'Time' must not be less than 0. Target value From Artword to Art Draw Artword & Speaker 5 Number of steps Artword & Speaker: To Sound... Articulatory synthesizer 22050 Sampling frequency (Hz) 25 Oversampling factor 0 Width 1 Width 2 Width 3 Pressure 1 Pressure 2 Pressure 3 Velocity 1 Velocity 2 Velocity 3 Sampling frequency width%d pressure%d velocity%d Artword & Speaker movie Create Speaker... Create a Speaker speaker Kind of speaker Female Male Child Number of tubes in glottis 1 2 10 Speaker Create Vocal Tract from phone... Create Vocal Tract from phone Phone a e i o u y1 y2 y3 jery p t k x pa ta ka pi ti ki pu tu ku Matrix: Formula... VocalTract Formula `x' is the distance form the glottis in metres, `col' is the section number, `self' is in m^2 label x := x1; for col := 1 to ncol do { self [col] := `formula' ; x := x + dx } formula VocalTract From Vocal Tract to Spectrum Compute transfer function 4097 Number of frequencies 5000 Maximum frequency (Hz) 0.1 Glottal damping Radiation damping Internal damping Maximum frequency New Objects Articulatory synthesis tutorial -- new articulatory synthesis -- Create Articulation... -- new vocal tract -- Edit Artword help Info Get target... Draw Draw... Modify Set target... Analyse To Art (slice)... Fill inner contour Draw mesh Synthesize To VocalTract Movie To Sound... Speaker help VocalTract help To Spectrum... Formula... Hack To Matrix \ \ \ J\ \ \ \ \ \ \ \ \ \ \ \ >\ \ \ \ I\ \ \ I\ S\ n\ \ \ N\ p\ \ \ T\ \ \ \ \ y\ \ L\ Y\ \ \ \ $\ 6\ c\ \ \ \ \ !\ c\ \ \ \ E\ \ \ \ I\ 6\ <\ \ I\ 6\ -\ \ \ \ \ \ \ &\ \ \ >\ \ \ I\ \ I\ \ \ This is a description of the articulatory synthesis package in P\s{RAAT}. For a detailed description of the physics and mathematics behind the model, see @@Boersma (1998)@, chapters 2 and 3. For examples of how to synthesize utterances, consult http://www.fon.hum.uva.nl/paul/diss/ch5/. How to start (after reading the @Intro) We are going to have the synthesizer say [apa]. We need a @Speaker and an @Artword object. 1. Create a speaker with @@Create Speaker...@ from the @@New menu@. 2. Create an articulation word of 0.5 seconds with @@Create Artword...@. 3. Edit the Artword by selecting it and clicking #Edit. 4. To set the glottis to a position suitable for phonation, use the ArtwordEditor to set the %Interarytenoid activity to 0.5 throughout the utterance. You set two targets: 0.5 at a time of 0 seconds, and 0.5 at a time of 0.5 seconds. 5. To prevent air escaping from the nose, close the nasopharyngeal port by setting the %LevatorPalatini activity to 1.0 throughout the utterance. 6. To generate the lung pressure needed for phonation, you set the %Lungs activity at 0 seconds to 0.2, and at 0.1 seconds to 0. 7. To force a jaw movement that closes the lips, set the %Masseter activity at 0.25 seconds to 0.7, and the %OrbicularisOris activity at 0.25 seconds to 0.2. 8. Select the Speaker and the Artword and click #Movie; you will see a closing-and-opening gesture of the mouth. 9. Select the Speaker and the Artword and click ##To Sound...# (see @@Artword & Speaker: To Sound...@). 10. Just click %OK; the synthesis starts. 11. If you are sitting at a 1997 computer, this will last for 5 minutes or so. If this is too slow for you, click %Interrupt. Otherwise, you can watch the vibrating vocal cords and the changing vocal-tract shape. 12. You can play, view, and analyse the resulting @Sound as you would any other. You can see and hear a sound movie if you select the Speaker, the Artword, and the Sound, and click #Play. One of the @@types of objects@ in P\s{RAAT}. See @@Articulatory synthesis@. An object of class Artword object represents the activities of several speech muscles as functions of time. Artword commands \bu @@Create Artword...@: creates an Artword with relaxed muscles \bu @@Artword & Speaker: To Sound...@: articulatory synthesis A command to synthesize a @Sound object from the selected @Speaker and the selected @Artword. This is the command that performs the actual articulatory synthesis. See @@Articulatory synthesis@. Arguments %%Sampling frequency% (Hz) the number of times per second that the equilibrium widths and lengths and the tensions of the muscles are recomputed from the Artword. This will also be the sampling frequency of the resulting sound and of the optional resulting tube widths, air pressures, and air velocities. The standard value is 22050 Hz. %Oversampling the number of times that the aerodynamic quantities and the state of the tube walls will be recomputed during each sample period. The standard value is 25. %%Width 1%, %%Width 2%, %%Width 3 the numbers (see below) of the tubes whose widths you want to monitor. E.g., if %%Width 1% is 36, the synthesizer will create a Sound object named "width36", which contains the width of tube 36 (the lower glottis) as a function of time, expressed in metres. To prevent the creation of a "width" object, specify "0" (the standard value). %%Pressure 1%, %%Pressure 2%, %%Pressure 3 the numbers (see below) of the tubes whose air pressures you want to monitor. E.g., if %%Pressure 3% is 37, the synthesizer will create a Sound object named "pressure37", which contains the air pressure of tube 37 (the upper glottis) as a function of time, expressed in Pascal. To prevent the creation of a "pressure" object, specify "0" (the standard value). %%Velocity 1%, %%Velocity 2%, %%Velocity 3 the numbers (see below) of the tubes whose air velocities you want to monitor. E.g., if %%Velocity 1% is 60, the synthesizer will create a Sound object named "velocity60", which contains the air velocity of tube 60 (in the mouth) as a function of time, expressed in metres per second. To prevent the creation of a "velocity" object, specify "0" (the standard value). Stability The internal sampling frequency for the aerodynamics is the specified %%sampling rate%, multiplied by the specified %oversampling. With the standard settings, this is 22050 times 25 = 550750 Hz. To ensure the stability of the synthesis, this internal sampling frequency should not be less than the velocity of sound (353 m/s) divided by the length of the shortest tube. For the standard "Female", "Male", and "Child" speakers, the shortest tube is the upper glottis, which has a length of 0.7, 1.0, and 0.3 millimetres, respectively. The minimum internal sampling frequencies, therefore, are 504286, 353000, and 1176667 Hertz, respectively. Time resolution To capture the microscopic pressure changes in the glottis, you will want maximum time resolution. For a female speaker, you could set %%sampling frequency% to 550750 Hz, and %oversampling to 1. Tube numbers Here are the tube numbers that you can use for the %width, %pressure, and %velocity arguments: 1..23: lungs (from bottom to top) 24..29: bronchi (from bottom to top) 30..35: trachea (from bottom to top) 36: lower glottis 37: upper glottis (not for a one-mass model) 38..49: pharynx (from bottom to top) 50..51: nasopharyngeal branching 52..64: mouth (from back to front) 65..78: nose (from back to front) 79..86: conus elasticus (only for a 10-mass model) 87..89: glottal shunt between the arytenoids (from bottom to top) Some structural properties: \bu Tube 1 is closed at the bottom. \bu Tubes 64 (lips) and 78 (nostrils) radiate into the air. \bu The nasopharyngeal branch is at tubes 50, 51, and 65. They are constrained to have equal lengths. \bu For a one-mass model of the vocal cords, tube 36 is connected to 38. \bu For a 10-mass model, tubes 32..35 are replaced with 79..86, so that tube 31 is connected to 79, and 86 is connected to 36. \bu A glottal shunt will be implemented if the speaker's "shunt.Dx" attribute is not zero. A branch is then made from tubes 34 and 35 (or 85 and 86) to 87, and from tube 89 to 38 and 39. A command to create an @Artword object with all muscle activities set to zero. See @@Articulatory synthesis@. %Name the name that you give to the created object. The standard name is "speaker", but if you work with multiple Speaker objects, give them sensible names to reduce confusion. A command to create a @Speaker object. See @@Articulatory synthesis@. the name that you give to the created object. The standard name is "artword", but you should give it a more sensible name, possibly something that represents the utterance that it is supposed to generate. %Duration (seconds) the duration of the resulting Artword. Should be as long as the utterance that you want to generate with it. The standard value is 1 second. A way to create a @VocalTract object. Purpose to translate a phone symbol like [a], [u], etc., into a vocal-tract area function. Behaviour The resulting VocalTract will appear in the list of objects, with the same name as the phone. Algorithm The area function of the resulting VocalTract is taken from the Russian speaker from @@Fant (1960)@. Speaker commands \bu @@Create Speaker... One of the @@types of objects@ in P\s{RAAT}. A VocalTract object represents the area function of the vocal tract, expressed in m^2, running from the glottis to the lips. A command for changing the data in all selected @VocalTract objects. See the @Formulas tutorial for examples and explanations. Articulatory synthesis ppgb Artword Artword & Speaker: To Sound... Create Artword... Create Speaker... Create Vocal Tract from phone... Speaker VocalTract VocalTract: Formula... \ \ \ \ \ \ \ \ ] ] # ] / ] ? ] P ] b ] s ] } ] ] ] ] ] ] ] ] ] ] ] ] ] %] 6] R] R] j V] \ |/@ R] lj \ Art_MUSCLE _ Lungs Interarytenoid Cricothyroid Vocalis Thyroarytenoid PosteriorCricoarytenoid LateralCricoarytenoid Stylohyoid Sternohyoid Thyropharyngeus LowerConstrictor MiddleConstrictor UpperConstrictor Sphincter Hyoglossus Styloglossus Genioglossus UpperTongue LowerTongue TransverseTongue VerticalTongue Risorius OrbicularisOris LevatorPalatini TensorPalatini Masseter Mylohyoid LateralPterygoid Buccinator art []: art [%s] Art art x] ] ] ] ] ] ] j ] ] ] \] \ 4@ ] lj ] ? numberOfTargets targets times totalTime data []: data [%s]: Trying to read "%s". my numberOfTargets Artword data ArtwordData Artword.c insert <= f -> numberOfTargets iTarget > 0 && iTarget < f -> numberOfTargets iTarget >= 1 iTarget <= f -> numberOfTargets Time (s) ? @@ j] 'j D ] %8g %8g %8g %8g %f Targets: Times: Values: listWindow list Remove target drawingArea Time: Time Value: Value Add target radioBox ArtwordEditor ? h㈵> @ ? @ l@ lA= ףp=@ h㈵> @ @@ v@v/@ ???Tqs*ɾ??MbP?Gz2WA#q>= ףp=? @|=fYA-?333333? }?{Gz? $@= ףp=? $= ףp=?Articulatory synthesis Starting volume: %.10g litres. Articulatory synthesis: %.4g seconds Artword_Speaker_to_Sound.c l2 != NULL Ending volume: %.10g litres. MbP? 4@ ? , J 4 @ : 0 6 D A @ R J@?333333?333333 @T@ $@ffffffA@= ףp=?Gz?Mbp?{Gz?{Gzt?{Gz? Q???? f@-DT! @ ?-DT!@?333333?333333?ffffff?-DT!? @ ? ? ? @ O MbP? ^@ ? @ $@ @ 4@ ? ? ? T@ D@ 9@ 2@ SAyqE->MbP? ?@ t ] n P ] Delta Delta.c numberOfTubes >= 1 ] ] ] ] ] ] ] ] !] #] %] '] ] !] #] %] .] 2] 6] 9] %] !] #] ;] 6] ] ] ] 0] 3] 3] j S] ;] @] ] W] a] ] t] 8 a] ] ~] P ] ] ] h ] | ] ] ] , ] ] ] ] ] ] ] ] ] ] ] ] ] <] )] 4] ] G] P] D] \] P] D] e] j] ] @ 3] lj ] X9vZd;O? rh?jt?~jt??W[?;OnMbpI +!rh?;On?9v?{Gz?Mbp?y&1|?y&1?;On?Mb?{Gz?Q ? Q?I +?~jt?9v?numberOfMasses length thickness mass k1 Dx Dy Dz x y a radius dx1 dx2 dy r dx weq []: %s weq [%d] relativeSize cord: lowerCord: upperCord: shunt: velum: palate: tip: neutralBodyDistance alveoli: teethCavity: lowerTeeth: upperTeeth: lowerLip: upperLip: nose: Trying to read "%s". weq Trying to read element %ld of "%s". 14 Speaker cord Speaker_CordDimensions lowerCord Speaker_CordSpring upperCord shunt Speaker_GlottalShunt velum Speaker_Velum palate Speaker_Palate tip Speaker_Tip alveoli Speaker_Alveoli teethCavity Speaker_TeethCavity lowerTeeth Speaker_LowerTeeth upperTeeth Speaker_UpperTeeth lowerLip Speaker_Lip upperLip nose Speaker_Nose Male Child Female ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ @ ^@ n@ t@ ^@ n@ d@ ^@ a@ T@ Q@ Q@ D@ A@ A@ 4@ 2@ 2@ $@ (@ (@ @ (@ (@ @ 2@ "@ @ 2@ 3@ @ MbP? $@ Y@ l@ .@ >@ 0@ @ &@ ,@ j@ @ .A 4@ @ @ @ @ ? @ ? ? (@ ^@ T@ D@ SAyqE->Speaker_to_Delta.c my cord.numberOfMasses == 1 || my cord.numberOfMasses == 2 || my cord.numberOfMasses == 10 ! t->left1 || t->left1->right1 == t || t->left1->right2 == t ! t->left2 || t->left2->right1 == t ! t->right1 || t->right1->left1 == t || t->right1->left2 == t ! t->right2 || t->right2->left1 == t 4 ] L ] d ] | ] Query - Draw - Modify - Extract - 4 Number of inputs 3 Number of outputs 0 Number of units in hidden layer 1 Number of units in hidden layer 2 The number of units in a hidden layer must be greater than or equal to 0. Create FFNet... Create FFNet 4-3 Name There was not enough memory to create the FFNet. Please reduce some of the numbers. Create FFNet (linear outputs)... 4-3L Create iris example... Create iris example For the feedforward neural net we need to know the: %d units FFNet: Get number of hidden units... FFNet: Get number of hidden units 1 Hidden layer number FFNet: Get number of hidden weights... FFNet: Get number of hidden weights %d weights (inclusive biases) %d weights Create Pattern 1x1 Dimension of a pattern Number of patterns Create Categories empty Feedforward neural networks %s FFNet: Reset... FFNet: Reset Warning: this command destroys all previous learning. New weights will be randomly chosen from the interval [-range, +range]. 0.1 Range FFNet: Select biases... FFNet: Select biases WARNING: This command induces very specific behaviour during a following learning phase. Layer number FFNet: Draw weights to layer Warning: Disapproved. Use "Draw weights.." instead. Scale by maximum of all weights to layer by maximum weight from 'from-unit' by maximum weight to 'to-unit' Garnish FFNet: Draw weights... FFNet: Draw weights FFNet: Draw cost history... FFNet: Draw cost history left Iteration_range right Iteration_range 0.0 left Cost_range right Cost_range FFNet: Extract weights... FFNet: Extract weights FFNet: Weights to Matrix Warning: Use "Extract weights.." instead. FFNet & Activation: To Categories Kind of labeling Winner-takes-all Stochastic FFnet & Eigen: Draw intersection X-component 2 Y-component xmin xmax ymin ymax X and Y component must differ from 0. FFNet & PCA: Draw decision plane Unit number Horizontal eigenvector number Vertical eigenvector number left Horizontal range right Horizontal range left Vertical range right Vertical range Replace weights by values from Matrix Layer Draw an activation Pattern (row) number Pattern To activations in layer You can use the FFNet as a classifier by selecting a FFNet and a Pattern together and choosing "To Categories...". You can teach a FFNet to classify by selecting a FFNet, a Pattern and a Categories together and choosing "Learn...". FFNet & Pattern: To Categories... FFNet & Pattern: To Categories Determine output category as FFNet & Pattern & Activation: Get total costs... FFNet & Pattern & Activation: Get total costs Cost function Minimum-squared-error Minimum-cross-entropy FFNet & Pattern & Activation: Get average costs... FFNet & Pattern & Activation: Get average costs FFNet & Pattern & Activation: Learn slow 100 Maximum number of epochs 1e-7 Tolerance of minimizer Specific for this minimization Specifics Learning rate 0.9 Momentum FFNet & Pattern & Activation: Learn FFNet & Pattern & Categories: Get total costs... FFNet & Pattern & Categories: Get total costs FFNet & Pattern & Categories: Get average costs... FFNet & Pattern & Categories: Get average costs Pattern & Categories: To FFNet... Pattern & Categories: To FFNet There is not enough memory to create %d output categories. Please try again with less categories. There are not enough categories in the Categories. Please try again with more categories in the Categories. Please try again with less hidden nodes in the hidden layer(s). FFNet & Pattern & Categories: Learn... FFNet & Pattern & Categories: Learn FFNet & Pattern & Categories: Learn slow... FFNet & Pattern & Categories: Learn slow Neural nets New Objects -- FFNet -- Advanced Create Pattern... Create Categories... FFNet help Draw topology Draw weights... Draw weights to layer... Draw cost history... Query structure Get number of outputs Get number of hidden units... Get number of inputs -- FFNet weights -- Get number of hidden weights... Get number of output weights Get minimum Reset... Select biases... Select all weights Extract weights... Weights to Matrix... & Pattern: Classify? & Pattern & Categories: Learn? Analyse To Categories... Draw Draw hyperplane intersections To Activation Modify Weights from Matrix... Draw activation... To Activation... Draw decision plane... To FFNet... Get total costs... Get average costs... Learn Learn... Learn slow... ?] P@] @] A] A] EB] B] B] ,C] C] C] E] F] @ @@ G] ;I] yI] I] J] K] #K] P] )Q] tR] R] S] S] T] U] U] qW] W] X] [] [] ^] '^] a] b] Bb] b] "d] d] e] e] ;f] Jf] Tf] }f] f] f] f] f] g] 8g] Ag] ]g] {g] g] g] g] h] Ph] h] h] h] h] h] i] "i] Oi] 0j] pj] zj] j] k] k] !k] 7k] @k] pj] tk] 0j] k] l] l] m] .m] 7k] Xm] pj] m] m] k] k] !k] pj] Jn] n] gp] p] p] q] q] q] q] r] )r] s] q] q] q] 0j] Is] Qs] k] ~s] s] pj] s] t] q] k] t] pj] *u] v] k] :v] Nv] |v] v] v] $w] x] k] :v] Nv] |v] v] v] $w] Px] k] v] $w] Wy] y] z] X{] {] {] |] ^|] 1}] }] ~] k] v] $w] ~] {] X] ] ] {] ] ] ] k] ۀ] ] [] u] ] ] '] s] ] Ƃ] ݂] I] S] ] I] F] ] I] F] ] I] T] ] I] T] V] Ć] 5] A term that is often used in the context of machine learning. An epoch is one complete presentation of the %%data set to be learned% to a learning machine. Learning machines like @@FFNet|feedforward neural nets@ that use iterative algorithms often need many epochs during their learning phase. A @@Discriminant|discriminant classifier@ is also a learning machine. However, in contrast with neural nets a discriminant classifier only needs one epoch to learn. This tutorial describes the use of @FFNet feedforward neural networks in P\s{RAAT}. @@Feedforward neural networks 1. What is a feedforward neural network?|1. What is a feedforward neural network?@ @@Feedforward neural networks 1.1. The learning phase|1.1 The learning phase @@Feedforward neural networks 1.2. The classification phase|1.2 The classification phase @@Feedforward neural networks 2. Quick start|2. Quick start@ @@Feedforward neural networks 3. FFNet versus discriminant classifier|3. FFNet versus discriminant classifier@ @@Feedforward neural networks 4. Command overview|4. Command overview@ A feedforward neural network is a biologically inspired classification algorithm. It consist of a (possibly large) number of simple neuron-like processing %units, organized in %layers. Every unit in a layer is connected with all the units in the previous layer. These connections are not all equal, each connection may have a different strength or %weight. The weights on these connections encode the knowledge of a network. Often the units in a neural network are also called %nodes. Data enters at the inputs and passes through the network, layer by layer, until it arrives at the outputs. During normal operation, that is when it acts as a classifier, there is no feedback between layers. This is why they are called %%feedforward% neural networks. In the following figure we see an example of a 2-layered network with, from top to bottom: an output layer with 5 units, a %hidden layer with 4 units, respectively. The network has 3 input units. The 3 inputs are shown as circles and these do not belong to any layer of the network (although the inputs sometimes are considered as a virtual layer with layer number 0). Any layer that is not an output layer is a %hidden layer. This network therefore has 1 hidden layer and 1 output layer. The figure also shows all the connections between the units in different layers. A layer only connects to the previous layer. The operation of this network can be divided into two phases: @@Feedforward neural networks 1.1. The learning phase|1. The learning phase @@Feedforward neural networks 1.2. The classification phase|2. The classification phase During the learning phase the weights in the FFNet will be modified. All weights are modified in such a way that when a pattern is presented, the output unit with the correct category, hopefully, will have the largest output value. How does learning take place? The FFNet uses a %supervised learning algorithm: besides the input pattern, the neural net also needs to know to what category the pattern belongs. Learning proceeds as follows: a pattern is presented at the inputs. The pattern will be transformed in its passage through the layers of the network until it reaches the output layer. The units in the output layer all belong to a different category. The outputs of the network as they are now are compared with the outputs as they ideally would have been if this pattern were correctly classified: in the latter case the unit with the correct category would have had the largest output value and the output values of the other output units would have been very small. On the basis of this comparison all the connection weights are modified a little bit to guarantee that, the next time this same pattern is presented at the inputs, the value of the output unit that corresponds with the correct category is a little bit higher than it is now and that, at the same time, the output values of all the other incorrect outputs are a little bit lower than they are now. (The differences between the actual outputs and the idealized outputs are propagated back from the top layer to lower layers to be used at these layers to modify connection weights. This is why the term %%backpropagation network% is also often used to describe this type of neural network. If you perform the procedure above once for every pattern and category pair in your data set you have have performed 1 @epoch of learning. The hope is that eventually, probably after many epochs, the neural net will remember these pattern-category pairs. You even hope that the neural net when the learning phase has terminated, will be able to %generalize and has learned to @@FFNet & Pattern: To Categories...|classify@ correctly any unknown pattern presented to it. Because real-life data many times contains noise as well as partly contradictory information these hopes can only be partly fulfilled. For @@FFNet & Pattern & Categories: Learn...|learning@ you need to select 3 different objects together: a FFNet (the %classifier), a Pattern (the %inputs) and a Categories (the %%correct outputs%). How long will the learning phase take? In general this question is hard to answer. It depends on the size of the neural network, the number of patterns to be learned, the number of epochs, the tolerance of the minimizer and the speed of your computer, how much computing time the learning phase may take. If computing time becomes excessive in your interactive environment then consider using the powerful @@Scripting|scripting@ facilities in P\s{RAAT} to process your learning job as a batch job. In the classification phase the weights of the network are fixed. A pattern, presented at the inputs, will be transformed from layer to layer until it reaches the output layer. Now classification can occur by selecting the category associated with the output unit that has the largest output value. For classification we only need to select an FFNet and a Pattern together and choose @@FFNet & Pattern: To Categories...|To Categories...@. In contrast to the @@Feedforward neural networks 1.1. The learning phase|learning phase@ classification is very fast. You may create the iris example set with the @@Create iris example...@ command that you will find under the ##Neural nets# option in the #New menu. Three new objects will appear in the @@List of Objects@: a @FFNet, a @Categories and a @Pattern. The #Pattern contains the @@iris data set@ in a 150 rows by 4 columns matrix. To guarantee that every cell in the Pattern is in the [0,1] interval, all measurement values were divided by 10. In the #Categories the three iris species %setosa, %versicolor, and %virginica were categorized with the numbers #1, #2 and #3, respectively. Because there are 4 data columns in the Pattern and 3 different iris species in the Categories, the newly created #FFNet has 4 inputs and 3 outputs. If you have entered a positive number in one of the fields in the form, the FFNet will have this number of units in a %%hidden layer%. The name of the newly created FFNet will reflect its topology. If you did opt for the default, 0 hidden units, the FFNet will be named 4-3. Learning the iris data The first thing you probably might want to do is to let the #FFNet learn the association in each pattern-category pair. To do this select all three objects together and choose @@FFNet & Pattern & Categories: Learn...|Learn...@. A form will appear, asking you to supply some settings for the learning algorithm. Learning starts after you have clicked the OK-button. Since the example network does not have too many weights that need to be adjusted and the learning data set is very small and computers nowadays are very fast, this will only take a very short time. Classify Now, if you are curious how well the FFNet has learned the iris data, you may select the #FFNet and the #Pattern together and choose @@FFNet & Pattern: To Categories...|To Categories...@. A new #Categories appears in the ##List of Objects# with the name %4-3_iris (if %%4-3% was the name of the FFNet and %iris% the name of the Pattern). We have two different Categories in the list of objects, the topmost one has the original categories, the other the categories as were assigned by the FFNet classifier. The obvious thing to do now is to compare the original categories with the assigned categories by making a @@Confusion|confusion table@. Select the two #Categories and choose @@Categories: To Confusion|To Confusion@ and a newly created @Confusion appears. Pressing the @Info button will show you an info window with, among others, the fraction correct. You might also want to @@Feedforward neural networks 3. FFNet versus discriminant classifier|compare the FFNet classifier with a discriminant classifier@. Create other neural net topologies With a #Pattern and a #Categories selected together, you can for example create a new #FFNet of a different topology. You might want to compare the FFNet classifier with a discriminant classifier. Unlike the FFNet, a @@Discriminant|discriminant@ classifier does not need any iterative procedure in the learning phase and can be used immediately after creation for classification. The following three simple steps will give you the confusion matrix based on discriminant analysis: 1. Select the Pattern and the Categories together and choose ##To Discriminant#. A newly created Discriminant will appear. 2. Select the Discriminant and the Pattern together and choose ##To Categories...#. A newly created @Categories will appear. 3. Select the two appropriate Categories and choose @@categories: To Confusion|To Confusion@. A newly created @Confusion will appear. After pushing the @Info button, the info window will show you the fraction correct. See also the @@Discriminant analysis@ tutorial for more information. FFNet commands Creation: \bu @@Pattern & Categories: To FFNet...@ \bu @@Create FFNet...@ Learning: \bu @@FFNet & Pattern & Categories: Learn...@ \bu @@FFNet & Pattern & Categories: Learn slow...@ Classification: \bu @@FFNet & Pattern: To Categories...@ Drawing: \bu @@FFNet: Draw topology@ \bu @@FFNet: Draw weights...@ \bu @@FFNet: Draw cost history...@ Queries \bu @@FFNet & Pattern & Categories: Get total costs...@ \bu @@FFNet & Pattern & Categories: Get average costs...@ \bu @@FFNet & Pattern & Activation: Get total costs...@ \bu @@FFNet & Pattern & Activation: Get average costs...@ Analysis: \bu ##FFNet & Pattern: To Activation...# Modification: \bu @@FFNet: Reset...@ \bu ##FFNet: Select biases...# \bu ##FFNet: Select all weights# One of the @@types of objects@ in P\s{RAAT}. A #FFNet models a feedforward neural net. A feedforward neural net can %learn associations between its %input and its %output. The @@Feedforward neural networks@ tutorial gives you an introduction to feedforward neural nets. You can choose this command after selecting 1 or more @FFNet's. Behaviour Draws all units and all connections of a feedforward neural net. Draws the weights in a layer of the selected @FFNet feedforward neural net. Arguments %%Layer number% determines the layer. %Garnish determines whether additional information is drawn. The weights are arranged in a matrix. The columns of this matrix are indexed by the units in the layer, while the rows are indexed by the units in the previous layer. There is one extra row for the biases.The values of the weights are shown as rectangles. The area of a rectangle is proportional to the value. Negative values are shown as filled black rectangles. %%Iteration range% determine the horizontal range of the plot. %%Cost range% determine the vertical range of the plot. determines whether a box and axis labels are drawn. Draws the history of the cost versus iteration number during previous learning. Extract all the weights, from all the units in the specified layer of the selected @FFNet, to a @TableOfReal. The weights will be arranged in the TableOfReal as follows: The table columns will be indexed by the unit numbers in the selected layer, while the rows will be indexed by the unit numbers from the previous layer. There will be one extra row to accommodate the bias weights. The rows and columns are labelled with layer number and unit number as "L%i-%j", where %i is the layer number and %j the unit number from that layer. The layer number for the rows is one less than the layer number in the columns. The last row is labelled as "Bias". Queries the selected @FFNet for the number of output units in the output layer. Queries the selected @FFNet for the number of inputs. For a network with only one layer, the inputs are connected directly to the output layer. In a two-layer network the inputs are connected to a hidden layer. Queries the selected @FFNet for the number of units in a hidden layer. Argument %%Hidden layer number% determines the layer that is queried. Layer numbering The number of hidden layers is always one less than the total number of layers in a FFNet. A network with the output units connected to the inputs therefore has only 1 layer, the output layer and no hidden layers. Queries the selected @FFNet for the number of weights in a hidden layer. WARNING This command destroys all previous learning. %%Range determines the upper limit of the [-%range, +%range] interval from which new weights will be randomly selected. All (selected) weights are reset to random numbers uniformly drawn from the interval [-%range, +%range]. This command also clears the cost history. Selects only the biases in one particular layer as subject for modification during learning of the @FFNet. determines the layer whose biases will be modified. This command induces very specific behaviour during a following learning phase. Instead of all the weights, only the biases in the specified layer will be changed during learning and the rest of the weights stay fixed. Create a new feedforward neural net of type @FFNet. %%Number of inputs% the dimension of the input of the neural net. %%Number of outputs (\>_ 1)% the number of different categories that you want the net to learn. %%Number of units in hidden layer 1, Number of units in hidden layer 2% determine the number of units in the hidden layers. If you want a neural net with no hidden layers, both numbers have to be 0. If you want a neural net with only 1 hidden layer then one of these numbers has to differ from 0. Create a @FFNet feedforward neural network whose output units are linear. A @FFNet feedforward neural net will be created together with two other objects: a @Pattern and a @Categories. The Pattern will contain the observations in the @@iris data set@, and the Categories will contain the 3 different iris species categorized by numbers. For this simple data you can leave both hidden layers empty. A data set with 150 random samples of flowers from the iris species %setosa, %versicolor, and %virginica collected by @@Anderson (1935)@. From each species there are 50 observations for sepal length, sepal width, petal length, and petal width in cm. This dataset was used by @@Fisher (1936)@ in his initiation of the linear-discriminant-function technique. A @Pattern is a @Matrix in which each row forms one input pattern (vector) for the neural net. The number of columns is the dimensionality of the input. The number of rows is the number of patterns. The categories for training a neural net with a @Pattern. Preconditions The number of categories in a @Categories must equal the number of rows in #Pattern. A @Matrix whose elements must be >= 0 and <= 1. Classification: the response of a particular layer in a neural net to a @Pattern.Learning: the desired response of the output layer in a neural net to a @Pattern. When you select @FFNet and @Eigen the decision planes of layer 1 are drawn in the PC-plane. The @FFNet is used as a classifier. Each pattern from the @Pattern will be classified into one of the FFNet's categories. Create a new @FFNet feedforward neural network. The number of inputs of the newly created FFNet will be equal to the number of columns in the @Pattern and the number of outputs will be equal to the number of unique categories in the @Categories. To learn an association you have to select a @FFNet, a @Pattern and a @Categories object. The number of columns in a #Pattern must equal the number of input units of #FFNet. Algorithm Steepest descent The number of rows in a #Pattern must equal the number of categories in a #Categories. The number of unique categories in a #Categories must equal the number of output units in #FFNet. You can choose this command after selecting one @Pattern, one @Categories and one @FFNet. %%Maximum number of epochs% the maximum number of times that the complete #Pattern dataset will be presented to the neural net. %%Tolerance of minimizer% when the difference in costs between two successive learning cycles is smaller than this value, the minimization process will be stopped. %%Cost function% Minimum-squared-error: %costs = \su__%allPatterns_ \su__%allOutputs_ (%o__%k_ - d__%k_)^2, where %o__%k_ : actual output of unit %k %d__%k_ : desired output of unit %k Minimum-cross-entropy: %costs = - \su__%allPatterns_ \su__%allOutputs_ (%d__%k_ \.c ln %o__%k_ + (1-%d__%k_) \.c ln (1-%o__%k_)) Algorithm The minimization procedure is a variant of conjugate gradient minimization, see for example @@Press et al. (1992)@, chapter 10, or @@Nocedal & Wright (1999)@, chapter 5. Query the selected @FFNet, @Pattern and @Categories for the total costs. All patterns are propagated and the total costs are calculated as is shown in @@FFNet & Pattern & Categories: Learn...@. Query the selected @FFNet, @Pattern and @Activation for the total costs. Query the selected @FFNet, @Pattern and @Categories for the average costs. All patterns are propagated and the total costs are calculated as is shown in @@FFNet & Pattern & Categories: Learn...@. These total costs are then divided by the number of patterns. Query the selected @FFNet, @Pattern and @Activation for the average costs. E. Anderson (1935), "The irises of the Gasp\e' peninsula", %%Bulletin of the American Iris Society% #59, 2-5. R.A. Fisher (1936), "The use of multiple measurements in taxonomic problems", %%Annals of Eugenics% #7, 179-188. J. Nocedal & S.J. Wright, %%Numerical optimization%, Springer, 1999. epoch djmw Feedforward neural networks Feedforward neural networks 1. What is a feedforward neural network? Feedforward neural networks 1.1. The learning phase Feedforward neural networks 1.2. The classification phase Feedforward neural networks 2. Quick start Feedforward neural networks 3. FFNet versus discriminant classifier Feedforward neural networks 4. Command overview FFNet FFNet: Draw topology FFNet: Draw weights... FFNet: Draw cost history... FFNet: Extract weights... FFNet: Get number of outputs FFNet: Get number of inputs FFNet: Get number of hidden units... FFNet: Get number of hidden weights... FFNet: Reset... FFNet: Select biases... Create FFNet... Create FFNet (linear outputs)... Create iris example... iris data set FFNet: Pattern FFNet: Categories Activation FFNet: Principal components FFNet & Pattern: To Categories... Pattern & Categories: To FFNet... FFNet & Pattern & Categories: Learn slow... FFNet & Pattern & Categories: Learn... FFNet & Pattern & Categories: Get total costs... FFNet & Pattern & Activation: Get total costs... FFNet & Pattern & Categories: Get average costs... FFNet & Pattern & Activation: Get average costs... Anderson (1935) Fisher (1936) Nocedal & Wright (1999) ] ] j h] p] ] ] ~] ] ] ] $] |b tn ] ] $ /] ;] ( B] , J] 0 S] 4 ]] d f] p] h f] w] l f] ] p f] ] t f] ] x f] ] | f] ] f] ] /] ] /] ] /] ? ?? $@ @ @?t@ ] lj Ȑ] nLayers nUnitsInLayer outputsAreLinear nonLinearityType costFunctionType outputCategories: size outputCategories [%ld]: nWeights w Trying to read "%s". FFNet 0 my nLayers outputCategories Categories my nWeights nNodes nInputs nOutputs dimension activity my nNodes isbias nodeFirst nodeLast wFirst wLast deriv error wSelected dw dwi A Layer number of 0 is not allowed. A negative layer number is not allowed. A layer number of %d is too big. s This FFNet has %d layer%s. Please set the layer number equal to 1. Please choose a layer number equal to 1 or 2. Please choose a layer number equal to 1, 2 or 3. Please choose a layer number in the range 1 to %d %d-%d -%d (s) I have %ld layer%s. A total of %ld units divided as: , LINEAR %ld in layer %ld (output%s) %ld in layer %ld (hidden) %ld in layer 0 (input) This net has %ld weights of which %ld are selected. FFNet.c numberOfLayers == 0 index > 0 && index <= my nWeights node > 0 && node <= my nNodes Units in layer %ld -> Input units -> bias Minimum squared error Minimum cross entropy Number of epochs iris L%d-%d Bias Dimensions don't fit. The number of rows in the TableOfReal does not equal the number of units in the layer that connect to layer %d. The number of columns in the TableOfReal does not equal the number of units in layer %d. Please quit, there is no appropriate layer in the FFNet for this TableOfReal. Please try again with layer number %d. Please try again with one of the other two layer numbers. ? FFNet & Activation: To Categories The neural net has no Categories (has the FFNet been trained yet?). The number of columns in the Activation must equal the number of outputs of FFNet. FFNet & Activation: To Categories Error creating label %ld. There is not enough memory to create a Categories. The Categories do not match the categories of the FFNet. The FFNet doesn't know the category "%s" from Categories. @FFNet_Eigen.c ix > 0 && iy > 0 Intersection for unit %ld outside range We cannot draw the intersection of the neural net decision plane for unit %d in layer %s with the plane spanned by the eigenvectors because both planes are parallel. There were no intersections in the drawing area. Please enlarge the drawing area. ? ?FFNet_weightsToMatrix: layer must be > 0 and < %ld. FFNet_weightsFromMatrix: layer must be > 0 and < %ld. FFNet_weightsFromMatrix:#columns in Matrix must equal #units in layer %ld (%ld) FFNet_weightsFromMatrix:#rows in Matrix must equal (#units in layer %ld) + 1 (%ld). FFNet & Pattern & Activation %s: %s The Pattern and the FFNet do not match. The number of colums in the Pattern (%d) must equal the number of inputs in the FFNet (%d). %s: %s The Activation and the FFNet do not match. The number of colums in the Activation (%d) must equal the number of outputs in the FFNet (%d) %s: %s The Pattern and the Activation do not match. The number of rows in the Pattern (%d) must equal the number of rows in the Activation (%). %s: %s The elements in the Pattern are not all in the interval [0, 1]. The input of the neural net can only process values that are between 0 and 1. You could use a "Formula..." to scale the Pattern values first. %s: %s The elements in the Activation are not all in the interval [0, 1]. The output of the neural net can only process values that are between 0 and 1. You could use "Formula..." to scale the Activation values first. Learn Get cost FFNet_Pattern_to_Activation: The Pattern and the FFNet do not match. The number of colums in the Pattern (%d) must equal the number of inputs in the FFNet (%d). FFNet_Pattern_to_Activation The elements in the Activation are not all in the interval [0, 1]. The output units of the neural net can only process values that are between 0 and 1. You could use "Formula..." to scale the Activation values first. FFNet & Pattern & Categories %s: %s The Pattern and the FFNet do not match. The number of colums in the Pattern (%d) must equal the number of inputs in the FFNet (%d). %s: %s The Pattern and the categories do not match. The number of rows in the Pattern (%d) must equal the number of categories (%d). %s: %s The elements in the Pattern are not all in the interval [0, 1]. The input of the neural net can only process values that are between 0 and 1. You could use "Formula..." to scale the Pattern values first. Learn Get cost FFNet_Pattern_to_Categories: FFNet has no output categories. FFNet_Pattern_to_Categories: The Pattern and the FFNet do not match. The number of colums in the Pattern (%d) must equal the number of inputs in the FFNet (%d). FFNet_Pattern_to_Categories The elements in the Pattern are not all in the interval [0, 1]. The input of the neural net can only process values that are between 0 and 1. You could use "Formula..." to scale the Pattern values first. p] ] ? I@ {Gz?Draw - Query - Cepstrum Cepstrum: Draw... Cepstrum: Draw 0.0 Minimum quefrency Maximum quefrency Minimum Maximum Garnish Cepstrumc: To DTW... Cepstrumc: To DTW Distance calculation between Cepstra 1.0 Cepstral weight Log energy weight Regression weight Regression weight log energy 0.056 Window for regression coefficients (seconds) Boundary conditions for time warp Match begin positions Match end positions Slope constraints no restriction 1/3 < slope < 3 1/2 < slope < 2 2/3 < slope < 3/2 Window for regression coefficients Formant: To LPC 16000.0 Sampling frequency (Hz) Sampling frequency LFCC LFCC: To LPC... LFCC: To LPC 0 Number of coefficients Number of coefficients must be greater or equal zero. %s LPC LPC: Draw gain... LPC: Draw gain From time (seconds) 0.0 (=all) To time (seconds) Minimum gain Maximum gain To time From time %s seconds LPC: Get number of coefficients... LPC: Get number of coefficients 1 Frame number Frame number is too large. Please choose a number between 1 and %d. -1 coefficients (frame number was not defined) %d coefficients LPC: Draw poles... LPC: Draw poles Time (seconds) Time LPC: To LFCC... LPC: To LFCC LPC: To Polynomial (slice)... LPC: To Polynomial LPC: To Spectrum (slice)... LPC: To Spectrum 20.0 Minimum frequency resolution (Hz) Bandwidth reduction (Hz) 50.0 De-emphasis frequency (Hz) De-emphasis frequency Bandwidth reduction Minimum frequency resolution LPC: To Spectrogram... LPC: To Spectrogram LPC: To VocalTract (slice)... LPC: To VocalTract Time (s) 0.17 Length (m) Length according to Wakita Length Warning 1: for formant analysis, use "To Formant" instead. Warning 2: if you do use "To LPC", you may want to resample first. Click Help for more details. 16 Prediction order 0.025 Analysis window duration (s) 0.005 Time step (s) Pre-emphasis frequency (Hz) Analysis window duration Time step Pre-emphasis frequency Pre-emphasis frequencies cannot be negative. Please use a positive or zero pre-emphasis frequency. Sound: To LPC (autocorrelation)... Sound: To LPC (autocorrelation) Sound: To LPC (covariance)... Sound: To LPC (covariance) Sound: To LPC (burg)... Sound: To LPC (burg) Sound: To LPC (marple)... Sound: To LPC (marple) 1e-6 Tolerance 1 Tolerance 2 Sound: To MFCC... Sound: To MFCC 12 0.015 Filter bank parameters 100.0 Position of first filter (mel) Distance between filters (mel) Maximum frequency (mel) Number of coefficients must be < 25. Distance between filters Maximum frequency Position of first filter m LPC & Sound: Filter... LPC & Sound: Filter Use LPC gain LPC & Sound: To LPC (robust)... Robust LPC analysis Analysis width (s) 1.5 Number of std. dev. 5 Maximum number of iterations 0.000001 Tolerance Variable location %s_r Analysis width Cepstrum help Draw... To Spectrum To Matrix Analyse To LPC To DTW... Hack To LPC... LFCC help LPC help Draw gain... Draw poles... Get sampling interval Get number of coefficients... Extract To Spectrum (slice)... To VocalTract (slice)... To Polynomial (slice)... To Formant To Formant (keep all) To LFCC... To Spectrogram... Filter... Filter (inverse) To LPC (robust)... To Formant (sl)... To LPC (autocorrelation)... To LPC (covariance)... To LPC (burg)... To LPC (marple)... To MFCC... Draw Get length ] <] ?] b] ] 6] @] }] ] ] "] b] ] ] z] ] -] 7] ] ] 4] @] ] |] 1] @] J] `] ] ] ] -] ] ] b] ] @] ] /] T] s] ] ] ] ] +] i] ] ] ] ] ] 1] :] -] u] i] ] ] ] -] ] i] -] ] ] ] ] @] -] ] ] i] -] {] 6] ] ] &] ] )] ] t] ~] -] ] C] ^] i] ] l] }] ] ] #] >] ] ] 6] K] ] ] ] ] ] S] |] ] ] i] ] ] ] #] M] ] ] 6] ] i] ] ] ] ] ] 7] T] -] ] ] ] ] ] ] ] -] ] ] ] ] -] t] ] ] A] ] @] ] ] ,] ] ?] {] ] ] >] ] ] f] ] ] ] |] ] ] '] c] ] ] ] /] ] ,] @] ] ] Q] b] ] ] 6] ] ] ] /] ] ,] @] ] ] Q] b] ] ] 6] 7] x] ] /] ] ,] @] ] ] Q] b] ] ] ] ] O] ]] 6] ] ] ] /] ] ,] @] ] ] Q] b] ] ] 6] 0] d] ] ] =] ] W] ] !] A command to paint the cepstral coefficients in shades of grey. ss %%From coefficient, To coefficient the range of coefficients that will be represented. You can choose this command after selecting 2 objects with cepstral coefficients (two @MFCC's or @LFCC's). With this command you perform dynamic time warping. Algorithm First we calculate distances between cepstral coefficients: The distance between frame %i (from me) and %j (from thee) is: %wc \.c %d1 + %wle \.c %d2 + %wr \.c %d3, where %wc, %wle & %wr are user-supplied weights and %d1 = \su (%k=1..%nCoefficients; (%c__%ik_ - %c__%jk_)^2) %d2 = (c__%i0_ - c__%j0_)^2 %d3 = \su (%k=1..%nCoefficients; (%r__%ik_ - %r__%jk_)^2), with %r__%ik_ the regression coefficient of the cepstral coefficients from the frames within a time span of %dtr seconds. c__%ij_ is %j-th cepstral coefficient in frame %i. Next we find the optimum path through the distance matrix with a Viterbi-algorithm. Copies the cepstral coefficients of the selected @CC object to a newly created @Matrix object. Behaviour %z__%ji_ = %c__%ij_, with 1 \<_ %i \<_ %nx and 1 \<_ j \<_ %numberOfCoefficients__%i_, where %z__%ji_ is the matrix element in row %j and column %i and %c__%ij_ is the %j-th cepstral coefficient in frame %i. One of the @@types of objects@ in P\s{RAAT}. Description An object of type Cepstrum represents the complex cepstrum. An object of type LFCC represents cepstral coefficients on a linear frequency scale as a function of time. The coefficients are represented in frames with constant sampling period. #LFCC commands Creation: \bu @@LPC: To LFCC... You can choose this command after selecting 1 or more @LFCC's. Settings %%Number of coefficients% the desired number of linear predictive coefficients. The transformation from cepstral coefficients to %a-coefficients as described in @@Markel & Gray (1976)@. An object of type LPC represents filter coefficients as a function of time. The coefficients are represented in frames with constant sampling period. LPC commands \bu @@Sound: To LPC (autocorrelation)...@ \bu @@Sound: To LPC (covariance)...@ \bu @@Sound: To LPC (burg)...@ \bu @@Sound: To LPC (marple)...@ Conversion \bu @@LPC: To LFCC...|To LFCC...@ \bu @@LPC: To Spectrogram...|To Spectrogram...@ \bu @@LPC: To Spectrum (slice)...|To Spectrum (slice)...@ \bu @@LPC: To Polynomial (slice)...|To Polynomial (slice)...@ You can choose this command after selecting 1 or more @LPC objects. %%From time (seconds), To time (seconds) the time domain along the %x-axis. %%Minimum gain, Maximum gain the range for the %y-axis. %Garnish determines whether to draw a bounding box and axis labels. Gain will be drawn as a function of time (gain also equals the prediction error energy). %Time the time of the nearest frame. The @@Roots|roots@ of the @@LPC: To Polynomial (slice)...|linear prediction polynomial@, constructed from the coefficients of the analysis frame, will be drawn in the complex plane. The transformation from a-coefficients to cepstral coefficients as described in @@Markel & Gray (1976)@. the desired number of cepstral coefficients. Copies the linear prediction coefficients of the selected @LPC object to a newly created @Matrix object. %z__%ji_ = %a__%ij_, with 1 \<_ %i \<_ %nx and 1 \<_ j \<_ %nCoefficients__%i_, where %z__%ji_ is the matrix element in row %j and column %i and %a__%ij_ is the %j-th linear prediction coefficient in frame %i. For each LPC_Frame, the zeros of the linear prediction polynomial are extracted. Zeros that are outside the unit circle are reflected into it. Next, formant frequencies and bandwidths are calculated from all the roots that have the imaginary part positive, i.e., that lie in the upper half of the unit circle. Formant frequencies smaller than 50 Hz or larger than (%Nyquist_frequency - 50) are discarded. The remaining frequencies and bandwidths are sorted and copied to the Formant_Frame. Finally, the %gain field of the LPC is copied to the %intensity field of the Formant_Frame. The root finder is Laguerre's method followed by root polishing, see @@Press et al. (1992)@. Warning \bu The formant values can be very inaccurate if you did not resample the Sound before the LPC-analysis (consult the @@Source-filter synthesis@ tutorial). \bu The results of the root finder may not always be accurate when more than 30 roots have to be found. A command that creates a Polynomial object from each selected @LPC object. %Time (s) defines the LPC frame whose coefficents will be selected. The linear prediction coefficients %a__1..%n_ of the selected LPC frame will be copied to polynomial coefficients %c__1..%n+1_ as follows: %c__%i_ = %a__%n\--%i+1_, %c__%n+1_ = 1 %%Time (seconds) the time at which the Spectrum must be calculated. %%Minimum frequency resolution (Hz) successive frequencies in the @Spectrum will be maximally this distance apart. %%Bandwidth reduction (Hz) formants with small bandwidths show up very well as peaks in the spectrum because the poles lie close to the contour along which the spectrum is computed (the unit circle in the z-plane). Peak enhancement can be realized by computing the spectrum in the z-plane along a contour of radius %r = exp (\-- %\pi \.c %BandwidthReduction / %samplingFrequency). This technique is also called off-axis spectrum computation. %%De-emphasis frequency (Hz) Performs de-emphasis when frequency is in the interval (0, @@Nyquist frequency@) The Spectrum at time %t will be calculated from the %nearest LPC_Frame according to: Spectrum (%f) = \Vr(%gain\.c%T/%df) / (1 + \su__%k=1..%numberOfCoefficients_ %a__%k_%z^^\--%k^), where %T is the sampling period and %z = exp (\--2 %\pi %i %f %T) and %df is the distance in Hz between two successive components in the Spectrum. 1. Allocate a large enough buffer[1..%nfft] to perform an fft analysis. 2. Make the first value of the buffer 1 and copy the prediction coefficients #a into the buffer. This results in buffer values: (1, %a__1_, ..., %a__%numberOfCoefficients_, 0, ..., 0). 3. If %deEmphasisFrequency is in the interval (0, nyquistFrequency) then "multiply" the buffer with (1 - %b %z^^\--1^), where %b = exp (\-- %\pi %deEmphasisFrequency %T). This results in buffer values: (1, %a__1_\--%b, %a__2_\--%b\.c%a__1_, ..., %a__%numberOfCoefficients_\--%b\.c%a__%numberOfCoefficients\--1_, \--%b\.c%a__%numberOfCoefficients_, 0, ..., 0). Note that the number of values in the buffer that differ from 0 has increased by one. 4. If %bandwidthReduction > 0 then multiply corresponding values in the buffer by %g^^%i\--1^ where %g = exp (2%\pi %bandwidthReduction %T / %nfft), and %i is the position index in the buffer. %i runs from 1 to %numberOfCoefficients+1+%t, where %t equals 1 when de-emphasis was performed, else 0. 5. Calculate the fft spectrum of the buffer with the coefficients. This results in complex amplitudes (%a__%j_,%b__%j_), %j=1..%nfft/2+1. 6. Calculate the LPC Spectrum by taking the inverse of the fft spectrum, i.e., each complex amplitude becomes (%a__%j_,%b__%j_)^^\--1^ = (%a__%j_,\--%b__%j_) / (%a__%j_^2 + %b__%j_^2) 7. Multiply all values with the scale factor \Vr(%gain\.c%T/%df). successive frequencies in the Spectrum will be maximally this distance apart formants with small bandwidths show up very well as darker regions in the spectrogram because the poles lie close to the contour along which a spectrum is computed (the unit circle in the z-plane). Peak enhancement can be realized by computing a spectrum in the z-plane along a contour of radius %r = exp (\-- %\pi \.c %BandwidthReduction / %samplingFrequency). Performs de-emphasis when value is in the interval (0, @@Nyquist frequency@) For each LPC_Frame the corresponding Spectrum will be calculated according to the algorithm explained in @@LPC: To Spectrum (slice)...@. For each frequency the power, i.e., the square of the complex values, will be stored in the corresponding area in the Spectrogram. %Length the length of the vocal tract. %%Length according to Wakita the length of the vocal tract is calculated according to the algorithm as described in @@Wakita (1977)@. A new @VocalTract area function is calculated from the prediction coefficients in the frame. When %%Length according to Wakita% is on, the optimal length is searched for in the range from 0.1 m to 0.25 m. This length calculation is extremely sensitive to the number of and the positions of the formants with respect to the @@Nyquist frequency@. For example, there is a large difference between the vocal tract length estimates if the highest formant is just below or just above the Nyquist frequency. The algorithm is not very reliable in vocal tract length estimation and we do not recommend using it. A command that creates a new Sound object from one @Sound and one @LPC object which have been selected together. %%Use LPC gain% Determines whether the gain from the LPC is used in the synthesis. Filters the selected Sound by the selected LPC-filter. When the LPC-gain is used the samples in the new Sound will be multiplied with the square root of the corresponding LPC-gain value. In #Z-domain notation: #O(%z) = #H(%z) \.c #E(%z), where #E(%z) is the selected filter input Sound, #H(%z) the selected LPC filter, and, #O(%z) the filter output (the new Sound that will appear in the List of objects). Given a filter (the selected LPC) and its output (the selected Sound), its input is reconstructed (the new Sound that will appear in the List of objects). In Z-domain notation: #E(%z) = #O(%z) / #H(%z), where #O(%z) is the filter output Sound, #H(%z) the LPC filter, and, #E(%z) the filter input Sound. (Selecting this newly generated Sound and the LPC, choosing the option `Filter...' generates a Sound that is identical to the Sound that originated the LPC.) An object of type MFCC represents mel frequency cepstral coefficients as a function of time. The coefficients are represented in frames with constant sampling period. MFCC commands \bu @@Sound: To MFCC...@ \bu @@MelFilter: To MFCC...@ A command to reconstruct @MelFilter objects from the selected @MFCC objects . the range of coefficients that will be used in the reconstruction. Details The output of the triangular filters in a mel filter bank will be synthezised by applying the inverse cosine transform: %P__%j_ = 2/N (%c__0_/2 + \Si__%j=%from_^^%to^ %c__%i_ cos (%j\pi/%N (%i-0.5)))), where %N represents the number of filters and %c__%i_ the %i-th cepstral coefficient. You can perform this analysis by selecting one or more @Sound objects and choosing the appropriate command to generate an @LPC. The acronym LPC stands for Linear Predictive Coding. In the LPC analysis one tries to predict %x__%n_ on the basis of the %p previous samples, %x\'p__%n_ = \su %a__%k_ %x__%%n-k%_ then {%a__1_, %a__2_, ..., %a__%p_} can be chosen to minimize the prediction power %%Q__p_% where %%Q__p_% = E[ |%x__%n_ - %x\'p__%n_|^2]. Several different algorithms exist for minimizing %%Q__p_%: \bu @@Sound: To LPC (autocorrelation)...|To LPC (autocorrelation)...@ \bu @@Sound: To LPC (covariance)...|To LPC (covariance)...@ \bu @@Sound: To LPC (burg)...|To LPC (burg)...@ \bu @@Sound: To LPC (marple)...|To LPC (marple)...@ With this command you create a new @LPC from every selected @Sound, using "the autocorrelation" method. You are advised not to use this command for formant analysis. For formant analysis, instead use @@Sound: To Formant (burg)...@, which also works via LPC (linear predictive coding). This is because ##Sound: To Formant (burg)...# lets you specify a maximum frequency, whereas the ##To LPC# commands automatically use the @@Nyquist frequency@ as their maximum frequency. If you do use one of the ##To LPC# commands for formant analysis, you may therefore want to downsample the sound first. For instance, if you want five formants below 5500 Hz but your Sound has a sampling frequency of 44100 Hz, you have to downsample the sound to 11000 Hz with the @@Sound: Resample...@ command. After that, you can use the ##To LPC# commands, with a prediction order of 10 or 11. %%Prediction order% the number of linear prediction coefficients, also called the %%number of poles%. Choose this number at least twice as large as the number of spectral peaks that you want to detect. %%Analysis window duration% (s) the effective duration of each analysis frame, in seconds. %%Time step% (s) the time step between two consecutive analysis frames. %%Pre-emphasis frequency% (Hz) a +6dB / octave filtering will be applied above this frequency. A pre-emphasis frequency of 48.47 Hz for a signal with a sampling frequency of 10 kHz approximately corresponds to a value of %a = 0.97 for the filter %y__%n_ = %x__%n_ - %a \.c %x__%n-1_. The relation between %a and the pre-emphasis frequency is: %a = exp (\--2\.c%\pi\.c%preemphasisFrequency/%samplingFrequency). If you do not want pre-emphasis, choose a frequency greater than the @@Nyquist frequency@. The autocorrelation algorithm is decribed in @@Markel & Gray (1976)@. With this command you create a new @LPC from every selected @Sound, using "the covariance" method. The covariance algorithm is decribed in @@Markel & Gray (1976)@. With this command you create a new @LPC from every selected @Sound, using "Marple's" method. %%Tolerance 1 stop the iteration when %E(%m) / %E(0) < %%Tolerance 1%, where %E(%m) is the prediction error for order %m. %%Tolerance 2 stop the iteration when (%E(%m) - %E(%m-1)) / %E(%m-1) < %%Tolerance 2. The algorithm is described in @@Marple (1980)@. With this command you create a new @LPC from every selected @Sound, using "Burg's" method. Burg's algorithm is described in @@Anderson (1978)@ A command that creates a @MFCC object from every selected @Sound object. The analysis proceeds in two steps: 1. We perform a filter bank analysis on a mel frequency scale (see @@Sound: To MelFilter...@ for details). 2. We convert the filter values to mel frequency cepstral coefficients (see @@MelFilter: To MFCC...@ for details). N. Anderson (1978), "On the calculation of filter coefficients for maximum entropy spectral analysis", in Childers, %%Modern Spectrum Analysis%, IEEE Press, 252-255. J.D. Markel & A.H. Gray, Jr. (1976), %%Linear Prediction of Speech%, Springer Verlag, Berlin. L. Marple (1980), " A new autoregressive spectrum analysis algorithm", %%IEEE Trans. on ASSP% #28, 441-454. H. Wakita (1977), "Normalization of vowels by vocal-tract length and its application to vowel identification", %%IEEE Trans. on ASSP% #25, 183-192. CC: Paint... djmw CC: To DTW... CC: To Matrix Cepstrum LFCC LFCC: To LPC... LPC LPC: Draw gain... LPC: Draw poles... LPC: To LFCC... LPC: To Matrix LPC: To Formant LPC: To Polynomial (slice)... LPC: To Spectrum (slice)... LPC: To Spectrogram... LPC: To VocalTract (slice)... LPC & Sound: Filter... LPC & Sound: Filter (inverse) MFCC MFCC: To MelFilter... Sound: LPC analysis Sound: To LPC (autocorrelation)... David Weenink & Paul Boersma Sound: To LPC (covariance)... Sound: To LPC (marple)... Sound: To LPC (burg)... Sound: To MFCC... Anderson (1978) Markel & Gray (1976) Marple (1980) Wakita (1977) |^ ^ ^ ^ ^ @ ^ ̨i ^ 0 ^ 8 ^ < ^ ^ ^ XSA ^ i @ ^ ? ? *G @nCoefficients a gain samplingPeriod maxnCoefficients (empty) frame []: %s frame [%ld]: Trying to read "%s". my nCoefficients LPC frame LPC_Frame my nx LPC info Name: %s Time domain: from %.8g to %.8g seconds. Prediction order: %ld Number of frames: %ld Time step: %.8g seconds First frame at: %.8g seconds Time (seconds) Gain + @ -DT! @ @ ?-DT! -DT!@ LPC_to_Formant %s: We cannot find the roots of a polynomial of order > 99. %s: Margin must be smaller than %s LPC to Formant LPC to Formant: frame %ld out of %ld %s: %d formant frames out of %d suspect. ? @ @ @ ?-DT! -DT! @ @LPC_Frame_into_Spectrum: Spectrum size not large enough. @ ? @ ? ?Sound_to_LPC %s: Analysis window duration too short. For a prediction order of %d the analysis window duration has to be greater than %s s. Please increase the analysis window duration or lower the prediction order. LPC analysis %s: LPC analysis of frame %d out of %d LPC_and_Sound_filterInverse %s: Sampling frequencies are not the same. %s: Domains of LPC and Sound are not equal. LPC_and_Sound_filter %s: Time domains of source and filter do not match. ^ ^ ^ 0 ^ ^ ^ ^ ^"^ F@ >@ ? ? A @ @@Query - Draw - Modify - Extract - Activation: Formula for col := 1 to ncol do { self [row, col] := `formula' ; x := x + dx } y := y + dy }} label self formula BarkFilter FilterBank: Draw spectrum (slice)... BarkFilter: Draw spectrum (slice) 0.1 Time (s) 0.0 left Frequency range (Bark) right Frequency range (Bark) left Amplitude range (dB) right Amplitude range (dB) Garnish Barks right Amplitude range left Amplitude range right Frequency range left Frequency range Time FilterBank: Draw filter functions... BarkFilter: Draw filter functions 0 left Filter range right Filter range Frequency scale Hertz Bark mel Amplitude scale in dB Categories: Append 1 category... Categories: Append 1 category Category Cannot edit a Categories from batch. -1 (undefined: number of elements differ!) %d differences %s praat_David_init.c c1 && c2 %s_%s CC: Paint... CC: Paint left Time range (s) right Time range (s) From coefficient To coefficient Minimum Maximum right Time range left Time range CC: Draw c0... CC: Draw c0 CC: To DTW... CC: To DTW Distance between cepstral coefficients 1.0 Cepstral weight Log energy weight Regression weight Regression weight log energy 0.056 Window for regression coefficients (s) Boundary conditions for time warp Match begin positions Match end positions Slope constraints no restriction 1/3 < slope < 3 1/2 < slope < 2 2/3 < slope < 3/2 Window for regression coefficients Eigen: Draw eigenvector... CCA: Draw eigenvector X or Y y x 1 Eigenvector number Multiply by eigenvalue? Component loadings Select part of the eigenvector: left Element range right Element range -1.0 Mark size (mm) + Mark string (+xo.) Connect points Mark string Mark size CCA: Get canonical correlation coefficient Coefficient number Eigen: Get eigenvector element... CCA: Get eigenvector element Element number CCA: Get zero correlation probability... CCA: Get zero correlation probability %.17g (=probability for chisq = %.17g and ndf = %d) %s_loadings CCA & TableOfReal: To TableOfReal (scores)... CCA & TableOfReal: To TableOfReal (scores) 0 (=all) Number of canonical correlations %s_scores CCA & TableOfReal: Predict... CCA & TableOfReal: Predict The data set from which to predict starts at... Column number ChebyshevSeries Create ChebyshevSeries... Create ChebyshevSeries cs Name Domain -1 Xmin Xmax ChebyshevSeries(x) = c[1] T[0](x) + c[2] T[1](x) + ... c[n+1] T[n](x) T[k] is a Chebyshev polynomial of degree k 0 0 1.0 Coefficients (c[k]) Xmin must be smaller than Xmax. Coefficients ClassificationTable Confusion Confusion: Condense... Confusion: Condense a Search Replace 0 (=unlimited) Replace limit Search and replace are Literals Regular Expressions %s fraction correct Confusion & Matrix: Draw confusions with arrows Category position lower level(%) left Horizontal range right Horizontal range left Vertical range right Vertical range Category position must be >= 0 Correlation Correlation: Confidence intervals... 0.95 Confidence level (0-1) Number of tests (Bonferroni correction) Approximation Ruben Fisher Confidence level Number of tests SSCP: Get diagonality (bartlett)... Correlation: Get diagonality (bartlett) Number of contraints %.17g (=probability, based on chisq = %.17g and ndf = %d) Covariance Covariance: Get significance of one mean... Covariance: Get significance of one mean Get probability that the mean with Index differs from Value (Null hypothesis: the observed difference is due to chance.) %.17g (=probability, based on t = %.17g and ndf = %d) Covariance: Get significance of means difference... Covariance: Get significance of means difference Get probability that the difference between means Index1 2 Index2 when the means are Paired and have Equal variances %.17g (=probability, based on t = %.17g and ndf = %.7g) Covariance: Get significance of one variance... Covariance: Get significance of one variance Get probability that the variance with %.17g (=probability, based on chisq = %.17g and ndf = %.7g) Covariance: Get significance of variances ratio... Covariance: Get significance of variances ratio Hypothesized ratio %.17g (=probability, based on F = %.17g, ndf1 = %d and ndf2 = %d) Covariance: Get fraction variance... Covariance: Get fraction variance From dimension To dimension Covariance: To TableOfReal (random sampling)... Covariance: To TableOfReal (random sampling) Number of data points %.17g (=probability, based chisq = %.17g and ndf = %d Discriminant Discriminant & Pattern: To Categories... Discriminant & Pattern: To Categories Pool covariance matrices Use apriori probabilities Discriminant & TableOfReal: To Configuration... Discriminant & TableOfReal: To Configuration Number of dimensions Number of dimensions must be greater equal zero. You can use the Discriminant as a classifier by selecting a Discriminant and a TableOfReal object together. Discriminant & TableOfReal: To ClassificationTable... Discriminant & TableOfReal: To ClassificationTable Discriminant: Get Wilks' lambda... Discriminant: Get Wilks' lambda Product (i=from..numberOfEigenvalues, 1 / (1 + eigenvalue[i])) From Number must be greater than or equal to one. Eigen: Get cumulative contribution of components... Discriminant: Get cumulative contribution of components From component To component Discriminant: Get partial discrimination probability... Discriminant: Get partial discrimination probability Number of dimensions must be greater than or equal to zero. Discriminant: Get concentration ellipse area... Discriminant: Get concentration ellipse area Group label Number of sigmas Discriminant plane X-dimension Y-dimension Group label does not exist. Discriminant: Get confidence ellipse area... Discriminant: Get confidence ellipse area Discriminant: Get determinant (group)... Discriminant: Get determinant (group) Discriminant: Invert eigenvector Index of eigenvector Discriminant: Draw sigma ellipses... Discriminant: Draw sigma ellipses 12 Label size Discriminant: Draw one sigma ellipse... Discriminant: Draw one sigma ellipse Label Discriminant: Draw confidence ellipses Discriminant: Draw one confidence ellipse Discriminant: Extract within-group SSCP... Discriminant: Extract within-group SSCP Group index %d Discriminant: Get number of observations... Discriminant: Get number of observations 0 (=total) Group DTW DTW: Draw path DTW: Draw distances along path DTW: Paint distances DTW: Get time along path... DTW: Get time along path In case of ambiguity choose: Highest Lowest In case of ambiguity choose diagonal DTW: Get maximum consecutive steps... DTW: Get maximum consecutive steps Direction X Y Diagonaal %d (=maximum number of consecutive steps in %s direction) DTW: Find path Boundary conditions DTW: Find path (band)... DTW: Find path (Sakoe-Chiba band) Adjustment window duration (s) Adjustment window includes end Directional weights X weight Y weight 2.0 Diagonal weight Adjustment window duration DTW: To Polygon (slopes)... DTW: To Polygon (slopes) Slope constraints: This number of Non-diagonal steps must be followed by at least this number of 0 (=no constraints) Diagonal steps DTW: To Polygon (band)... DTW: To Polygon (band) The command "Draw eigenvalues (scree)..." has been removed. To get a scree plot use "Draw eigenvalues..." with the arguments 'Fraction of eigenvalues summed' and 'Cumulative' unchecked. Eigen: Draw eigenvalues... Eigen: Draw eigenvalues left Eigenvalue range right Eigenvalue range Fraction of eigenvalues summed Cumulative Eigen: Draw eigenvector Eigen: Get eigenvalue... Eigen: Get eigenvalue Eigenvalue number DO_Eigen_getEigenvalue: Eigenvalue number must be smaller than %d Eigen: Get sum of eigenvalues... Eigen:Get sum of eigenvalues Eigen: Get eigenvector element Eigen & Matrix: Project... Eigen & Matrix: Project StringsIndex: Get class label... StringsIndex: Get class label Class index Element index must be less than or equal %d. StringsIndex: Get label... StringsIndex: Get label Element index Index: Get index... Index: Get index StringsIndex: Get class index... StringsIndex: Get class index Class label Index: Extract part... Index: Extract part left Range right Range %s_part Index: To Permutation... Index: To Permutation Permute within classes Excitations: Formula for all objects in Excitations do { for col := 1 to ncol do { self [col] := `formula' ; x := x + dx } } Excitations: Get item Item number Excitations: To Pattern Join FilterBank: Draw filters FilterBank: Draw one contour 40.0 Height (dB) Height FilterBank: Draw contours FilterBank: Draw frequency scales... FilterBank: Draw frequency scales Horizontal frequency scale left Horizontal frequency range right Horizontal frequency range Vertical frequency scale left Vertical frequency range right Vertical frequency range FilterBank: Paint image FilterBank: Paint contours FilterBank: Paint cells FilterBank: Paint surface FilterBank: Get frequency in Hertz... FilterBank: Get frequency in Hertz 10.0 Frequency Unit %s Hertz FilterBank: Get frequency in Bark... FilterBank: Get frequency in Bark 93.17 %s Bark FilterBank: Get frequency in mel... FilterBank: Get frequency in mel 1000.0 %s mel FilterBank: Equalize intensities 80.0 Intensity (dB) Intensity FormantFilter FormantFilter: Draw filter functions 100.0 Bandwidth (Hz) Bandwidth FormantFilter: Draw spectrum (slice) left Frequency range (Hz) right Frequency range (Hz) Hz FunctionTerms: Draw Extrapolate FunctionTerms: Draw basis function FunctionTerms: Evaluate FunctionTerms: Get coefficient p(x) = c[1] + c[2] x + ... c[n+1] x^n Index too large. Polynomial: Get maximum... FunctionTerms: Get maximum Interval Polynomial: Get minimum... FunctionTerms: Get minimum Polynomial: Get x of maximum... FunctionTerms: Get x of maximum Polynomial: Get x of minimum... FunctionTerms: Get x of minimum FunctionTerms: Set coefficient p(x) = c[1]F[0] + c[2]F[1] + ... c[n+1]F[n] F[k] is of degree k FunctionTerms: Set domain Xmax must be larger than Xmin. ISpline Create ISpline... Create ISpline ispline ISpline(x) = c[1] I[1](x) + c[2] I[1](x) + ... c[n] I[n](x) all I[k] are polynomials of degree "Degree" Relation: numberOfCoefficients == numberOfInteriorKnots + degree 3 Degree 1.2 2.0 1.2 1.2 3.0 0.0 0.3 0.5 0.6 Interior knots Create LegendreSeries... Create LegendreSeries ls LegendreSeries(x) = c[1] P[0](x) + c[2] P[1](x) + ... c[n+1] P[n](x) P[k] is a Legendre polynomial of degree k LegendreSeries LongSound: Append to existing sound file LongSound: Write to AIFF file aiff LongSound: Write to AIFC file aifc LongSound: Write to WAV file wav LongSound: Write to NeXT/Sun file au LongSound: Write to NIST file nist Matrix: Draw as squares... Matrix: Draw as squares Matrix: Draw distribution... Matrix: Draw distribution Selection of (part of) Matrix Selection of Matrix values Minimum value Maximum value Display of the distribution 10 Number of bins Minimum frequency Maximum frequency Matrix: Draw cumulative distribution Matrix: Scale self[row, col] := self[row, col] / `Scale factor' Scale factor Extremum in matrix Extremum in each row Extremum in each column illegal value for scale. Matrix: Solve equation... Matrix: Solve equation 1.19e-7 Tolerance %s_solution Matrix: Scatter plot Column for X-axis Column for Y-axis X and Y component must differ from 0. Matrix: To Pattern %ld Get frequency of row Row number Get time of column Get value in cell 0.5 Frequency out of range. Time out of range. %.8g (delta t: %.8g, f: %.8g) MelFilter MelFilter: Draw filter functions Mel MelFilter: Draw spectrum (slice) left Frequency range (mel) right Frequency range (mel) Mels MelFilter: To MFCC... MelFilter: To MFCC Number of coefficients MFCC MFCC: To MelFilter... MFCC: To MelFilter Position of first filter (mel) Distance between filters (mel) Distance between filters Position of first filter Create MSpline... Create MSpline mspline MSpline(x) = c[1] M[1](x) + c[2] M[1](x) + ... c[n] M[n](x) all M[k] are polynomials of degree "Degree" Relation: numberOfCoefficients == numberOfInteriorKnots + degree + 1 MSpline Pattern: Draw Pattern number Pattern: Formula y := 1; for row := 1 to nrow do { x := 1; for col := 1 to ncol do { self [row, col] := `formula' ; x := x + 1 } y := y + 1 }} Pattern: Set value... Pattern: Set value New value Row number must not be greater than number of rows. Column number must not be greater than number of columns. PCA You can get principal components by selecting a PCA and a TableOfReal together and choosing "To Configuration...". You can get a new Covariance object rotated to the directions of the direction vectors in the PCA object by selecting a PCA and a Covariance object together. You can reconstruct the original TableOfReal as well as possible from the principal components in the Configuration and the direction vectors in the PCA object. PCA & TableOfReal: Get fraction variance... PCA & TableOfReal: Get fraction variance left Principal component range right Principal component range PCA & TableOfReal: To Configuration... PCA & TableOfReal: To Configuration PCA: Get equality of eigenvalues... PCA: Get equality of eigenvalues Conservative test PCA: Get number of components (VAF)... PCA: Get number of components (VAF) Variance fraction (0-1) Variance fraction The variance fraction must be in interval (0-1). PCA: Get fraction variance accounted for... PCA: Get fraction variance accounted for The second component must be greater than or equal to the first component. PCA: Invert eigenvector PCA: To TableOfReal (reconstruct 1)... PCA: To TableOfReal (reconstruct) 1.0 1.0 PCA & PCA: To Procrustes... PCA & PCA: To Procrustes left Eigenvector range right Eigenvector range %s degrees (=angle of intersection between the two pc1-pc2 eigenplanes) Permutation Create Permutation... Create Permutation p Number of elements Identity Permutation Permutation: Get value... Permutation: Get value %d (value, at index=%d) Permutation: Get index... Permutation: Get index %d (index, at value=%d) Permutation: Swap blocks... Permutation: Swap blocks To Block size Permutation: Swap one from range... Permutation: Swap one from range A randomly chosen element from is swapped with the element at Forbid same Permutation: Permute randomly... Permutation: Permute randomly %s_randomly Permutation: Rotate... Permutation: Rotate Step size %s_rotate%d Permutation: Reverse... Permutation: Reverse %s_reverse Permutation: Permute randomly (blocks)... Permutation: Permute blocks randomly Permute within blocks No doublets %s_blocks%d Permutation: Interleave... Permutation: Interleave Offset %s_interleave %s_inverse To apply a number of permutations they all must have the same number of elements. multiply%d Polygon: Translate Polygon: Rotate Angle (degrees) Angle Polygon: Scale polygon Polygon & Categories: Draw Polynomial Create Polynomial... Create Polynomial Domain of polynomial -3 4 2.0 -1.0 -2.0 1.0 Polynomial: Get area... Polynomial: Get area Polynomial: Scale x... Polynomial: Scale x New domain Polynomial: Get value (complex)... Polynomial: Get value (complex) Real part Imaginary part %s + %s i Polynomial: To Spectrum... Polynomial: To Spectrum 5000.0 Nyquist frequency (Hz) 1025 Number of frequencies (>1) Number of frequencies "Number of frequencies" must be greater than 2. Nyquist frequency %s_%s_mul Polynomials: Divide... Polynomials: Divide Want quotient Want remainder Either 'Want quotient' or 'Want remainder' must be choosen %s_q %s_r Roots Roots: Draw Minimum of real axis Maximum of real axis Minimum of imaginary axis Maximum of imaginary axis o Mark string (+x0...) Roots: Get root Root number --undefined-- - %.17g %s %.17g i Roots: Get real part Roots: Get imaginary part Roots: Set root 1.0/sqrt(2) Roots: To Spectrum... Roots: To Spectrum yes no Double precision floating point properties of this machine, as calculated by algorithms from the Binary Linear Algebra System (BLAS) Radix: %d Number of digits in mantissa: %d Smallest exponent before (gradual) underflow (expmin): %d Largest exponent before overflow (expmax): %d Does rounding occur in addition: %s Quantization step (d): %.17g Quantization error (eps): %.17g (= d/2) Underflow threshold: %.17g (= radix ^ (expmin - 1)) Safe minimum (such that its inverse does not overflow): %.17g Overflow threshold: %.17g (= (1 - eps) * radix ^ expmax) Starting time (s) Finishing time (s) 22050.0 Sampling frequency (Hz) Starting time Finishing time Sampling frequency A Sound cannot have a duration of zero. A Sound cannot have a duration less than zero. Please set the finishing time to something greater than 0 seconds. Please lower the starting time or raise the finishing time. A Sound cannot have a negative sampling frequency. Please set the sampling frequency to something greater than zero, e.g. 44100 Hz. A Sound cannot have zero samples. Please raise the finishing time. A Sound cannot have %s samples; the maximum is %s samples. Please lower the finishing time or the sampling frequency. Please raise the starting time, lower the finishing time, or lower the sampling frequency. memory There is not enough memory to create a Sound that contains %s samples. You could lower the finishing time or the sampling frequency and try again. You could raise the starting time or lower the finishing time or the sampling frequency, and try again. Sound & Pitch: To FormantFilter... Sound & Pitch: To FormantFilter 0.015 Analysis window duration (s) 0.005 Time step (s) Filter bank parameters Position of first filter (Hz) 50.0 Distance between filters (Hz) 1.1 Relative bandwidth Time step Analysis window duration Sound & Pitch: Change gender... Sound & Pitch: Change gender 75.0 Minimum pitch (Hz) 1.2 Formant shift ratio 0.0 (=no change) New pitch median (Hz) 1.0 (=no change) Pitch range factor Duration factor Minimum pitch New pitch median Create Sound from gamma-tone... Create a gamma-tone gammatone Gamma Frequency (Hz) 150.0 Initial phase (radians) Addition factor Scale amplitudes Frequency cannot be larger than half the sampling frequency. Please use a frequency smaller than %s. Gamma can not be negative. Please use a positive or zero gamma. Bandwidth can not be negative. Please use a positive or zero bandwidth. Initial phase Create Sound from Shepard tone... Create a Shepard tone shepardTone 4.863 Lowest frequency (Hz) Number of components 4.0 Frequency change (semitones/s) 30.0 Amplitude range (dB) Octave shift fraction ([0,1)) Amplitude range Octave shift fraction Amplitude range can not be negative. Please use a positive or zero amplitude range. Frequency change Lowest frequency Sound: To BarkFilter... Sound: To BarkFilter Position of first filter (bark) Distance between filters (bark) Maximum frequency (bark) Sound: To FormantFilter... Sound: To FormantFilter Pitch analysis 600.0 Maximum pitch (Hz) Maximum pitch Sound: To MelFilter... Sound: To MelFilter Maximum frequency (mel) Sound: To Pitch (shs)... Sound: To Pitch (shs) 0.01 15 Max. number of candidates (Hz) Algorithm parameters 1250.0 Maximum frequency component (Hz) Max. number of subharmonics 0.84 Compression factor (<=1) Ceiling (Hz) 48 Number of points per octave Maximum frequency component Ceiling Minimum pitch should be smaller than ceiling. Maximum frequency must be greaterequal ceiling. Compression factor Max. number of candidates Sound: To SPINET... Sound: To SPINET 0.040 Gammatone filter bank 70.0 Minimum filter frequency (Hz) Maximum filter frequency (Hz) 250 Number of filters 500.0 Minimum filter frequency Maximum filter frequency Maximum frequency must be larger than minimum frequency. Sound: Filter (gammatone)... Sound: Filter (gammatone) Centre frequency (Hz) Centre frequency Sound: Change gender... Sound: Change gender Pitch measurement parameters Pitch floor (Hz) Pitch ceiling (Hz) Modification parameters Pitch floor Pitch ceiling Maximum pitch should be greater than minimum pitch. Read Sound from raw Little Endian file Read Sound from raw 16-bit Little Endian file Sound: Write to raw 16-bit Big Endian file raw Sound: Write to raw 16-bit Little Endian file Spectrograms: To DTW Spectrum: Draw phases... Spectrum: Draw phases From frequency (Hz) To frequency (Hz) 0.0 (= auto) Minimum phase (dB/Hz) Maximum phase (dB/Hz) Unwrap Maximum phase Minimum phase To frequency From frequency Spline: Draw knots Spline: Scale x... Spline: Scale x SSCP SSCP: Draw confidence ellipse Index for X-axis Index for Y-axis SSCP: Draw sigma ellipse... SSCP: Draw sigma ellipse %s_centroid SSCP: Get confidence ellipse area... SSCP: Get confidence ellipse area SSCP: Get fraction variation... SSCP: Get fraction variation SSCP: Get sigma ellipse area... SSCP: Get sigma ellipse area %.17g SSCP: Get centroid element Number SSCP_getCentroidElement: "Number" must be smaller than %d. SSCP: Get diagonality (bartlett) %.17g (=probability, based on chisq= %.17g, ndf = %d) SSCP: To Covariance... SSCP: To Covariance Number of constraints appended Strings: Set string... Strings: Set string String Strings: Change Search and replace are: Strings: Extract part From index To index Strings: To Permutation... Strings: To Permutation Sort SVD: To TableOfReal... SVD: To TableOfReal First component Last component pb pvn m10w10c10 columns_appended Create TableOfReal (Pols 1973)... Create TableOfReal (Pols 1973) Include formant levels pols_50males Create TableOfReal (Van Nierop 1973)... vannierop_25females Create TableOfReal (Weenink 1985)... Speakers group Men Women Children m w c %s10 TableOfReal: Draw scatter plot... TableOfReal: Draw scatter plot Select the part of the table Horizontal axis column number Vertical axis column number left Row number range right Row number range Select the drawing area limits Use row labels TableOfReal: Draw scatter plots matrix From column To column Fraction white TableOfReal: Draw biplot... TableOfReal: Draw biplot Split factor TableOfReal: Draw box plots... TableOfReal: Draw box plots From row To row TableOfReal: To Configuration (lda)... TableOfReal: To Configuration (lda) TableOfReal: To CCA... TableOfReal: To CCA Dimension of dependent variate TableOfReal: To Configuration (pca)... TableOfReal: To Configuration (pca) TableOfReal: To SSCP... TableOfReal: To SSCP Begin row End row Begin column End column TableOfReal: Cholesky decomposition Upper (else L) Inverse Upper TableOfReal: To Pattern and Categories... TableOfReal: To Pattern and Categories left Row range right Row range left Column range right Column range TableOfReal: Get column sum Column TableOfReal: Get row sum Row TableOfReal: To TableOfReal (means by row labels)... TableOfReal: Means by row labels Expand %s_byrowlabels TableOfReal & Matrix: Copy Matrix-columns into TableOfReal-rows Into TableOfReal Start column TableOfReal &FilterBank: Copy frames into rows Begin frame End frame TextGrid: Extend time... TextGrid: Extend time Extend domain by (s) At End Start Extend domain by TextGrid: Set tier name... TextGrid: Set tier name Tier number: Tier number Paint... Draw... To Matrix To DTW... Project... Get eigenvalue... Get sum of eigenvalues... Get number of eigenvectors Get eigenvector dimension Get eigenvector element... Draw eigenvalues... Draw eigenvalues (scree)... Draw eigenvector... Get number of classes To Permutation... Extract part... -- frequency scales -- Get frequency in Hertz... Get frequency in Bark... Get frequency in mel... Equalize intensities... Draw filters... Draw one contour... Draw contours... Paint image... Paint contours... Paint cells... Paint surface... Draw frequency scales... To Intensity Copy frames into rows... Draw basis function... Get number of coefficients Get coefficient... Get degree -- function specifics -- Get value... Get minimum... Get x of minimum... Get maximum... Get x of maximum... Set domain... Set coefficient... Analyse Get time from column... -- frequencies -- Get lowest frequency Get highest frequency Get number of frequencies Get frequency distance Get frequency from row... -- get value -- Get value in cell... Draw knots... Get order Scale x... -- statistics -- Get number of observations Get degrees of freedom Get centroid element... Get ln(determinant) Extract centroid To TableOfReal Report floating point properties Goodies Objects New Create Sound from tone complex... Create Table... Create formant table (Pols & Van Nierop 1973) Create formant table (Peterson & Barney 1952) Create formant table (Weenink 1985) Create TableOfReal... Read from special sound file Read Sound from raw 16-bit Little Endian file... Read Read Sound from raw 16-bit Big Endian file... Modify Formula... Hack BarkFilter help Draw spectrum (slice)... Draw filter functions... Edit Get difference Get number of differences Get fraction different Append 1 category... Extract To unique Categories To Confusion Synthesize Permute items To Strings ChebyshevSeries help To Polynomial Get number of correlations Get correlation... Get zero correlation probability... To TableOfReal (scores)... To TableOfReal (loadings) Predict... Confusion help -- confusion statistics -- Get fraction correct Get row sum... Get column sum... Get grand sum To TableOfReal (marginals) Condense... To difference matrix Draw Draw confusion... Covariance help Get diagonality (bartlett)... Get significance of one mean... Get significance of means difference... Get significance of one variance... Get significance of variances ratio... Get fraction variance... To TableOfReal (random sampling)... Difference To Correlation To PCA ClassificationTable help To Strings (max. prob.) Correlation help Confidence intervals... Discriminant help -- sscps -- Draw sigma ellipses... Draw one sigma ellipse... Draw confidence ellipses... -- eigen structure -- -- discriminant -- Get number of functions Get dimension of functions Get number of groups Get number of observations... -- tests -- Get Wilks lambda... Get cumulative contribution of components... Get partial discrimination probability... Get homogeneity of covariances (box) -- ellipses -- Get sigma ellipse area... Get confidence ellipse area... Get ln(determinant_group)... Get ln(determinant_total) Invert eigenvector... Align eigenvectors Extract pooled within-groups SSCP Extract within-group SSCP... Extract between-groups SSCP Extract group centroids Extract group standard deviations Extract group labels & TableOfReal: To ClassificationTable? To Categories... Project Modify Discriminant Set group labels To Configuration... To ClassificationTable... DTW help Draw path... Paint distances... Get distance (weighted) Get maximum consecutive steps... Get time along path... Find path... Find path (band)... To Polygon (band)... To Polygon (slopes)... To Matrix (distances) Swap axes Index help Get class label... Get class index... Get label... Get index... To Formant... To Excitations Extract Excitation... Append Convert To Pattern... Add to Excitations FormantFilter help ISpline help LegendreSeries help Append to existing sound file... Write to NIST file... Write to stereo AIFF file... Write to stereo AIFC file... Write to stereo WAV file... Write to stereo NeXt/Sun file... Write to stereo NIST file... Scatter plot... Draw as squares... Draw distribution... Draw cumulative distribution... Transpose Solve equation... To VocalTract To Activation MelFilter help To MFCC... MFCC help To MelFilter... MSpline help Set value... To Discriminant PCA help -- pca -- Get equality of eigenvalues... Get fraction variance accounted for... Get number of components (VAF)... Get angle between pc1-pc2 planes To Procrustes... To TableOfReal (reconstruct 1)... & TableOfReal: To Configuration? & Configuration (reconstruct)? & Covariance: Project? To TableOfReal (reconstruct) Permutation help Get number of elements Swap blocks... Swap one from range... Permute randomly... Permute randomly (blocks)... Interleave... Rotate... Reverse... Invert Multiply Translate... Scale... Reverse X Reverse Y Polynomial help -- area -- Get area... -- monic -- Scale coefficients (monic) Get value (complex)... To Spectrum... To Roots To Polynomial (derivative) To Polynomial (primitive) Divide... Roots help Get number of roots -- roots -- Get root... Get real part of root... Get imaginary part of root... Set root... Polish roots Write to raw 16-bit Big Endian file... Write to raw 16-bit Little Endian file... To Pitch (cc)... To Pitch (shs)... To Pitch (SPINET)... To Cochleagram (edb)... To FormantFilter... To BarkFilter... Filter (formula)... Filter (gammatone)... Deepen band modulation... Change gender... To Spectrum (slice)... Draw (log freq)... Draw phases... Conjugate To Sound (fft) To Matrix (unwrap) To Spectrogram To Cepstrum SSCP help Draw sigma ellipse... Draw confidence ellipse... Get total variance Get fraction variation... To Covariance... To Categories Genericize Set string... Change... To Distributions To TableOfReal... Append columns Multivariate statistics - To SSCP... To Covariance To Correlation (rank) To CCA... To TableOfReal (means by row labels)... -- configurations -- To Configuration (pca)... To Configuration (lda)... To Pattern and Categories... Split into Pattern and Categories... To Permutation (sort row labels) To SVD To GSVD To Eigen (gsvd) To TableOfReal (cholesky)... Draw top and bottom lines... -- scatter plots -- Draw scatter plot... Draw scatter plot matrix... Draw box plots... Draw biplot... Permute strings Copy columns into rows... Permute rows Scale times... Extend time... Remove tier... Set tier name... 333333@333333 ? i@ ; @ 8? 9@ ?ɿ I@ N@ W@ pb@ Q?ffffff? 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An affine transform is a combination of a linear transformation #%A and a translation #%t that transforms a vector #%x to a new vector #%y in the following way: #%y = #%A x + #%t Get the inverse of the selected @AffineTransform object. The inverse from is: #%x = #%A^^-1^ - #%A^^-1^#%t. We describe how band filtering in the frequency domain is performed. We start with a @Sound and end with a filter bank representation of this sound. We assume a standard analysis context: a sound divided into frames according to a certain %%window length% and %%time step%. We will simulate a filterbank with %N filters. The algorithm for each sound frame proceeds in the following way: 1. Apply a Gaussian window to the sound frame. 2. Convert the windowed frame into a @Spectrum object. 3. Convert the spectral amplitudes to %energy values by squaring the real and imaginary parts and multiplying by %df, the frequency distance between two successive frequency points in the spectrum. Since the Spectrum object only contains positive frequencies, we have to multiply all energy values, except the first and the last frequency, by another factor of 2 to compensate for negative frequencies. 4. For each of the %N filters in the filter bank: determine the inner product of its filter function with the energies as determined in the previous step. The result of each inner product is the energy in the corresponding filter. 5. Convert the energies in each filter to power by dividing by the %%window length%. 6. Correct the power, due to the windowing of the frame, by dividing by the integral of the %squared windowing function. 7. Convert all power values to %dB's according to 10 * log10 (%power / 4 10^^-10^). In general, if we have %k independent significance tests at the %\al level, the probability %p that we will get no significant differences in all these tests is simply the product of the individual probabilities: (1 - %\al)^^%k^. For example, with %\al = 0.05 and %k = 10 we get %p = 0.95^^10^ = 0.60. This means, however, we now have a 40\% chance that one of these 10 tests will turn out significant, despite each individual test only being at the 5\% level. In order to guarantee that the overall significance test is still at the %\al level, we have to adapt the significance level %\al\'p of the individual test. This results in the following relation between the overall and the individual significance level: (1 - %\al\'p)^^%k%^ = 1 - %\al. This equation can easily be solved for %\al\'p: %\al\'p = 1 - (1-%\al)^^1/%k^, which for small %\al reduces to: %\al\'p = %\al / %k This is a very simple recipe: If you want an overall significance level %\al and you perform %k individual tests, simply divide %\al by %k to obtain the significance level for the individual tests. A box plot provides a simple graphical summary of data. These plots originate from the work of @@Tukey (1977)@. Definitions The following figure shows an annotated box plot. To understand the box plot we need the following definitions: %q25 = lower quartile, 25\% of the data lie below this value %q50 = median, 50\% of the data lie below this value %q75 = upper quartile, 25\% of the data lie above this value The following definitions all depend on these quantiles: %hspread = |%q75 \-- %q25| (50\% interval) %lowerOuterFence = %q25 \-- 3.0 * %hspread (not in figure) %lowerInnerFence = %q25 \-- 1.5 * %hspread (not in figure) %upperInnerFence = %q75 + 1.5 * %hspread %upperOuterFence = %q75 + 3.0 * %hspread %lowerWhisker = smallest data value larger then %lowerInnerFence %upperWhisker = largest data value smaller then %upperInnerFence The box plot is a summary of the data in which: \bu the horizontal lines of the rectangle correspond to %q25, %q50 and %q75, respectively. \bu the dotted line corresponds to the mean. \bu the outliers outside the %outerFences are drawn with an 'o'. \bu the outliers in the intervals (%lowerOuterFence, %lowerInnerFence) and (%upperInnerFence, %upperOuterFence) are drawn with an '*'. \bu the whisker lines outside the rectangle connect %q25 with %lowerWhisker, and, %q75 with %upperWhisker, respectively. With no outliers present, the whiskers mark minimum and/or maximum of the data. An object of type BarkFilter represents an acoustic time-frequency representation of a sound: the power spectral density %P(%z, %t), expressed in dB's. It is sampled into a number of points around equally spaced times %t__%i_ and frequencies %z__%j_ (on a Bark scale). Inside a BarkFilter With @Inspect you will see that this type contains the same attributes a @Matrix. The bootstrap data points are a random sample of size %n drawn %%with% replacement from the sample (%x__1_,...%x__n_). This means that the bootstrap data set consists of members of the original data set, some appearing zero times, some appearing once, some appearing twice, etc. More information can be found in @@Efron & Tibshirani (1993)@. An object of type Categories represents an ordered collection of categories. Each category is a simple text string. Categories commands Creation: \bu ##Create an empty Categories# \bu @@FFNet & Pattern: To Categories...@ Viewing and editing: \bu @CategoriesEditor Analysis: \bu @@Categories: To Confusion@ \bu @@Categories: Difference@ Synthesis \bu @@Categories: Append@ \bu ##Categories: Permute...# \bu ##Categories: To unique Categories# Inside a Categories With @Inspect you will see the following attributes: %size the number of simple categories. %item[] the categories. Each category is an object of type #SimpleString. A command to compute the difference between two selected @Categories objects. Behaviour Each element in the first object is compared with the corresponding object in the second object according to its compare method. The number of different %categories will be shown in the @@Info window@. A command to compute the @Confusion matrix from two selected @Categories objects. Algorithm A confusion matrix is constructed from both #Categories objects in the following way: The first Categories object is considered the stimulus Categories and its unique (sorted) categories form the row indices of the confusion matrix, the unique (sorted) categories of the second object form the column indices of this matrix. Next, each element in the first #Categories object is compared with the corresponding object in the second object and the element in the confusion matrix addressed by this pair is incremented by 1. You can choose this command after selecting 2 objects of type @Categories. A new object is created that contains the second object appended after the first. You can choose this command after selecting one #Categories. A @CategoriesEditor will appear on the screen, with the selected #Categories in it. An editor for manipulating @Categories. To make a selection, use the left mouse button. The Ctrl key extends a selection (discontinuously). The Shift key extends a selection contiguously. Any object that represents cepstral coefficients as a function of time. One of the @@types of objects@ in P\s{RAAT}. An object of type CCA represents the @@Canonical correlation analysis@ of two multivariate datasets. Commands \bu @@TableOfReal: To CCA...@ Get the probability that for the selected @CCA object the chosen canonical correlation coefficient is different from zero. Arguments %Index is the index of the canonical correlation coefficient that you want to test. Wilks' statistic: the probability that coefficient \ro__%index_ differs from zero is %probability = chiSquareQ (\ci^2, %ndf), where the %%number of degrees of freedom% parameter equals %ndf = (%n__y_ - %index +1)(%n__x_ - %index +1) and the chi-squared parameter is \ci^2 = \--(%numberOfObservations - (%n__y_ + %n__x_ +3)/2) log (\La__%index_), In the formulas above the variables %n__y_ and %n__x_ are the dimensions of the dependent and the independent data sets whose canonical correlations have been obtained, and Wilks' lambda is: \La__index_ = \Pi__%i=%index..min(%ny,%nx)_ (1 \-- \ro__%i_^^2^) Determine from the selected @CCA and @Correlation objects the correlations of the canonical variables with the original variables. These correlations are called %%canonical factor loadings%, or also %%structure correlation coefficients%. Determine from the selected @CCA and @TableOfReal objects the correlations of the canonical variables with the original variables. These correlations are called %%canonical factor loadings%, or also %%structure correlation coefficients%. Determines the scores on the dependent and the independent canonical variates from the selected @CCA and @TableOfReal objects. %%Number of canonical correlations% determines the dimension, i.e., the number of elements of the resulting canonical score vectors. The newly created table will have twice this number of columns because we have calculated score vectors for the dependent and the independent variates. The scores on the dependent set are determined as #T__%y_ #Y, where #T__%y_ is the dependent part in the table and #Y is a matrix with %numberOfCanonicalCorrelations eigenvectors for the dependent variate. The scores for the independent variates are then determined in an analogous way as #T__%x_ #X. The scores for the dependent data will be in the lower numbered columns, the scores for the independent part will be in the higher numbered columns of the newly created object. This tutorial will show you how to perform canonical correlation analysis with P\s{RAAT}. 1. Objective of canonical correlation analysis In canonical correlation analysis we try to find the correlations between two data sets. One data set is called the %dependent set, the other the %independent set. In P\s{RAAT} these two sets must reside into one @TableOfReal object. The lower numbered columns of this table will then be interpreted as the dependent part, the rest of the columns as the independent part. The dimension of, i.e., the number of columns in, the dependent part may not exceed the dimension of the independent part. As an example, we will use the dataset from @@Pols et al. (1973)@ with the frequencies and levels of the first three formants from the 12 Dutch monophthongal vowels as spoken in /h_t/ context by 50 male speakers. We will try to find the canonical correlation between formant frequencies (the %dependent part) and levels (the %independent part). The dimension of both groups of variates is 3. In the introduction of the @@discriminant analysis@ tutorial you can find how to get these data, how to take the logarithm of the formant frequency values and how to standardize them. The following script summarizes: Create TableOfReal (Pols 1973)... yes Formula... if col < 4 then log10 (self) else self endif Standardize columns Before we start with the %canonical correlation analysis we will first have a look at the %Pearson correlations of this table and calculate the @Correlation matrix. It is given by: F1 F2 F3 L1 L2 L3 F1 1 -0.338 0.191 0.384 -0.505 -0.014 F2 -0.338 1 0.190 -0.106 0.526 -0.568 F3 0.191 0.190 1 0.113 -0.038 0.019 L1 0.384 -0.106 0.113 1 -0.038 0.085 L2 -0.505 0.526 -0.038 -0.038 1 0.128 L3 -0.014 -0.568 0.019 0.085 0.128 1 The following script summarizes: select TableOfReal pols_50males To Correlation Draw as numbers... 1 0 decimal 3 The correlation matrix shows that high correlations exist between some formant frequencies and some levels. For example, the correlation coefficient between F2 and L2 equals 0.526. In a canonical correlation analysis of the dataset above, we try to find the linear combination %u__1_ of %F__1_, %F__2_ and %F__3_ that correlates maximally with the linear combination %v__1_ of %L__1_, %L__2_ and %L__3_. When we have found these %u__1_ and %v__1_ we next try to find a new combination %u__2_ of the formant frequencies and a new combination %v__2_ of the levels that have maximum correlation. These %u__2_ and %v__2_ must be uncorrelated with %u__1_ and %v__1_. When we express the above with formulas we have: %u__1_ = %y__11_%F__1_+%y__12_%F__2_ + %y__13_%F__3_ %v__1_ = %x__11_%L__1_+%x__12_%L__2_ + %x__13_%L__3_ \ro(%u__1_, %v__1_) = maximum, \ro(%u__2_, %v__2_) = submaximum, \ro(%u__2_, %u__1_) = \ro (%u__2_, %v__1_) = \ro (%v__2_, %v__1_) = \ro (%v__2_, %u__1_) = 0, where the \ro(%u__i_, %v__i_) are the correlations between the ##canonical variates# %u__i_ and %v__i_ and the %y__%ij_'s and %x__%ij_'s are the ##canonical coefficients# for the dependent and the independent variates, respectively. 2. How to perform a canonical correlation analysis Select the TableOfReal and choose from the dynamic menu the option @@TableOfReal: To CCA...|To CCA...@. This command is available in the "Multivariate statistics" action button. We fill out the form and supply 3 for %%Dimension of dependent variate%. The resulting CCA object will bear the same name as the TableOfReal object. The following script summarizes: To CCA... 3 3. How to get the canonical correlation coefficients You can get the canonical correlation coefficients by queries of the CCA object. You will find that the three canonical correlation coefficients, \ro(%u__1_, %v__1_), \ro(%u__2_, %v__2_) and \ro(%u__3_, %v__3_) are approximately 0.86, 0.53 and 0.07, respectively. The following script summarizes: cc1 = Get correlation... 1 cc2 = Get correlation... 2 cc3 = Get correlation... 3 printline cc1 = 'cc1', cc2 = 'cc2', cc3 = 'cc3' 4. How to obtain canonical scores Canonical #scores, also named canonical variates, are the linear combinations: %u__%i_ = %y__%i1_%F__1_+%y__%i2_%F__2_ + %y__%i3_%F__3_, and, %v__%i_ = %x__%i1_%L__1_+%x__%i2_%L__2_ + %x__%i3_%L__3_, where the index %i runs from 1 to the number of correlation coefficients. You can get the canonical scores by selecting a CCA object together with the TableOfReal object and choose @@CCA & TableOfReal: To TableOfReal (scores)...|To TableOfReal (scores)...@ When we now calculate the ##Correlation# matrix of these canonical variates we get the following table: u1 u2 u3 v1 v2 v3 u1 1 . . 0.860 . . u2 . 1 . . 0.531 . u3 . . 1 . . 0.070 v1 0.860 . . 1 . . v2 . 0.1 . . 1 . v3 . . 0.070 . . 1 The scores with a dot are zero to numerical precision. In this table the only correlations that differ from zero are the canonical correlations. The following script summarizes: select CCA pols_50males plus TableOfReal pols_50males To TableOfReal (scores)... 3 Draw as numbers if... 1 0 decimal 2 abs(self) > 1e-14 5. How to predict one dataset from the other @@CCA & TableOfReal: Predict...@ Additional information can be found in @@Weenink (2003)@. The Chebyshev polynomials %T__%n_(%x) of degree %n are special orthogonal polynomial functions defined on the domain [-1, 1]. Orthogonality: __-1_\in^^1^ %W(%x) %T__%i_(%x) %T__%j_(%x) %dx = \de__%ij_ %W(%x) = (1 \-- %x^^2^)^^\--1/2^ (-1 < x < 1) They obey certain recurrence relations: %T__%n_(%x) = 2 %x %T__%n-1_(%x) \-- %T__%n-2_(%x) %T__0_(%x) = 1 %T__1_(%x) = %x An object of type ChebyshevSeries represents a linear combination of @@Chebyshev polynomials@ %T__%k_(%x). ChebyshevSeries (%x) = \Si__%k=1..%numberOfCoefficients_ %c__%k_ %T__%k_(%x) A command to transform the selected @ChebyshevSeries object into a @@Polynomial@ object. We find polynomial coefficients %c__%k_ such that \Si__%k=1..%numberOfCoefficients_ %c__%k_ %x^^%k^ = \Si__%k=1..%numberOfCoefficients_ %l__%k_ %T__%k_(%x) We use the recurrence relation for @@Chebyshev polynomials@ to calculate these coefficients. An object of type ClassificationTable represents the result of a classification experiment. The numbers in a row show how well a particular input matches the classes represented by the column labels. The higher the number the better the match. The percentage of bivariate normally distributed data covered by an ellipse whose axes have a length of %numberOfSigmas\.c\si can be obtained by integration of the p.d.f. over an elliptical area. This results in the following equation as can be verified from equation 26.3.21 in @@Abramowitz & Stegun (1970)@: %percentage = (1 - exp (-%numberOfSigmas^^2^/2))\.c 100\% , where the %numberOfSigmas is the radius of the "ellipse": (%x/%\si__x_)^2 + (%y/%\si__y_)^2 = %numberOfSigmas^2. The %numberOfSigmas = 1 ellipse covers 39.3\% , the %numberOfSigmas = 2 ellipse covers 86.5\% and the %numberOfSigmas = 3 ellipse covers 98.9\% of the data. The confidence interval gives an estimated range of values which is likely to include an unknown population parameter. The estimated range is calculated from a given set of observations. Examples At the \al level of significance a two sided confidence interval for the true mean \mu for normally distributed data with mean %%mean% and known standard deviation %\si can be constructed as: %%mean% - %z__\al/2_ \si / \Vr%N \<_ \mu \<_ %%mean% + %z__\al/2_ \si / \Vr%N, where %z__\al/2_ = invGaussQ (\al/2) and %N is the number of observations. If the standard deviation is %not known, we have to estimate its value (%s) from the data and the formula above becomes: %%mean% - %t__%%\al/2;N%_ %s / \Vr%N \<_ \mu \<_ %%mean% + %t__%%\al/2;N%_ %s / \Vr%N, where %t__%%\al/2;N%_ = invStudentQ (%\al/2, %N-1). For %\al=0.05 and %N=20 we get %z__0.025_=1.96 and %t__0.025;20_=2.039. This shows that when we have to estimate the standard deviation from the data, the confidence interval is wider than when the standard deviation is known beforehand. The confidence level is the probability value 1-\al associated with a @@confidence interval@, where \al is the level of significance. It can also be expressed as a percentage 100(1-\al)\% and is than sometimes called the %%confidence coefficient%. An object of type Confusions represents a confusion matrix, with stimuli as row labels and responses as column labels. The entry at position [%i][%j] represents the number of times response %j was given to the stimulus %i. Creating a Confusion from data in a text file Suppose you have two objects A and B. In one way or another, you have acquired the following confusions: %\de__%AA_ = 6, %\de__%AB_ = 2 , %\de__%BA_ = 1, and %\de__%BB_ = 7. You can create a simple text file like the following: "ooTextFile" ! to make Praat recognize your file "Confusion" ! The line that tells Praat about the contents 2 "A" "B" ! Number of columns, and column labels 2 ! Number of rows "A" 6 2 ! Row label A, A-A value, A-B value "B" 1 7 ! Row label B, B-A value, B-B value This text file can be read with the @@Read from file...@ command. \bu @@Categories: To Confusion Drawing \bu ##Draw as numbers... \bu ##Draw as squares... Query \bu ##Get column mean (index)... \bu ##Get column mean (label)... \bu ##Get column stdev (index)... \bu ##Get column stdev (label)... \bu @@Confusion: Get fraction correct|Get fraction correct Modification \bu ##Formula... \bu ##Remove column (index)... \bu ##Insert column (index)... \bu ##Set row label (index)... \bu ##Set row label (label)... \bu ##Set column label (index)... \bu ##Set column label (label)... \bu @@Confusion: To Similarity...@ \bu @@Confusion: To Dissimilarity (pdf)...@ Inside a Confusion %numberOfRows the number of stimuli. %numberOfColumns the number of responses. %rowLabels the names of the stimuli. columnLabels the names of the responses. Groups row and column labels of the selected @Confusion object in order to reduce its dimension. %Search the pattern to match %Replace the pattern that replaces the match(es) %%Replace limit% limits the maximum number of times that a match/replace cycle may occur within each label. %Search and replace are defines whether the search and replace strings are taken litterally or as a @@Regular expressions|regular expression@. First all row and column labels are changed according to the search and replace specification. Next all rows or columns that have the same labels are summed. A @@query@ to ask the selected @Confusion matrix for the fraction of correct classifications. The "fraction correct" is defined as the quotient of the number of correct classifications and the sum of the entries in the matrix. Correct classifications have identical row and column labels. A new @TableOfReal object is created from the selected @Confusion object with one extra row and column. The first element of the extra row will contain the sum of the confusions in the the first %column, the first element of the extra column will contain the sum of the confusions in the the first %row, etc... The bottom-right element will contain the sum of all confusions. An object of type Correlation represents the correlation coefficients of a multivariate data set. Calculates @@confidence interval@s for the correlation coefficients from the selected @Correlation object(s) and saves these intervals in a new @TableOfReal object. %%Confidence level% the @@confidence level@ you want for the confidence intervals. %%Number of tests% determines the @@Bonferroni correction@ for the significance level. If the default value (zero) is chosen, it will be set equal to the number of correlations involved (a matrix of dimension %n has %n\.c(%n-1)/2 correlations). %%Approximation% defines the approximation that will be used to calculate the confidence intervals. It is either Fisher's z transformation or Ruben's transformation. According to @@Boomsma (1977)@, Ruben's approximation is more accurate than Fisher's. We obtain intervals by the large-sample conservative multiple tests with Bonferroni inequality and the Fisher or Ruben transformation. We put the upper values of the confidence intervals in the upper triangular part of the matrix and the lower values of the confidence intervals in lower triangular part of the resulting TableOfReal object. In %%Fisher's approximation%, for each element %r__%ij_ of the correlation matrix the confidence interval is: #[ tanh (%z__%ij_ - %z__%\al\'p_ / \Vr(%N - 3)) , tanh (%z__%ij_ + %z__%\al\'p_ / \Vr(%N - 3)) #], where %z__%ij_ is the Fisher z-transform of the correlation %r__%ij_: %z__%ij_ = 1/2 ln ((1 + %r__%ij_) / (1 - %r__%ij_)), %z__%\al\'p_ the Bonferroni corrected %z-value %z__%\al/(2\.c%numberOfTests)_, %\al = 1 - %confidenceLevel, and %N the number of observations that the correlation matrix is based on. In %%Ruben's approximation% the confidence interval for element %r__%ij_ is: #[ %x__1_ / \Vr(1 - %x__1_^2), %x__2_ / \Vr(1 - %x__2_^2) #] in which %x__1_ and %x__2_ are the smallest and the largest root from %a %x^^2^ + %b %x + %c = 0, with %a = 2%N - 3 - %z__%\al\'p_^^2^ %b = - 2 %r\'p \Vr((2%N - 3)(2%N - 5)) %c = (2%N - 5 - %z__%\al\'p_^^2^) %r\'p^^2^ - 2%z__%\al\'p_^^2^, and %r\'p = %r__%ij_ / \Vr(1 - %r__%ij_^2), An object of type Covariance represents the sums of squares and cross products of a multivariate data set divided by the number of observations. An object of type Covariance contains the same attributes as an object of type @SSCP. Since an object of type Covariance contains the mean values (the centroids), the covariances as well as the number of observations it has all the information necessary to be the subject of all kinds of statistical tests on means and variances. You can choose this command after selecting two objects of type @Covariance. We test the hypothesis that the samples that gave rise to the two covariance matrices #%M__1_ and #%M__2_, were drawn from the same distribution. The test statistic is %L\'p which is distributed as a \ci^2 variate with %p(%p+1)/2 degrees of freedom. %L\'p = %L \.c (1 \-- (2%p + 1 \-- 2 / (%p + 1)) / (6 \.c ( %N \-- 1))), where, %L = (%N \-- 1) \.c (ln determinant (#%M__1_) \-- ln determinant (#%M__2_)) + trace (#%M__2_ \.c #%M__1_^^\--1^) \-- %p), %p is dimension of covariance matrix and %N is the number of observations underlying the covariance matrix. For more details on this test, see e.g. page 292 of @@Morrison (1990)@. Gets the level of significance for one mean from the selected @Covariance object being different from a hypothesized mean. the position of the element in the means vector (centroid) that you want to test. %%Value the hypothesized mean %\mu (see below). This is the standard test on means when the variance is unknown. The test statistic is %t = (%mean - %\mu) \Vr%(N / %s^2), which has the Student %t distribution with %ndf = %N-1 degrees of freedom. In the formulas above, %mean is the element of the mean vector at position %index, %\mu is the hypothesized mean, %N is the number of observations, %s^2 is the variance at position [%index][%index] in the covariance matrix. The returned probability %p is the %%two-sided% probability %p = 2 * studentQ (%t, %ndf) A low probability %p means that the difference is significant. A command to ask the selected @Covariance object for the fraction of the total variance that is accounted for by the selected dimension(s). %%From dimension%, %%To dimension% define the range of components. By choosing both numbers equal, you get the fraction of the variance "explained" by that dimension. Details The total variance is the sum of the diagonal elements of the covariance matrix #C, i.e., its trace. The fraction is defined as: \Si__%i=%from..%to_ %%C__ii_% / \Si__%i=1..%numberOfRows_ %%C__ii_% Gets the level of significance for the %difference of two means from the selected @Covariance object being different from a hypothesized value. %%Index1, Index2 the positions of the two elements of the means vector whose difference is compared to the hypothesized difference. the hypothesized difference (%\mu). %%Paired samples determines whether we treat the two means as being dependent. %%Equal variances determines whether the distribution of the difference of the means is a Student t-distribution (see below). This is Student's t-test for the significance of a difference of means. The test statistic is: %t = (%mean__1_ - %mean__2_ - %\mu) \Vr (%N / %s^2) with %ndf degrees of freedom. In the formula above %mean__1_ and %mean__2_ are the elements of the means vector, %\mu is the hypothesized difference and %N is the number of observations. The value that we use for the (combined) variance %s^2 is: %s^2 = %var__1_ + %var__2_ - 2 * %covar__12_, when the samples are %paired, and %s^2 = %var__1_ + %var__2_ when they are not. The %var__1_ and %var__2_ are the variance components for %mean__1_ and %mean__2_, respectively, and %covar__12_ is their covariance. When we have %%paired samples% we assume that the two variances are not independent and their covariance is subtracted, otherwise their covariance is not taken into account. Degrees of freedom parameter %ndf usually equals 2(%N-1). If the two variances are significantly different, the statistic %t above is only %approximately distributed as Student's %t with degrees of freedom equal to: %ndf = (%N-1) \.c (%var__1_ + %var__2_)^2 / (%var__1_^2 + %var__2_^2). The returned probability %p will be the %%two-sided% probability Gets the probability for one variance from the selected @Covariance object being different from a hypothesized variance. the position of the variance element. %%Hypothesized variance the hypothesized variance \si^2 The test statistic %\ci^2 = (%N-1)%s^2 / \si^2, is distributed as a chi-squared variate with %ndf = %N-1 degrees of freedom. The returned probability %p will be %p = chiSquareQ (%\ci^2, %ndf) Gets the probability for the ratio of two variances from the selected @Covariance object being different from a hypothesized ratio. %%Index1, index2 determine the variances %%Hypothesized ratio the hypothesized ratio %F %f = %s__1_^2 / %s__2_^2 / %ratio is distributed as Fisher's F distribution with %ndf__1_ = %N-1 and %ndf__2_ = %N-1 degrees of freedom for the numerator and denominator terms, respectively. %p = 2 * fisherQ (%f, %ndf__1_, %ndf__2_) If %s__2_^2 > %s__1_^2 we use 1/%f to determine the probability. Generate a @TableOfReal object by random sampling from a multi-variate normal distribution whose @Covariance matrix is the selected object. %%Number of data points determines the number of data points that will be generated. Each data point occupies one row in the generated table. The algorithm proceeds as follows: 1. Calculate the eigenvalues $v__%i_ and eigenvectors %#e__%i_ of the %m \xx %m Covariance matrix. In general there will also be %m of these. Let #%E be the %m \xx %m matrix with eigenvector %#e__%j_ in column %j (%j=1..%m). 2. Generate a vector #x whose elements %x__%k_ equal %x__%k_ = randomGauss (0, \Vr (%v__%k_)). Each %x__%k_ is a random deviate drawn from a Gaussian distribution with mean zero and standard deviation equal to the square root of the corresponding eigenvalue %v__%k_. 3. Calculate the vector #y = #%E #x, obtained by multiplying the vector #x with the matrix #%E. 4. Add the centroid to #y and copy the elements of #y to the corresponding row of the TableOfReal object. 5. Repeat steps 2, 3 and 4 until the desired number of data points has been reached. 6. Copy the column labels from the Covariance object to the TableOfReal object. Extract those rows from the selected @TableOfReal object whose Mahalanobis distance, with respect to the selected @Covariance object, are within the quantile range. A command to create a @ChebyshevSeries from a list of coefficients. %Xmin, %Xmax define the domain of the polynomials. %Coefficients define the coefficients of each @@Chebyshev polynomials|Chebyshev polynomial@. The coefficient of the polynomial with the highest degree comes last. A command to create an @ISpline from a list of coefficients. define the domain of the polynomial @spline. %Degree defines the degree of the polynomial @spline. define the coefficients of the basis polynomials. %%Interior knots define the positions in the domain where continuity conditions are defined. The number of coefficients and the number of interior knots must satisfy the following relation: %numberOfCoefficients = %numberOfInteriorKnots + %degree A command to create an @MSpline from a list of coefficients. %numberOfCoefficients = %numberOfInteriorKnots + %degree + 1 A command to create an @Polynomial from a list of coefficients. define the domain of the polynomial. defines the degree of the basis polynomials. define the coefficients of the polynomial. The coefficient of the highest power of %x comes last. A command to create a @LegendreSeries from a list of coefficients. define the coefficients of each @@Legendre polynomials|Legendre polynomial@. The coefficient of the polynomial with the highest degree comes last. A command to create a @Sound as a @@gamma-tone@. %Name the name of the resulting Sound object. %%Minimum time%, %%Maximum time% (s) the start and end time of the resulting Sound. %%Sampling frequency% (Hz) the @@sampling frequency@ of the resulting Sound. %Gamma the exponent of the polynomial. %Frequency (Hz), %Bandwidth (Hz) determine the frequency and damping of the cosine wave in the gamma-tone. %%Initial phase% (radians) the initial phase of the cosine wave. %%Addition factor% (default: 0) determines the degree of asymmetry in the spectrum of the gamma-tone. The zero default value gives a gamma-tone. A value unequal to zero results in a so called %gamma-chirp. A negative value is used in auditory filter modeling to guarantee the usual direction of filter asymmetry, which corresponds to an upward glide in instantaneous frequency. %%Scale amplitudes determines whether the amplitudes will be scaled to fit in the range (-1, 1). Purpose to create a Sound according to the following formula: %t^^%\ga\--1^ e^^\--2%\pi\.c%bandwidth\.c%t^ cos (2%%\pi\.cfrequency\.ct% + %additionFactor\.cln(%t) + %initialPhase), The %gamma %chirp function has a monotonically frequency-modulated carrier (the chirp) with instantaneous frequency %instantaneousFrequency(%t) = %frequency + %additionFactor / (2\.c\pi\.c%t) and an envelope that is a gamma distribution function. It is a theoretically optimum auditory filter, in the sense that it leads to minimal uncertainty in the joint time and scale representation of auditory signal analysis. For faithful modelling of the inner ear, @@Irino & Patterson (1996)@ conclude that a value of approximately 1.5 * ERB (%frequency) is appropriate for %bandwidth. ERB stands for @@equivalent rectangular bandwidth@. Their formula for ERB is: ERB(%f) = 6.23 10^^\--6^ %f^2 + 93.39 10^^\--3^ %f + 28.52. To avoid @aliasing in the chirp sound, a sound is only generated during times where the instantaneous frequency is greater than zero and smaller than the @@Nyquist frequency@. One of the commands that create a @Sound. %%Lowest frequency% (Hz) the frequency of the lowest component in the tone complex. %%Number of components% the number of frequency components in the tone complex. %%Frequency change% (semitones/s) determines how many semitones the frequency of each component will change in one second. The number of seconds needed to change one octave will then be 12 divided by this number. You can make rising, falling and monotonous tone complexes by chosing a positive, negative or zero value. %%Amplitude range% (dB) determines the relative size in decibels of the maximum and the minimum amplitude of the components in a tone complex. These relative amplitudes will then be 10^^\--%amplitudeRange/20^. %%Octave shift fraction% [0,1)] shifts all frequency components by this fraction at the start. You will probably only need this if you want to generate static tone complexes as the example script below shows. To create a Sound that is a continuous variant of the sound sequences used by @@Shepard (1964)@ in his experiment about the circularity in judgments of relative pitch. The tone consists of many sinusoidal components whose frequencies might increase exponentially in time. All frequencies are always at successive intervals of an octave and sounded simultaneously. Thus the frequency of each component above the lowest is at each moment in time exactly twice the frequency of the one just below. The amplitudes are large for the components of intermediate frequency only, and tapered off gradually to subthreshold levels for the components at the highest and lowest extremes of frequency. For a rising tone complex, the Sound is generated according to the following specification: %s(%t) = \su__%i=1..%numberOfComponents_ %A__%i_(%t) sin (arg__%i_(%t)), where arg__%i_(%t) = \in 2%\pi f__%i_(%\ta) %d\ta , and f__%i_(%t) = %lowestFrequency \.c 2^^(%i \-- 1 + octaveShiftFraction + %t/(12/%frequencyChange_st)^, with %A__%i_(%t) = 10^^((%L__min_ + (%L__max_ \-- %L__min_) (1 \-- cos 2%\pi%\te__%i_(%t)) / 2) / 20)^, where, %L__max_ = 0, %L__min_ = 10^^\--%amplitudeRange/20^, and, %\te__%i_(%t) = 2\pi log2 (%f(%t) / %lowestFrequency) / %numberOfComponents. The maximum frequency that can be reached during a sweep by any single tone is: %maximumFrequency = %lowestFrequency\.c2^^%numberOfComponents^. A component that reaches the maximum frequency falls instantaneously to the lowest frequency and then starts rising again. The absolute @@sound pressure level@ of the resulting sound will not be set, it is only guaranteed that the peak value is just below 1. You can always scale the intensity with the ##Scale Intensity...# command. Example The following script generates 12 static Shepard tone complexes, 1 semitone 'apart', with a cosine window to temper the abrupt start and finish. twin = 0.010 fwin = 1 / (2 * twin) for i to 12 fraction = (i-1)/12 Create Sound from Shepard tone... s'i' 0 0.1 22050 4.863 10 0 34 'fraction' Formula... if x<twin then self*(1+cos(2*pi*fwin*(x+twin)))/2 else self fi Formula... if x>xmax-twin then self*(1+cos(2*pi*fwin*(x-xmax+twin)))/2 else self fi endfor A command to create a @Table object filled with the fundamental frequency and the first three formant frequency values from 10 American-English monophthongal vowels as spoken in a /h_d/ context by 76 speakers (33 men, 28 women and 15 children). Every vowel was pronounced twice, so that there are 1520 recorded vowels in total. Table layout The created table will contain 9 columns: Column 1, labelled as %Type speaker type: "m", "w" or "c" (for %man, %women or %child). Column 2, labelled as %Sex speaker sex: either "m" or "f" (for %male or %female). Column 3, labelled as %Speaker speaker id: a number from 1 to 76. Column 4, labelled as %Vowel the vowel name. The following list gives the vowel in a %h_d context word together with its representation in this column: (%heed, iy), (%hid, ih), (%head, eh), (%had, ae), (%hod, aa), (%hawed, ao), (%hood, uh), (%%who'd%, uw), (%hud, ah), (%heard, er). Column 5, labelled as %IPA the IPA notation for the vowels. Column 6, labelled as %F0 the fundamental frequency in Hertz. Column 7, 8 and 9, labelled as %F1, %F2 and %F3 the frequencies in Hertz of the first three formants. We originally downloaded the data from a University of Pennsylvania FTP site, where they were reportedly based on a printed version supplied by Ignatius Mattingly. More details about these data and how they were measured can be found in @@Peterson & Barney (1952)@. A command to create a @Table object filled with the frequencies and the levels of the first three formants from the 12 Dutch monophthong vowels as spoken in /h_t/ context by 50 male and 25 female speakers. The created table will contain 10 columns Column 1, labeled as %Sex speaker sex: Either "m" or "f" (for %male or %female). Column 2, labeled as %Speaker speaker id: a number from 1 to 75. Column 3, labeled as %Vowel the vowel name. The following list gives the vowel in p_t context word together with its representation in this column: (%poet, oe), (%paat, aa), (%poot, oo), (%pat, a), (%peut, eu), (%piet, ie), (%puut, uu), (%peet, ee), (%put, u), (%pet, e), (%pot, o), (%pit, i). Column 4, labeled as %IPA the IPA-notation for the vowels Column 5, 6 and 7, labeled as %F1, %F2 and %F3 Column 8, 9 and 10, labeled as %L1, %L2 and %L3 the levels in decibel below overall SPL of the first three formants. More details about these data and how they were measured can be found in @@Pols et al. (1973)@ and @@Van Nierop et al. (1973)@. A command to create a @Table object filled with the fundamental frequency and the first three formant frequency values from 12 Dutch monophthongal vowels as spoken in isolation by 30 speakers (10 men, 10 women and 10 children). Every vowel was pronounced only once, so that there are 360 recorded vowels in total. A reduced form, with only the formant frequecy values, is also available as a @@Create TableOfReal (Weenink 1985)...|TableOfReal@. the vowel name. The following list gives the vowel in Dutch p_t context words together with its representation in this column: (%poet, oe), (%paat, aa), (%poot, oo), (%pat, a), (%peut, eu), (%piet, ie), (%puut, uu), (%peet, ee), (%put, u), (%pet, e), (%pot, o), (%pit, i). the frequencies in Hertz of the first three formants. The formant frequency values have been determined by means of LPC analysis with a varying prediction order. See @@Weenink (1985)@. A command to create a @TableOfReal filled with the first three formant frequency values and (optionally) the levels from the 12 Dutch monophthongal vowels as spoken in /h_t/ context by 50 male speakers. The first three columns will contain the frequencies in Hz, the next three columns the levels in decibels below the overall SPL of the measured vowel segment. Each row will be labelled with its corresponding vowel symbol. More details about these data and how they were measured can be found in the paper of @@Pols et al. (1973)@. A command to create a @TableOfReal filled with the first three formant frequency values and (optionally) the levels from the 12 Dutch monophthongal vowels as spoken in /h_t/ context by 25 female speakers. More details about these data and how they were measured can be found in the paper of @@Van Nierop et al. (1973)@. A command to create a @TableOfReal filled with the first three formant frequency values from the 12 Dutch monophthongal vowels as spoken in isolation by either 10 men or 10 women or 10 children. The three columns will contain the formant frequencies in Hz. Each row will be labelled with its corresponding vowel symbol. More details about these data and how they were measured can be found in the paper of @@Weenink (1985)@. An object of type Discriminant represents the discriminant structure of a multivariate data set with several groups. This discriminant structure consists of a number of orthogonal directions in space, along which maximum separability of the groups can occur. \bu @@Discriminant analysis@ tutorial \bu @@TableOfReal: To Discriminant@ \bu Draw eigenvalues... \bu Draw eigenvector... \bu @@Discriminant: Draw sigma ellipses...|Draw sigma ellipses...@ This tutorial will show you how to perform discriminant analysis with P\s{RAAT} As an example, we will use the dataset from @@Pols et al. (1973)@ with the frequencies and levels of the first three formants from the 12 Dutch monophthongal vowels as spoken in /h_t/ context by 50 male speakers. This data set has been incorporated into P\s{RAAT} and can be called into play with the @@Create TableOfReal (Pols 1973)...@ command that can be found in the "New / TableOfReal" menu. In the list of objects a new TableOfReal object will appear with 6 columns and 600 rows (50 speakers \xx 12 vowels). The first three columns contain the formant frequencies in Hz, the last three columns contain the levels of the first three formants given in decibels below the overall sound pressure level of the measured vowel segment. Each row is labelled with a vowel label. Pols et al. use logarithms of frequency values, we will too. Because the measurement units in the first three columns are in Hz and in the last three columns in dB, it is probably better to standardize the columns. The following script summarizes our achievements up till now: Formula... if col < 4 then log10 (self) else self fi \# change the column labels too, for nice plot labels. Set column label (index)... 1 standardized log (\% F\_ \_ 1\_ ) Set column label (index)... 2 standardized log (\% F\_ \_ 2\_ ) Set column label (index)... 3 standardized log (\% F\_ \_ 3\_ ) Set column label (index)... 4 standardized \% L\_ \_ 1\_ Set column label (index)... 5 standardized \% L\_ \_ 2\_ Set column label (index)... 6 standardized \% L\_ \_ 3\_ To get an indication of what these data look like, we make a scatter plot of the first standardized log-formant-frequency against the second standardized log-formant-frequency. With the next script fragment you can reproduce the following picture. Viewport... 0 5 0 5 Draw scatter plot... 1 2 0 0 -2.9 2.9 -2.9 2.9 10 y + y Apart from a difference in scale this plot is the same as fig. 3 in the Pols et al. article. 1. How to perform a discriminant analysis Select the TableOfReal and choose from the dynamic menu the option @@TableOfReal: To Discriminant|To Discriminant@. This command is available in the "Multivariate statistics" action button. The resulting Discriminant object will bear the same name as the TableOfReal object. The following script summarizes: To Discriminant 2. How to project data on the discriminant space You select a TableOfReal and a Discriminant object together and choose: @@Discriminant & TableOfReal: To Configuration...|To Configuration...@. One of the options of the newly created Configuration object is to draw it. The following picture shows how the data look in the plane spanned by the first two dimensions of this Configuration. The directions in this configuration are the eigenvectors from the Discriminant. plus Discriminant pols_50males To Configuration... 0 Draw... 1 2 -2.9 2.9 -2.9 2.9 12 y + y If you are only interested in this projection, there also is a short cut without an intermediate Discriminant object: select the TableOfReal object and choose @@TableOfReal: To Configuration (lda)...|To Configuration (lda)...@. 3. How to draw concentration ellipses Select the Discriminant object and choose @@Discriminant: Draw sigma ellipses...|Draw sigma ellipses...@. In the form you can fill out the coverage of the ellipse by way of the %%Number of sigmas% parameter. You can also select the projection plane. The next figure shows the 1-%\si concentration ellipses in the standardized log %F__1_ vs log %F__2_ plane. When the data are multinormally distributed, a 1-%\si ellipse will cover approximately 39.3\% of the data. The following code summarizes: select Discriminant pols_50males Draw sigma ellipses... 1.0 no 1 2 -2.9 2.9 -2.9 2.9 12 yes 4. How to classify Select together the Discriminant object (the classifier), and a TableOfReal object (the data to be classified). Next you choose @@Discriminant & TableOfReal: To ClassificationTable...|To ClassificationTable@. Normally you will enable the option %%Pool covariance matrices% and the pooled covariance matrix will be used for classification. The ClassificationTable can be converted to a @Confusion object and its fraction correct can be queried with: @@Confusion: Get fraction correct@. In general you would separate your data into two independent sets, \s{TRAIN} and \s{TEST}. You would use \s{TRAIN} to train the discriminant classifier and \s{TEST} to test how well it classifies. Several possibilities for splitting a dataset into two sets exist. We mention the @@Jackknife|jackknife@ ("leave-one-out") and the @@Bootstrap|bootstrap@ methods ("resampling"). A command to draw for each group from the selected @Discriminant an ellipse that covers part of the multivariate data. %%Number of sigmas determines the @@concentration ellipse|data coverage@. %%Discriminant plane When on, the selected %X and %Y-dimension will refer to the eigenvectors of the discriminant space, and, consequently, the projection of the hyper ellipsoid onto the space spanned by these eigenvectors will be drawn. When off, the selected %X and Y-dimension will refer to the original dimensions. %Xmin, %Xmax, %Ymin, %Ymax determine the limits of the drawing area. %%Label size determines the size of the labels at the centre of the ellipse. No labels will be drawn when a value less than or equal to zero is chosen. Extract the @SSCP for group %%index% from the selected @Discriminant object. Extract the pooled within-group @SSCP from the selected @Discriminant object. A command to test the selected @Discriminant for the significance of discrimination afforded by the remaining %n\--%k eigenvectors after the acceptance of the first %k eigenvectors. The test statistic is: %\ci^2 = \--(%degreesOfFreedom\--(%numberOfGroups+%dimension)/2) ln \La\'p, where %degreesOfFreedom = (%dimension\--%k)(%numberOfGroups\--%k\--1), and, \La\'p = \Pi__%j=%k+1..%numberOfEigenvalues_ 1 / (1 + %%eigenvalue[j]%) A command to ask the selected @Discriminant for the contribution of the %j^^th^ discriminant function (component) to the total variance. The contribution is defined as: %%eigenvalue[j]% / \Si__%i=1..%numberOfEigenvalues_ %%eigenvalue[i]% A command to ask the selected @Discriminant for the value of Wilks' lamda (a multivariate measure of group differences over several variables). %From the first eigenvalue number from which the value for lambda has to be calculated. Wilks' lambda is defined as: %\La = \Pi__%i=%from..%numberOfEigenvalues_ 1 / (1 + %eigenvalue[%i]) Because lambda is a kind of %inverse measure, values of lambda which are near zero denote high discrimination between groups. A command to query the @Discriminant object for the area of the concentration ellipse of one of its groups. When on, the selected %X and %Y-dimension will refer to the eigenvectors of the discriminant space, and, consequently, the area of the projection of the hyper ellipsoid onto the space spanned by these eigenvectors will be calculated. When off, the selected %X and Y-dimension will refer to the original dimensions. See @@SSCP: Get sigma ellipse area... A command to query the @Discriminant object for the area of the confidence ellipse of one of its groups. See @@SSCP: Get confidence ellipse area... A command to use the selected @Discriminant to classify each pattern from the selected @Pattern into a category. Arguments as in @@Discriminant & TableOfReal: To ClassificationTable...@. A command to project the selected @SSCP object on the eigenspace defined by the selected @Discriminant object. Further details can be found in @@Eigen & SSCP: Project@ A command to use the selected @Discriminant to classify each row from the selected @TableOfReal. The newly created @ClassificationTable will then contain the posterior probabilities of group membership. %%Pool covariance matrices when on, all group covariance matrices are pooled and distances will be determined on the basis of only this pooled covariance matrix (see below). The posterior probabilities of group membership %p__%j_ for a vector #x are defined as: %p__%j_ = %p(%j\| #%x) = exp (\--%d__%j_^^2^(#%x) / 2) / \su__%k=1..%numberOfGroups_ exp (\--%d__%k_^^2^(#%x) / 2), where %d__%i_^^2^ is the generalized squared distance function: %d__%i_^^2^(#%x) = ((#%x\--#%\mu__%i_)\'p #\Si__%i_^^-1^ (#%x\--#%\mu__%i_) + ln determinant (#\Si__%i_)) / 2 \-- ln %aprioriProbability__%i_ that depends on the individual covariance matrix #\Si__%i_ and the mean #%\mu__%i_ for group %i. When the covariances matrices are %pooled, the squared distance function can be reduced to: %d__%i_^^2^(#%x) = ((#%x\--#%\mu__%i_)\'p #\Si^^-1^ (#%x\--#%\mu__%i_) \-- ln %aprioriProbability__%i_, and #\Si is now the pooled covariance matrix. The a priori probabilities normally will have values that are related to the number of %training vectors %n__%i_ in each group: %aprioriProbability__%i_ = %n__%i_ / \Si__%k=1..%numberOfGroups_ %n__%k_ A command to project each row in the selected @TableOfReal onto a space spanned by the eigenvectors of the selected @Discriminant. %%Number of dimensions specifies the number of eigenvectors taken into account, i.e., determines the dimension of the resulting @Configuration. When the default value (0) is given the resulting Configuration will have the maximum dimension as allowed by the number of eigenvectors in the selected Discriminant. Precondition The number of columns in the TableOfReal must equal the dimension of the eigenvectors in the Discriminant. See also @@Eigen & TableOfReal: Project...@. An object of type DTW represents the dynamic time warp structure of two objects. \bu @@CC: To DTW...@ (from 2 objects with cepstral coefficients) \bu ##Spectrogram: To DTW...# (from 2 Spectrogram objects) Query: \bu @@DTW: Get time along path...@ Finds the optimal path for the selected @DTW satisfying constraints within a Sakoe-Chiba band. %%Adjustment window duration The maximum distance from the start of the sound that a path may start. This is the parameter that determines the @@Sakoe & Chiba (1978)@ band. %%Adjustment window includes end determines whether the adjustment window includes the endpoint. When off and when the durations of the two objects in the DTW differ by more than the adjustment window duration, the last part of the longest object cannot be matched at all. %%X weight, Y weight, Diagonal weight determine the weights in the cumulative distance calculation. To visualize the Sakoe-Chiba band, select a DTW and chose @@DTW: To Polygon (band)...|To Polygon (band)...@. Next select ##Draw...# (don't forget to make the drawing domains equal to the domains of the two objects in the DTW). For more information see the article of @@Sakoe & Chiba (1978)@. Finds the optimal path for the selected @DTW satisfying slope constraints. %%Non-diagonal steps, Diagonal steps implement a slope constraint. Every %%nonDiagonalSteps% steps in a X or Y direction must be followed by at least %%diagonalSteps% steps in the diagonal direction. By chosing %nonDiagonalSteps = 0 you explicitly forbid non-diagonal steps, while %diagonalSteps = 0 does not impose any slope constraints at all. For the constraint 1/2 <= slope <= 2, set %nonDiagonalSteps = 2 and %diagonalSteps = 1. For the constraint 1/3 <= slope <= 3, set %nonDiagonalSteps = 3 and %diagonalSteps = 1. To visualize the slope constraints, select a DTW and chose @@DTW: To Polygon (slopes)...|To Polygon (slopes)...@. Next select ##Draw...# (don't forget to make the drawing domains equal to the domains of the two objects in the DTW). Get the maximum number of consecutive steps in the chosen direction along the optimal path from the selected @DTW. Queries the selected @DTW object for the time along the minimal path given the time along the "x-direction". %Time the time along the "x-direction". %%In case of ambiguity choose%, determines which time to return when several possibilities exist. Ambiguity arises when the path at chosen time frame has insertions (a plot of the path will then show a line parallel to the y-direction in this time frame). The options %highest and %lowest return the highest and lowest value of this parallell line. With no insertions present, the returned times will be exactly equal for both options. When the %input time is in the interval [%xmin, %xmax], the %returned time will be in the interval [%ymin, %ymax], where [%xmin, %xmax] and [%ymin, %ymax] are the domains of the two "objects" from which the DTW-object was constructed.For all other input times we assume that the two object are aligned. The returned time value will therefore simply equal the input time. Swap the x and y-axes of the selected @DTW. A command to convert for a selected @DTW the Sakoe-Chiba band, as implemented by the window adjustment duration parameter, to a @Polygon object. The polygon shows the boundaries of the search domain for the optimal path. A command to convert for a selected @DTW the slope constraints to a @Polygon object. The polygon shows the boundaries of the search domain for the optimal path. An object of type Eigen represents the eigen structure of a matrix whose eigenvalues and eigenvectors are real. Inside an Eigen %numberOfEigenvalues the number of eigenvalues and eigenvectors %dimension the dimension of an eigenvector. %eigenvalues[1..%numberOfEigenvalues] the real eigenvalues. %eigenvectors[1..%numberOfEigenvalues][1..%dimension] the real eigenvectors, stored by row. A command to draw the eigenvalues of the selected @Eigen object(s). %%Fraction of eigenvalues summed% defines whether or not fractions are plotted. Fractions %f__%i_ will be calculated for each number %e__%i_ by dividing this number by the sum of all numbers %e__%j_: %f__%i_ = %e__%i_ / \su__%j=1..%numberOfEigenvalues_ %e__%j_. %%Cumulative% defines whether or not cumulative values are plotted. Cumulative values %c__%i_ will be calculated for each number %e__%i_ by summing the first %i numbers %e__%j_: %c__%i_ = \su__%j=1..%i_ %e__%j_). A @@Scree plot|scree@ plot can be obtained if both %%Fraction of eigenvalues summed% and %%Cumulative% are unchecked. A command to draw an eigenvector from the selected @Eigen. %Eigenvector %number determines the eigenvector to be drawn. %Component %loadings when on, the eigenvector is multiplied with the square root of the corresponding eigenvalue. (For @@PCA@-analysis this means that you will draw the so called %%component loading vector%. You will be able to compare quantitatively the elements in different component loading vectors because the %i-th element in the %j-th component loading vector gives the covariance between the %i-th original variable and the %j-th principal component.) %%Element range% determine the first and last element of the vector that must be drawn. %Minimum, %Maximum determine the lower and upper bounds of the plot (choosing Maximum < Minimum will draw the %%inverted% eigenvector). %Mark %size, %Mark %string determine size and type of the marks that will be drawn. %Garnish determines whether a bounding box and margins will be drawn. A command to ask the selected @Eigen for the contribution of the %j^^th^ eigenvalue to the total sum of eigenvalues. A command to ask the selected @Eigen for the contribution of the sum of the eigenvalues[%from..%to] to the total sum of eigenvalues. \Si__%i=%from..%to_ %%eigenvalue[i]% / \Si__%i=1..%numberOfEigenvalues_ %%eigenvalue[i]% A command to query the selected @Eigen for the %i^^th^ eigenvalue. A command to query the selected @Eigen for the %j^^th^ element of the %i^^th^ eigenvector. A command to project the columns of the @Matrix object onto the eigenspace of the @Eigen object. %%Number of dimensions%, defines the dimension, i.e., the number of rows, of the resulting object. Project each column of the Matrix on the coordinate system given by the eigenvectors of the Eigen object. This can be done as follows: %y__%ji_ = \Si__%k=1..%numberOfColums_ %e__jk_ %x__%ki_, where %y__%ji_ is the %j-th element of the %i-th column of the resulting (matrix) object, %e__%jk_ is the %k-th element of the %j-th eigenvector and, %x__%ki_ is the %k-th element of the %i-th column of the selected matrix object. A command to project the @SSCP object onto the eigenspace of the @Eigen object. Transform the SSCP object as if it was calculated in a coordinate system given by the eigenvectors of the Eigen object. This can be done as follows: #%S__%t_ = #%E\'p #%S #%E, where where #%E\'p is the transpose of the matrix with eigenvectors #%E, #%S is the square matrix with sums of squares and crossproducts, and #%S__%t_ the newly created square matrix. The dimension of #%S__%t_ may be smaller than the dimension of #%S. A command to project the rows of the @TableOfReal object onto the eigenspace of the @Eigen object. defines the dimension, i.e., the number of columns, of the resulting object. Project each row of the TableOfReal on the coordinate system given by the eigenvectors of the Eigen object. This can be done as follows: %y__%ij_ = \Si__%k=1..%numberOfColums_ %e__jk_ %x__%ik_, where %e__%jk_ is the %k-th element of the %j-th eigenvector, %x__%ik_ is the %k-th element of the %i-th row and %y__%ij_ is the %j-th element at the %i-th row of the matrix part of the resulting object. The %%equivalent rectangular bandwidth% (ERB) of a filter is defined as the width of a rectangular filter whose height equals the peak gain of the filter and which passes the same total power as the filter (given a flat spectrum input such as white noise or an impulse). A collection of objects of type @Excitation. You can create an #Excitations by selecting one or more #Excitation's and selecting ##To Excitations#. You can add one or more #Excitation's to an #Excitations by selecting one #Excitations and one or more #Excitation's and selecting ##Add to Excitations# (the #Excitation's will be removed from the list of objects). You can choose this command after selecting two objects of type @Excitations. A new object is created that contains the second object appended after the first. A command to convert every selected @Excitations to a @Pattern object. %Join the number of subsequent @Excitation objects to combine into one row of @Pattern. E.g. if an #Excitation has length 26 and %join = 2 then each row of #Pattern contains 52 elements. The number of rows in #Pattern will be %%my size% / 2. In the conversion process the elements of an #Excitation will be divided by 100.0 in order to guarantee that all patterns have values between 0 and 1. A @query to the selected FilterBank object. Return value a frequency value in Hertz. An object of type FormantFilter represents an acoustic time-frequency representation of a sound: the power spectral density %P(%f, %t), expressed in dB's. It is sampled into a number of points around equally spaced times %t__%i_ and frequencies %f__%j_ (on a linear frequency scale). Inside a FormantFilter A gamma-tone is the product of a rising polynomial, a decaying exponential function, and a cosine wave. It can be described with the following formula: gammaTone (%t) = %a %t^^%\ga\--1^ e^^\--2%\pi\.c%bandwidth\.c%t^ cos (2%%\pi\.cfrequency\.ct% + %initialPhase), where %\ga determines the order of the gamma-tone. The gammatone function has a monotone carrier (the tone) with an envelope that is a gamma distribution function. The amplitude spectrum is essentially symmetric on a linear frequency scale. This function is used in some time-domain auditory models to simulate the spectral analysis performed by the basilar membrane. It was popularized in auditory modeling by @@Johannesma (1972)@. @@Flanagan (1960)@ already used it to model basilar membrane motion. The %%generalized singular value decomposition% (gsvd) of an %m \xx %n matrix #%A and a %p \xx %n matrix #%B is given by the pair of factorizations #%A = #%U #%\Si__1_ [#%0, #%R] #%Q\'p and #%B = #%V #%\Si__2_ [#%0, #%R] #%Q\'p The matrices in these factorizations have the following properties: \bu #%U [%m \xx %m], #%V [%p \xx %p] and #%Q [%n \xx %n] are orthogonal matrices. In the reconstruction formula's above we maximally need only the first %n columns of matrices #%U and #%V (when %m and/or %p are greater than %n). \bu #%R [%r \xx %r], is an upper triangular nonsingular matrix. %r is the rank of [#%A\'p, #%B\'p]\'p and %r \<_ %n. The matrix [#%0, #%R] is %r \xx %n and its first %n \xx (%n \-- %r) part is a zero matrix. \bu #%\Si__1_ [%m \xx %r] and #%\Si__2_ [%p \xx %r] are real, nonnegative and "diagonal". In practice, the matrices #%\Si__1_ and #%\Si__2_ are never used. Instead a shorter representation with numbers %\al__%i_ and %\be__%i_ is used. These numbers obey 0 \<_ \al__%i_ \<_ 1 and \al__%i_^^2^ + \be__%i_^^2^ = 1. The following relations exist: #%\Si__1_\'p #%\Si__1_ + #%\Si__2_\'p #%\Si__2_ = #%I, #%\Si__1_\'p #%\Si__1_ = #diag (%\al__1_^^2^, ..., %\al__%r_^^2^), and, #%\Si__2_\'p #%\Si__2_ = #diag (%\be__1_^^2^, ..., %\be__%r_^^2^). The ratios \al__%i_ / \be__%i_ are called the %%generalized singular values% of the pair #%A, #%B. Let %l be the rank of #%B and %k + %l (= %r) the rank of [#%A\'p, #%B\'p]\'p. Then the first %k generalized singular values are infinite and the remaining %l are finite. (When %#B is of full rank then, of course, %k = 0). Special cases \bu If #%B is a square nonsingular matrix, the gsvd of #%A and #%B is equivalent to the singular value decomposition of #%A #%B^^\--1^. \bu The generalized eigenvalues and eigenvectors of #%A\'p #%A - %\la #%B\'p #%B can be expressed in terms of the gsvd. The columns of the matrix #%X, constructed as X = Q*( I 0 ) ( 0 inv(R) ), form the eigenvectors. The important eigenvectors, of course, correspond to the positions where the %l eigenvalues are not infinite. $$invFisherQ$ (%q, %df1, %df2) returns the value %f for which $$@fisherQ (%f, %df1, %df2) = %q. $$fisherQ$ (%f, %df1, %df2) returns the area under Fisher's F-distribution from %f to +\oo. An object of type ISpline represents a linear combination of basis i@spline functions. Each basis %ispline is a monotonically increasing polynomial function of degree %p. ISpline (%x) = \Si__%k=1..%numberOfCoefficients_ %c__%k_ %ispline__%k_(%x) A technique for estimating the bias and standard deviation of an estimate. Suppose we have a sample #%x = (%x__1_, %x__2_,...%x__n_) and wish to estimate the bias and standard error of an estimator \Te. The jackknife focuses on the samples that leave out one observation at a time: the %i-th jackknife sample consists of the data with the %i-th observation removed. The Legendre polynomials %P__%n_(%x) of degree %n are special orthogonal polynomial functions defined on the domain [-1, 1]. __-1_\in^^1^ %W(%x) %P__%i_(%x) %P__%j_(%x) %dx = \de__%ij_ %W(%x) = 1 (-1 < x < 1) %n %P__%n_(%x) = (2%n \-- 1) %x %P__%n-1_(%x) \-- (%n \-- 1) %P__%n-2_(%x) %P__0_(%x) = 1 %P__1_(%x) = %x We may %change the domain of these polynomials to [%xmin, %xmax] by using the following transformation: %x\'p = (2%x \-- (%xmax + %xmin)) / (%xmax - %xmin). We subsequently use %P__%k_(%x\'p) instead of %P__%k_(%x). An object of type LegendreSeries represents a linear combination of @@Legendre polynomials@ %P__%k_(%x). LegendreSeries (%x) = \Si__%k=1..%numberOfCoefficients_ %c__%k_ %P__%k_(%x) A command to transform the selected @LegendreSeries object into a @@Polynomial@ object. \Si__%k=1..%numberOfCoefficients_ %c__%k_ %x^^%k^ = \Si__%k=1..%numberOfCoefficients_ %l__%k_ %P__%k_(%x) We use the recurrence relation for @@Legendre polynomials@ to calculate these coefficients. A command to draw the distribution histogram of the values in the selected part of a @Matrix. %%Horizontal range%, %%Vertical range% determine the part of the matrix whose distribution will be drawn. %%Minimum value%, %%Maximum value% determine the range of values that will be considered in the distribution. To treat all bin widths equally, the range will include the %%Minimum value% and exclude the %%Maximum value% (see below). %%Number of bins% determines the number of bars in the distribution histogram. %%Minimum frequency%, %%Maximum frequency% determine the limits of the vertical axis. For a particular matrix element %z, the histogram bin number %%i% that will be incremented obeys the following relation: %%lowerBinBorder%__%i_ \<_ %z < %%lowerBinBorder%__%i_+ %%binWidth%, where %%binWidth% = (%%maximumValue% - %%minimumValue%)/%%numberOfBins%, and %%lowerBinBorder%__%i_ = %%minimumValue% + (%i - 1)\.c%%binWidth%. In this way all bins will be based on exactly the same width, as each binning interval includes its lower border and excludes its upper border (i.e., each interval is closed to the left and open to the right). Solve the general matrix equation #A #x = #b for #x. The matrix #A can be any general %m \xx %n matrix, #b is a %m-dimensional and #x a %n-dimensional vector. The @Matrix contains #A as its first %n columns and #b as its last column. The %n-dimensional solution is returned as a #Matrix with %n columns. When the number of equations (%m) is %greater than the number of unknowns (%n) the algorithm gives the best least-squares solution. If on the contrary you have %fewer equations than unknowns the solution will not be unique. Method Singular value decomposition with backsubstitution. Zero will be substituted for eigenvalues smaller than %tolerance \.c %%maximum_eigenvalue% (when the user-supplied %tolerance equals 0.0 a value of 2.2 \.c 10^^-16^ \.c %%number_of_unknowns% will be used as %tolerance). See for more details: @@Golub & van Loan (1996)@ chapters 2 and 3. An object of type MelFilter represents an acoustic time-frequency representation of a sound: the power spectral density %P(%f, %t), expressed in dB's. It is sampled into a number of points around equally spaced times %t__%i_ and frequencies %f__%j_ (on a Mel frequency scale). Inside a MelFilter A command to create a @MFCC object from each selected @MelFilter object. Mel frequency cepstral coefficients result from the Discrete Cosine Transform of the filterbank spectrum (in dB). The following formula shows the relation: %c__%i_ = \Si__%j=1_^^%N^ %P__%j_ cos (%i\pi/%N (%j-0.5))), where %N represents the number of filters and %P__%j_ the power in dB in the %j^^%th^ filter. This transformation was first used by @@Davis & Mermelstein (1980)@. An object of type MSpline represents a linear combination of basis m@spline functions. Each basis %mspline is a positive polynomial function of degree %p. MSpline (%x) = \Si__%k=1..%numberOfCoefficients_ %c__%k_ %mspline__%k_(%x) An object of type Pattern represents a sequence of patterns that can serve as inputs for a neural net. All elements in a Pattern have to be in the interval [0,1]. Pattern commands \bu ##Create Pattern with zeroes...# \bu @@TableOfReal: To Pattern and Categories...@ Synthesis: \bu @@Pattern & Categories: To FFNet...@ Inside a Pattern With @Inspect you will see that this type contains the same attributes as a @Matrix. One of the @@types of objects@ in P\s{RAAT}. See the @@Principal component analysis@ tutorial. An object of type PCA represents the principal components analysis of a multivariate dataset. \bu @@Principal component analysis@ tutorial \bu @@TableOfReal: To PCA@ Inside a PCA With @Inspect you will see that this type contains the same attributes as an @Eigen with the following extras: %numberOfObservations the number of observations in the multivariate dataset that originated the PCA, usually equal to the dataset's number of rows. %labels[1..%dimension] the label that corresponds to each dimension. %centroid the centroids of the originating multivariate data set. A command to query the selected @PCA for the fraction %%variance accounted for% by the selected components. %%Principal component range% defines the range of the principal components. If you choose both numbers equal, you get the fraction of the "variance" explained by that one component. A command to query the selected @PCA for the %i^^th^ eigenvalue. A command to query the selected @PCA for the %j^^th^ element of the %i^^th^ eigenvector. A command to get the probability that some of the eigenvalues of the selected @PCA object are equal. A low probability means that it is not very likely that that these numbers are equal. We test the hypothesis %H__0_: %\la__%from_ = ... = %\la__%to_ that %r (= %to\--%from+1) of the eigenvalues \la of the covariance matrix are equal. The remaining eigenvalues are unrestricted as to their values and multiplicities. The alternative hypothesis to %H__0_ is that some of the eigenvalues in the set are distinct. %%Eigenvalue range% define the range of eigenvalues to be tested for equality. %%Conservative test when on, a more conservative estimate for %n is chosen (see below). \ci^2 = \--%n \Si__%j=%from..%to_ ln %eigenvalue[%j] + %n %r ln (\Si__%j=%from..%to_ %eigenvalue[%j] / %r), with %r(%r+1)/2 \--1 degrees of freedom. Here %n = %totalNumberOfCases \-- 1. A special case occurs when the variation in the last %r dimensions is spherical. In a slightly more conservative test we may replace %n by %n\--%from\--(2%r^2+%r+2)/6%r. Also see @@Morrison (1990)@, page 336. A command to ask the selected @PCA for the minimum number of components that are necessary to explain the given fraction %%variance accounted for%. %%Variance accounted for% (fraction) the fraction variance accounted for that must be explained. A command to reconstruct a single data item. The result is stored as a @TableOfReal with only one row. the weight for the eigenvectors. The algorithm is explained in @@PCA & Configuration: To TableOfReal (reconstruct)@. A command to reconstruct a @TableOfReal from the selected @Configuration and @PCA. The TableOfReal is reconstructed from the eigenvectors of the PCA and elements of the Configuration are the weight factors: %#t__%i_ = \Si__%k_ %c__%ik_ #%e__%k_, where %#t__%i_ is the %i-th row in the resulting TableOfReal object, %c__%ik_ is the element at row %i and column %k in the Configuration object and #%e__%k_ the %k-th eigenvector from the PCA object. A command to calculate the angle between two planes. Each plane is spanned by the first two eigenvectors from the corresponding @@PCA@. The algorithm is described in section 12.4.3 of @@Golub & van Loan (1996)@: First we form the projection of one set of eigenvectors on the other set. This results in a 2\xx2 matrix #C: #C = #E__1_\'p #E__2_, where #E__1_ and #E__2_ are 2\xx%%dimension% and %%dimension%\xx2 matrices that contain the first two eigenvectors of the PCA's, respectively. Next, we compute the @@singular value decomposition@ of #C: #C = #U #\Si #V\'p Now the cosine of the angle between the two planes is given by \si__2_ and the angle in degrees is therefore: arccos (\si__2_)\.c180/\pi A command to calculate a @Procrustes from the two selected @@PCA@'s. Determines the orthogonal @@Procrustes transform@. Algorithm 12.4.1 in @@Golub & van Loan (1996)@. A command to construct a @Configuration from the selected @TableOfReal and @PCA. determines the dimension of the resulting Configuration. The TableOfReal is projected on the eigenspace of the PCA, i.e., each row of the TableOfReal is treated as a vector, and the inner product with the eigenvectors of the PCA determine its coordinates in the Configuration. Because the algorithm performs a projection, the resulting Configuration will ##only be centered#, i.e., its centroid will be at ##0#, if the data in the TableOfReal object are centered too. A command to query the selected @PCA and @TableOfReal object for the explained fraction of the variance if the TableOfReal object were projected onto the PCA space. 1. The TableOfReal is @@TableOfReal: To Covariance|converted@ to a Covariance object. 2. The Covariance object is @@PCA & Covariance: Project|projected@ on the PCA eigenspace and the newly obtained projected Covariance object is @@Covariance: Get fraction variance...|queried@ for the fraction variance. An object of type Polynomial represents a polynomial function on a domain. A polynomial of degree %n is defined as: %p(%x) = %c__1_ + %c__2_ %x + %c__3_ %x^^2^ + ... c__%n+1_ %x^^%n^. The real numbers %c__%k_ are called the polynomial %coefficients. Creation \bu @@Create Polynomial...@ (in the ##New menu#) \bu @@LPC: To Polynomial (slice)...@ (from prediction coefficients) \bu @@LegendreSeries: To Polynomial@ \bu @@ChebyshevSeries: To Polynomial@ \bu ##Draw...# Queries \bu @@Polynomial: Get function value...|Get function value...@: get %p(%x) \bu ##Get coefficient value...#: get %c__%i_ \bu @@Polynomial: Get minimum...|Get minimum...@: minimum of %p(%x) on an interval \bu @@Polynomial: Get x of minimum...|Get x of minimum...@ \bu @@Polynomial: Get maximum...|Get maximum...@: maximum of %p(%x) on an interval \bu @@Polynomial: Get x of maximum...|Get x of maximum...@ \bu @@Polynomial: Get area...|Get area...@ \bu ##Set domain...#: new domain \bu ##Set coefficient value...#: change one coefficient Conversion \bu @@Polynomial: To Spectrum...|To Spectrum...@ (evaluation over unit-circle) \bu @@Polynomial: To Polynomial (derivative)|To Polynomial (derivative)@ \bu @@Polynomial: To Polynomial (primitive)|To Polynomial (primitive)@ \bu @@Polynomial: To Roots|To Roots@: roots of polynomial A command to compute the area below the selected @Polynomial object. define the interval. The area is defined as __%xmin_\in^^xmax^ %p(%x) %dx. A command to compute %p(%x) for the selected @Polynomial object. A command to compute, on a specified interval, the maximum value of the selected @Polynomial object. A command to compute, on a specified interval, the location of the maximum of the selected @Polynomial object. A command to compute, on a specified interval, the minimum value of the selected @Polynomial object. A command to compute, on a specified interval, the location of the minimum of the selected @Polynomial object. A command to multiply two @@Polynomial|polynomials@ with each other. The result of multiplying 1 + 2 %x and 2 \-- %x^2 will be the polynomial: 2 + 4 %x \-- %x^2 \-- 2 %x^3. A command to compute the derivative of the selected @Polynomial object. A command to compute the primitive of the selected @Polynomial object. A command to transform the selected @Polynomial object to a new domain. define the new domain The polynomial is transformed from domain [%x__min_, %x__max_] to domain [%Xmin, %Xmax] in such a way that its form stays the same. This is accomplished by first calculating: %f(%x\'p) = \Si__%k=1..%numberOfCoefficients_ %c__%k_ %x\'p^^%k^, where %x\'p = %a %x + %b, and then collecting terms of equal degree. The %a and %b are defined as %a = (%x__min_ \-- %x__max_) / (%Xmin \-- %Xmax) %b = %x__min_ \-- %a %Xmin A command to compute the @@Roots|roots@ of the selected @Polynomial objects. The roots are found from the polished eigenvalues of a special companion matrix. For further explanation on these methods see @@Press et al. (1992)@. A command to compute the @@Spectrum|spectrum@ of the selected @Polynomial objects. %%Nyquist frequency% (Hz) defines the highest frequency in the spectrum. The lowest frequency of the spectrum will be 0 Hz. %%Number of frequencies defines the number of frequencies in the spectrum. We calculate the spectrum by evaluating the polynomial at regularly spaced points %z__%k_ on the upper half of a circle with radius %r = 1 in the complex plane. The upperhalf of the unit circle, where %k\.c%\fi is in the interval [0, %\pi], will be mapped to frequencies [0, @@Nyquist frequency@] in the spectrum. The complex values %z__%k_ (%k=1..%numberOfFrequencies) are defined as: %z__%k_ = %r e^^%i %k %\fi^, where, %\fi = \pi / (%numberOfFrequencies \-- 1) and %r = 1. This tutorial describes how you can perform principal component analysis with the P\s{RAAT}. Principal component analysis (PCA) involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called %%principal components%. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Traditionally, principal component analysis is performed on a square symmetric matrix of type @SSCP (pure sums of squares and cross products), @Covariance (scaled sums of squares and cross products), or @Correlation (sums of squares and cross products from standardized data). The analysis results for objects of type SSCP and Covariance do not differ, since these objects only differ in a global scaling factor. A Correlation object has to be used if the variances of individual variates differ much, or if the units of measurement of the individual variates differ. The result of a principal component analysis on such objects will be a new object of type @PCA. 1. Objectives of principal component analysis \bu To discover or to reduce the dimensionality of the data set. \bu To identify new meaningful underlying variables. 2. How to start We assume that the multi-dimensional data have been collected in a @TableOfReal object which is a rectangular matrix with (optional) row and column labels. If the variances of the individual columns in the TableOfReal differ much or the measurement units of the columns differ then you should first standardize the data. You can do this by choosing @@TableOfReal: Standardize columns|Standardize columns@. Performing a principal component analysis on a standardized data matrix has the same effect as performing the analysis on the correlation matrix (the covariance matrix from standardized data is equal to the correlation matrix of these data). Select the TabelOfReal object from the list of objects and choose @@TableOfReal: To PCA|To PCA@. This results in a new PCA object in the list of objects. We can now make a @@Scree plot|scree@ plot of the eigenvalues, @@Eigen: Draw eigenvalues...|Draw eigenvalues...@ to get an indication of the importance of each eigenvalue. The exact contribution of each eigenvalue (or a range of eigenvalues) to the "explained variance" can also be queried: @@PCA: Get fraction variance accounted for...|Get fraction variance accounted for...@. You might also check for the equality of a number of eigenvalues: @@PCA: Get equality of eigenvalues...|Get equality of eigenvalues...@. 3. Determining the number of components There are two methods to help you to choose the number of components. Both methods are based on relations between the eigenvalues. \bu Plot the eigenvalues, @@Eigen: Draw eigenvalues...|Draw eigenvalues...@ If the points on the graph tend to level out (show an "elbow"), these eigenvalues are usually close enough to zero that they can be ignored. \bu Limit variance accounted for, @@PCA: Get number of components (VAF)...|Get number of components (VAF)...@. 4. Getting the principal components Principal components are obtained by projecting the multivariate datavectors on the space spanned by the eigenvectors. This can be done in two ways: 1. Directly from the TableOfReal without first forming a @PCA object: @@TableOfReal: To Configuration (pca)...|To Configuration (pca)...@. You can then draw the Configuration or display its numbers. 2. Select a PCA and a TableOfReal object together and choose @@PCA & TableOfReal: To Configuration...|To Configuration...@. In this way you project the TableOfReal onto the PCA's eigenspace. 5. Mathematical background on principal component analysis The mathematical technique used in PCA is called eigen analysis: we solve for the eigenvalues and eigenvectors of a square symmetric matrix with sums of squares and cross products. The eigenvector associated with the largest eigenvalue has the same direction as the first principal component. The eigenvector associated with the second largest eigenvalue determines the direction of the second principal component. The sum of the eigenvalues equals the trace of the square matrix and the maximum number of eigenvectors equals the number of rows (or columns) of this matrix. 6. Algorithms If our matrix happens to be symmetric, with some sort of sums of squares and cross products, we solve for the eigenvalue and eigenvectors by first performing a Householder reduction to tridiagonal form, followed by the QL algorithm with implicit shifts. If, conversely, our starting point is a non-square or non-symmetric data matrix #%A (that could originate from a TableOfReal), we do not have to form explicitly the matrix with sums of squares and cross products, #%A\'p#%A. Instead, we proceed by a numerically more stable method, and form the @@singular value decomposition@ #%U #%\Si #%V\'p of #%A. The matrix #%V then contains the eigenvectors, and the squared diagonal elements of #%\Si contain the eigenvalues. A command to project the @Covariance object onto the eigenspace of the @PCA object. Further details can be found in @@Eigen & SSCP: Project@. A command to project the @SSCP object onto the eigenspace of the @PCA object. This tutorial describes the %syntax of regular expressions in P\s{RAAT} Introduction A %%regular expression% is a text string that describes a %set of strings. Regular expressions (regex) are useful as a way to search for patterns in text strings and, optionally, replace them by another pattern. Some regex match only one string, i.e., the set they describe has only one member. For example, the regex "ab" matches the string "ab" and no others. Other regex match more than one string, i.e., the set they describe has more than one member. For example, the regex "a*" matches the string made up of any number (including zero) of "a"s. As you can see, some characters match themselves (such as "a" and "b") and these characters are called %ordinary characters. The characters that don't match themselves, such as "*", are called %special characters or %meta characters. Many special characters are only special characters in the %search regex and are ordinary characters in the substitution regex. You can read the rest of this tutorial sequentially with the help of the "<1" and ">1" buttons. 1. @@Regular expressions 1. Special characters|Special characters@ (\bs \^ \$ { } [ ] ( ) . + ? \| - &) 2. @@Regular expressions 2. Quantifiers|Quantifiers@ (how often do we match). 3. @@Regular expressions 3. Anchors|Anchors@ (where do we match) 4. @@Regular expressions 4. Special constructs with parenthesis|Special constructs with parenthesis@ (grouping constructs) 5. @@Regular expressions 5. Special control characters|Special control characters@ (difficult-to-type characters like \bsn) 6. @@Regular expressions 6. Convenience escape sequences|Convenience escape sequences@ (\bsd \bsD \bsl \bsL \bss \bsS \bsw \bsW \bsB) 7. @@Regular expressions 7. Octal and hexadecimal escapes|Octal and hexadecimal escapes@ (things like \bs053 or \bsX2B) 8. @@Regular expressions 8. Substitution special characters|Substitution special characters@ (\bs1..\bs9 \bsU \bsu \bsL \bsl &) More in depth coverage of regular expressions can be found in @@Friedl (1997)@. The following characters are the %meta characters that give special meaning to the regular expression search syntax: #\bs# the backslash %escape character. The backslash gives special meaning to the character following it. For example, the combination "\bsn" stands for the %newline, one of the @@Regular expressions 5. Special control characters|control characters@. The combination "\bsw" stands for a "word" character, one of the @@Regular expressions 6. Convenience escape sequences|convenience escape sequences@ while "\bs1" is one of the @@Regular expressions 8. Substitution special characters|substitution special characters@. Example: The regex "aa\bsn" tries to match two consecutive "a"s at the end of a line, inclusive the newline character itself. Example: "a\bs+" matches "a+" and not a series of one or "a"s. ##\^ # the caret is the start of line @@Regular expressions 3. Anchors|anchor@ or the negate symbol. Example: "\^ a" matches "a" at the start of a line. Example: "[\^ 0-9]" matches any non digit. ##\$ # the dollar is the end of line @@Regular expressions 3. Anchors|anchor@. Example: "b\$ " matches a "b" at the end of a line. Example: "\^ b\$ " matches the empty line. ##{ }# the open and close curly bracket are used as range @@Regular expressions 2. Quantifiers|quantifiers@. Example: "a{2,3}" matches "aa" or "aaa". ##[ ]# the open and close square bracket define a character class to match a %single character. The "\^ " as the first character following the "[" negates and the match is for the characters %not listed. The "-" denotes a range of characters. Inside a "[ ]" character class construction most special characters are interpreted as ordinary characters. Example: "[d-f]" is the same as "[def]" and matches "d", "e" or "f". Example: "[a-z]" matches any lowercase characters in the alfabet. Example: "[\^ 0-9]" matches any character that is not a digit. Example: A search for "[][()?<>$^.*?^]" in the string "[]()?<>$^.*?^" followed by a replace string "r" has the result "rrrrrrrrrrrrr". Here the search string is %one character class and all the meta characters are interpreted as ordinary characters without the need to escape them. ##( )# the open and close parenthesis are used for grouping characters (or other regex). The groups can be referenced in both the search and the @@Regular expressions 8. Substitution special characters|substitution@ phase. There also exist some @@Regular expressions 4. Special constructs with parenthesis|special constructs with parenthesis@. Example: "(ab)\bs1" matches "abab". ##.# the dot matches any character except the newline. Example: ".a" matches two consecutive characters where the last one is "a". Example: ".*\bs.txt\$ " matches all strings that end in ".txt". ##*# the star is the match-zero-or-more @@Regular expressions 2. Quantifiers|quantifier@. Example: "\^ .*\$ " matches an entire line. ##+# the plus is the match-one-or-more quantifier. ##?# the question mark is the match-zero-or-one quantifier. The question mark is also used in @@Regular expressions 4. Special constructs with parenthesis|special constructs with parenthesis@ and in @@Regular expressions 2. Quantifiers|changing match behaviour@. ##\| # the vertical pipe separates a series of alternatives. Example: "(a|b|c)a" matches "aa" or "ba" or "ca". ##< ># the smaller and greater signs are @@Regular expressions 3. Anchors|anchors@ that specify a left or right word boundary. ##-# the minus indicates a range in a character class (when it is not at the first position after the "[" opening bracket or the last position before the "]" closing bracket. Example: "[A-Z]" matches any uppercase character. Example: "[A-Z-]" or "[-A-Z]" match any uppercase character or "-". ##&# the and is the "substitute complete match" symbol. Quantifiers specify how often the preceding @@Regular expressions|regular expression@ should match. ##*# Try to match the preceding regular expression zero or more times. Example: "(ab)c*" matches "ab" followed by zero or more "c"s, i.e., "ab", "abc", "abcc", "abccc" ... ##+# Try to match the preceding regular expression one or more times. Example: "(ab)c+" matches "ab" followed by one or more "c"s, i.e., "abc", "abcc", "abccc" ... ##{%m, %n}# Try to match the preceding regular expression between %m and %n times. If you leave %m out, it is assumed to be zero. If you leave %n out it is assumed to be infinity. I.e., "{,%n}" matches from %zero to %n times, "{%m,}" matches a minimum of %m times, "{,}" matches the same as "*" and "{n}" is shorthand for "{n, n"} and matches exactly %n times. Example: "(ab){1,2}" matches "ab" and "abab". ##?# Try to match zero or one time. Changing match behaviour Default the quantifiers above try to match as much as possible, they are %greedy. You can change greedy behaviour to %lazy behaviour by adding an extra "?" after the quantifier. Example: In the string "cabddde", the search "abd{1,2}" matches "abdd", while the search for "abd{1,2}?" matches "abd". Example: In the string "cabddde", the search "abd+" matches "abddd", while the search for "abd+?" matches "abd". Anchors let you specify a very specific position within the search text. ##\^ # Try to match the (following) regex at the beginning of a line. Example: "\^ ab" matches "ab" only at the beginning of a line and not, for example, in the line "cab". ##\$ # Try to match the (following) regex at the end of a line. ##<# Try to match the regex at the %start of a word. The character class that defines a %word can be found at the @@Regular expressions 6. Convenience escape sequences|convenience escape sequences@ page. ##># Try to match the regex at the %end of a word. ##\bsB# Not a word boundary Some special constructs exist with parenthesis. ##(?:#%regex#)# is a grouping-only construct. They exist merely for efficiency reasons and facilitate grouping. ##(?=#%regex#)# is a positive look-ahead. A match of the regular expression contained in the positive look-ahead construct is attempted. If the match succeeds, control is passed to the regex following this construct and the text consumed by this look-ahead construct is first unmatched. ##(?!#%regex#)# is a negative look-ahead. Functions like a positive look-ahead, only the %regex must %not match. Example: "abc(?!.*abc.*)" searches for the %last occurrence of "abc" in a string. ##(?i#%regex#)# is a case insensitive regex. ##(?I#%regex#)# is a case sensitive regex. Default a regex is case sensitive. Example: "(?iaa)" matches "aa", "aA", "Aa" and "AA". ##(?n#%regex#)# matches newlines. ##(?N#%regex#)# doesn't match newlines. All the constructs above do not capture text and can not be referenced, i.e., the parenthesis are not counted. However, you can make them capture text by surrounding them with %ordinary parenthesis. Special control characters in a @@Regular expressions|regular expression@ specify characters that are difficult to type. #\bsa alert (bell). #\bsb backspace. #\bse ASCII escape character. #\bsf form feed (new page). #\bsn newline. #\bsr carriage return. Example : a search for "\bsr\bsn" followed by a replace "\bsr" changes Windows text files to Macintosh text files. Example : a search for "\bsr" followed by a replace "\bsn" changes Macintosh text files to Unix text files. Example : a search for "\bsr\bsn" followed by a replace "\bsn" changes Windows text files to Unix text files. #\bst horizontal tab. #\bsv vertical tab. Convenience escape sequences in a @@Regular expressions|regular expression@ present a shorthand for some character classes. #\bsd matches a digit: [0-9]. Example: "-?\bsd+" matches any integer. #\bsD %not a digit: [\^ 0-9]. #\bsl a letter: [a-zA-Z]. #\bsL %not a letter: [\^ a-zA-Z]. #\bss whitespace: [ \bst\bsn\bsr\bsf\bsv]. #\bsS %not whitespace: [\^ \bst\bsn\bsr\bsf\bsv]. #\bsw "word" character: [a-zA-Z0-9\_ ]. Example: "\bsw+" matches a "word", i.e., a string of one or more characters that may consist of letters, digits and underscores. #\bsW %not a "word" character: [\^ a-zA-Z0-9\_ ]. #\bsB any character that is %not a word-delimiter. An octal number can be represented by the octal escape "\bs0" and maximally three digits from the digit class [0-7]. The octal number should not exceed \bs0377. A hexadecimal number can be represented by the octal escape "\bsx" or "\bsX"and maximally two characters from the class [0-9A-F]. The maximum hexadecimal number should not exceed \bsxFF. Example: \bs053 and \bsX2B both specify the "+" character. The substitution string is mostly interpreted as ordinary text except for the @@Regular expressions 5. Special control characters|special control characters@, the @@Regular expressions 7. Octal and hexadecimal escapes|octal and hexadecimal escapes@ and the following character combinations: #\bs1 ... #\bs9 are backreferences at sub-expressions 1 ... 9 in the match. Any of the first nine sub-expressions of the match string can be inserted into the replacement string by inserting a `\bs' followed by a digit from 1 to 9 that represents the string matched by a parenthesized expression within the regular expression. The numbering is left to right. Example: A search for "(a)(b)" in the string "abc", followed by a replace "\bs2\bs1" results in "bac". #& reference at entire match. The entire string that was matched by the search operation will be substituted. Example: a search for "." in the string "abcd" followed by the replace "&&" doubles every character in the result "aabbccdd". #\bsU #\bsu to uppercase. The text inserted by "&" or "\bs1" ... "\bs9" is converted to %uppercase ("\bsu" only changes the %first character to uppercase). Example: A search for "(aa)" in the string "aabb", followed by a replace "\bsU\bs1bc" results in the string "AAbcbb". #\bsL #\bsl to lowercase. The text inserted by "&" or "\bs1" ... "\bs9" is converted to %lowercase ("\bsl" only changes the %first character to lowercase). Example: A search for "(AA)" with a replace "\bsl\bs1bc" in the string "AAbb" results in the string "aAbcbb". An object of type Roots represents the (complex) roots of a @@Polynomial|polynomial@ function. \bu @@Polynomial: To Roots@ \bu ##Draw...# (in the complex plane) \bu ##Get root...#: get complex root \bu ##Get real part of root...# \bu ##Get imaginary part of root...# A scree plot shows the sorted eigenvalues, from large to small, as a function of the eigenvalue index. The %%singular value decomposition% (svd) of a real %m \xx %n matrix #A is the factorization #A = #U #\Si #V\'p, The matrices in this factorization have the following properties: #U [%m \xx %n] and #V [%n \xx %n] are orthogonal matrices. The columns #u__%i_ of #U =[#u__1_, ..., #u__%n_] are the %%left singular vectors%, and the columns #v__%i_ of #V [#v__1_, ..., #v__%n_] are the %%right singular vectors%. #\Si [%n \xx %n] = diag (%\si__1_, ..., %\si__%n_) is a real, nonnegative, and diagonal matrix. Its diagonal contains the so called %%singular values% %\si__%i_, where %\si__1_ \>_ ... \>_ %\si__%n_ \>_ 0. A command to create a new Sound object with manipulated characteristics from the selected @Sound and @Pitch. With this command you can have finer grained control over the pitch than with the @@Sound: Change gender...@ command. Accurate pitch measurement determines the quality of the @PSOLA synthesis. The settings are described in @@Sound: Change gender...@ (except that we don't need the %%Maximum pitch% here, since it will be determined from the selected Pitch. A command to create a new @Sound with manipulated characteristics. The quality of the @@PSOLA|manipulation@ depends on the pitch measurement. The arguments that control the pitch measurement are: %%Minimum pitch% (default 75 Hz) pitch candidates below this frequency will not be considered. %%Maximum pitch% (default 600 Hz) pitch candidates above this frequency will be ignored. The arguments that control the manipulation are: %%Formant shift ratio% determines the frequencies of the formants in the newly created Sound. If this ratio equals 1 no frequency shift will occur and the formant frequencies will not change. A ratio of 1.2 will change a male voice to a voice with approximate female formant characteristics. A ratio of 1/1.2 will change a female voice to a voice with approximate male formant characteristics. %%New pitch median% (default 0.0 Hz: same as original) determines what the median pitch of the new Sound will be. The pitch values in the newly created Sound will be calculated from the pitch values in the selected Sound by multiplying them by a factor %%newPitchMedian / oldPitchMedian%. This factor equals 1.0 if the default value for the new pitch median (0.0) is chosen. %%Pitch range factor% (default 1.0) determines an %extra% scaling of the new pitch values around the %new% pitch median. A factor of 1.0 means that no additional pitch modification will occur (except the obvious one described above). A factor of 0.0 monotonizes the new sound to the new pitch median. %%Duration factor% (default 1.0) The factor with which the sound will be lengthened. The default is 1.0. If you take a value less than 1.0, the resulting sound will be shorter than the original. A value larger than 3.0 will not work. If you want more control over the synthesis you can supply your own Pitch object and use the @@Sound & Pitch: Change gender...@ command. The shifting of frequencies is done via manipulation of the sampling frequency. Pitch and duration changes are generated with @PSOLA synthesis. The new pitch values are calculated in a two step process. We first multiply all the pitches with the factor %%newPitchMedian / oldPitchMedian% according to: %newPitch = %pitch * %newPitchMedian / %oldPitchMedian. It follows that if the %newPitchMedian equals the %oldPitchMedian no change in pitch values will occur in the first step. Subsequently, the pitch range scale factor determines the final pitch values in the following linear manner: %finalPitch = %newPitchMedian + (%newPitch \-- %newPitchMedian) * %pitchRangeScaleFactor Hence, it follows that no further scaling occurs if %pitchRangeScaleFactor equals 1.0. A command to filter a Sound by a fourth order gammatone bandpass filter. %%Centre frequency%, %Bandwidth determine the passband of the filter. The impulse response of the filter is a 4-th order @@gamma-tone@. This filter is implemented as a simple 8-th order recursive digital filter with 4 zeros and 8 poles (these 8 poles consist of one conjugate pole pair to the 4-th power). In the Z-domain its formula is: %#H (%z) = (1 + \su__%i=1..4_ %a__%i_%z^^%\--i^) / (1 + \su__%j=1..8_ %b__%j_%z^^%\--j^) The derivation of the filter coefficients %a__%i_ and %b__%j_ is according to @@Slaney (1993)@. The gain of the filter is scaled to unity at the centre frequency. A command that creates a @BarkFilter object from every selected @Sound object by @@band filtering in the frequency domain@ with a bank of filters. The filter functions used are: 10 log %#H(%z) = 7 - 7.5 * (%z__%c_ - %z - 0.215) - 17.5 * \Vr (0.196 + (%z__%c_ - %z - 0.215)^2) where %z__%c_ is the central (resonance) frequency of the filter in Bark. The bandwidths of these filters are constant and equal 1 Bark. A command that creates a @FormantFilter object from every selected @Sound object by @@band filtering in the frequency domain@ with a bank of filters whose bandwidths depend on the pitch of the signal. The analysis proceeds in two steps: 1. We perform a pitch analysis (see @@Sound: To Pitch...@ for details). 2. We perform a filter bank analysis on a linear frequency scale. The bandwidth of the filters depends on the measured pitch (see @@Sound & Pitch: To FormantFilter...@ for details). A command that creates a @FormantFilter object from the selected @Sound and @Pitch objects by @@band filtering in the frequency domain@ with a bank of filters whose bandwidths depend on the Pitch. %#H(%f, %F__0_) = 1 / (((%f__%c_^^2^ - %f^2) /%f\.c%B(%F__0_)))^2 + 1), where %f__%c_ is the central (resonance) frequency of the filter. %B(%F__0_) is the bandwidth in Hz and determined as %B(%F__0_) = %relativeBandwidth\.c%F__0_, where %F__0_ is the fundamental frequency as determined from the Pitch object. Whenever the value of %F__0_ is undefined, a value of 100 Hz is taken. A command that creates a @MelFilter object from every selected @Sound object by @@band filtering in the frequency domain@ with a bank of filters. The filter functions used are triangular in shape on a %linear frequency scale. The filter function depends on three parameters, the lower frequency %f__%l_, the central frequency %f__%c_ and the higher frequency %f__%h_. On a %mel scale, the distances %f__%c_-%f__%l_ and %f__%h_-%f__%c_ are the same for each filter and are equal to the distance between the %f__%c_'s of successive filters. The filter function is: %#H(%f) = 0 for %f \<_ %f__%l_ and %f \>_ %f__%h_ %#H(%f) = (%f - %f__%l_) / (%f__%c_ - %f__%l_) for %f__%l_ \<_ %f \<_ %f__%c_ %#H(%f) = (%f__%h_ - %f) / (%f__%h_ - %f__%c_) for %f__%c_ \<_ %f \<_ %f__%h_ A command that creates a @Pitch object from every selected @Sound object. to perform a pitch analysis based on a spectral compression model. The concept of this model is that each spectral component not only activates those elements of the central pitch processor that are most sensitive to the component's frequency, but also elements that have a lower harmonic relation with this component. Therefore, when a specific element of the central pitch processor is most sensitive at a frequency %f__0_, it receives contributions from spectral components in the signal at integral multiples of %f__0_. The spectral compression consists of the summation of a sequence of harmonically compressed spectra. The abscissa of these spectra is compressed by an integral factor, the rank of the compression. The maximum of the resulting sum spectrum is the estimate of the pitch. Details of the algorithm can be found in @@Hermes (1988)@ %%Time step% (default 0.01 s) the measurement interval (frame duration), in seconds. %%Minimum pitch% (default 50 Hz) candidates below this frequency will not be recruited. This parameter determines the length of the analysis window. %%Max. number of candidates% (default 15) The maximum number of candidates that will be recruited. %%Maximum frequency% (default 1250 Hz) higher frequencies will not be considered. %%Max. number of subharmonics% (default 15) the maximum number of harmonics that add up to the pitch. %%Compression factor% (default 0.84) the factor by which successive compressed spectra are multiplied before the summation. %%Number of points per octave% (default 48) determines the sampling of the logarithmic frequency scale. %Ceiling (default 500 Hz) candidates above this frequency will be ignored. Returns a new Spectrum object that is the product of the two selected @Spectrum objects. Reverses the sign of the complex part of the selected @Spectrum object(s). An object of type SSCP represents the sums of squares and cross products of a multivariate data set. Besides the matrix part, an object of type SSCP also contains a vector with centroids. Inside a SSCP With @Inspect you will see that this type contains the same attributes as a @TableOfReal with the following extras: A command to draw for the selected @SSCP an ellipse that covers a part of the multivariate data. A command to query the selected @SSCP object for the area of a sigma ellipse. 1. The four array elements in the SSCP-matrix that correspond to the chosen dimensions are copied into a two-dimensional matrix #%S (symmetric of course). 2. The eigenvalues of #%S are determined, call them %s__1_ and %s__2_. 3. The lengths %l__%i_ of the axes of the ellipse can be obtained as the square root of the %s__i_ multiplied by a scale factor: %l__%i_ = %scaleFactor \.c \Vr (%s__%i_ ), where %scaleFactor = %numberOfSigmas / \Vr(%numberOfObservations \-- 1). 4. The area of the ellipse will be %\pi\.c%l__1_\.c%l__2_. A command to query the selected @SSCP object for the area of a confidence ellipse. 3. The lengths %l__1_ and %l__2_ of the two axes of the ellipse can be obtained as (see for example @@Johnson (1998)@, page 410): %l__%i_ = %scaleFactor \.c \Vr (%s__%i_ ), where %scaleFactor = \Vr (%f \.c %p \.c (%n \-- 1) / (%n \.c (%n \-- %p))), in which %f = $$@@invFisherQ@$ (1 \-- %confidenceLevel, %p, %n \-- %p), where %p is the numberOfRows from the SSCP object and %n the %numberOfObservations. Tests the hypothesis that the selected @SSCP matrix object is diagonal. %%Number of constraints modifies the number of independent observations. The default value is 1. The test statistic is |#R|^^N/2^, the N/2-th power of the determinant of the correlation matrix. @@Bartlett (1954)@ developed the following approximation to the limiting distribution: \ci^2 = -(%N - %numberOfConstraints - (2%p + 5) /6) ln |#R| In the formula's above, %p is the dimension of the correlation matrix, %N-%numberOfConstraints is the number of independent observations. Normally %numberOfConstraints would equal 1, however, if the matrix has been computed in some other way, e.g., from within-group sums of squares and cross-products of %k independent groups, %numberOfConstraints would equal %k. We return the probability %\al as %\al = chiSquareQ (\ci^2 , %p(%p-1)/2). A very low %\al indicates that it is very improbable that the matrix is diagonal. A command to ask the selected @SSCP object for the fraction of the total variation that is accounted for by the selected dimension(s). Further details can be found in @@Covariance: Get fraction variance...@. A command that creates a @@CCA|canonical correlation@ object from the selected @SSCP object. %%Dimension of dependent variate (ny)% defines a partition of the square %n x %n SSCP matrix S into the parts S__yy_ of dimension %ny x %ny, S__xx_ of dimension %nx x %nx, and the parts S__xy_ and S__yx_ of dimensions %nx x %ny and %ny x %nx, respectively. The partition for the square SSCP-matrix is as follows: The canonical correlation equations we have to solve are: (1) (#S__%yx_ #S__%xx_^^-1^ #S__%yx_\'p -\la #S__%yy_)#y = #0 (2) (#S__%yx_\'p #S__%yy_^^-1^ #S__%yx_ -\la #S__%xx_)#x = #0 where #S__%yy_ [%ny \xx %ny] and #S__%xx_ [%nx \xx %nx] are symmetric, positive definite matrices belonging to the dependent and the independent variables, respectively. These two equations are not independent and we will show that both equations have the same eigenvalues and that the eigenvectors #x for equation (2) can be obtained from the eigenvectors #y of equation (1). We can solve equation (1) in several ways, however, the numerically stablest algorithm is probably by performing first a Cholesky decomposition of #S__xx_ and #S__yy_, followed by a @@generalized singular value decomposition@. The algorithm goes as follows: The Cholesky decompositions ("square roots") of #S__yy_ and #S__xx_ are: #S__yy_ = #U\'p #U and #S__xx_ = #H\'p #H, where #U and H are upper triangular matrices. From these decompositions, the inverse for #S__xx_^^-1^ is easily computed. Let #K be the inverse of #H, then we can write: #S__xx_^^-1^ = #K #K\'p. We next substitute in equation (1) and rewrite as: ((#K\'p#S__yx_\'p)\'p (#K\'p#S__yx_\'p) - \la #U\'p #U)#x = 0 This equation can be solved for eigenvalues and eigenvectors by the generalized singular value decomposition because it is of the form #A\'p#A -\la #B\'p#B. Now, given the solution for equation (1) we can find the solution for equation (2) by first multiplying (1) from the left with #S__yx_\'p#S__yy_^^-1^, resulting in: (#S__yx_\'p#S__yy_^^-1^#S__yx_#S__xx_^^-1^#S__yx_\'p -\la #S__yx_\'p) #y = 0 Now we split of the term #S__xx_^^-1^#S__yx_\'p and obtain: (#S__yx_\'p#S__yy_^^-1^#S__yx_ - \la #S__xx_) #S__xx_^^-1^#S__yx_\'p #y = 0 This equation is like equation (2) and it has therefore the same eigenvalues and eigenvectors. (We also proved this fact in the algorithmic section of @@TableOfReal: To CCA...@.) The eigenvectors #x is now #x = #S__xx_^^-1^#S__yx_\'p #y. A command that creates a @Covariance object from each selected @SSCP object. determines the factor by which each entry in the SSCP-matrix is scaled to obtain the Covariance matrix. The relation between the numbers %c__%ij_ in the covariance matrix and the numbers %s__%ij_ in the originating SSCP matrix is: %c__%ij_ = %s__%ij_ / (%numberOfObservations - %numberOfConstraints) Normally %numberOfConstraints will equal 1. However, when the originating SSCP was the result of summing %g SSCP objects, as is, for example, the case when you obtained the total within-groups SSCP from the individual group SSCP's, %numberOfConstraints will equal %g. Extract those rows from the selected @TableOfReal object whose Mahalanobis distance, with respect to the selected @SSCP object, are within the quantile range. A test on the mean of a normal variate when the variance is unknown. In Praat, the t-test is used to query a @Covariance object and: 1. get the significance of one mean. See @@Covariance: Get significance of one mean...@. 2. get the significance of the %difference between two means. See @@Covariance: Get significance of means difference...@. You should use a t-test when you want to test a hypothesis about the mean of one column in a @TableOfReal object, or, if you want to test a hypothesis about the difference between the means of two columns in this object. You can perform these t-tests in Praat by first transforming the TableOfReal object into a Covariance object (see @@TableOfReal: To Covariance@) and then choosing the appropriate query method on the latter object. Changes the row labels of the selected @TableOfReal object according to the specification in the search and replace fields. Both search and replace fields may contain @@regular expressions|Regular expressions@. The %%Replace limit% parameter limits the number of replaces that may occur within each label. Changes the column labels of the selected @TableOfReal object according to the specification in the search and replace fields. A command to draw a biplot for each column in the selected @TableOfReal object. %%Xmin%, %%Xmax%, %%Ymin%, %%Ymax% determine the drawing boundaries. %Split factor determines the weighing of the row and column structure (see below). 1. Get the @@singular value decomposition@ #U #\Si #V\'p of the table. 2. Calculate weighing factors %\la for row and columns %\la__r,1_ = %\si__1_^^%splitFactor^ %\la__c,1_ = %\si__1_^^1-%splitFactor^ %\la__r,2_ = %\si__2_^^%splitFactor^ %\la__c,2_ = %\si__2_^^1-%splitFactor^ where %\si__1_ and %\si__2_ are the first and the second singular values 3. For the rows (%i from 1..%numberOfRows) form: %xr__%i_ = %U__%i1_ %\la__%r,1_ %yr__%i_ = %U__%i2_ %\la__%r,2_ 4. For the columns (%i from 1..%numberOfColumns) form: %xc__%i_ = %V__%i1_ %\la__%c,1_ %yc__%i_ = %V__%i2_ %\la__%c,2_ 5. Plot the points (%xr__%i_, yr__%i_) and (%xc__%i_, yc__%i_) in the same figure with the corresponding row and column labels. A command to draw a @@box plot@ for each column in the selected @TableOfReal object. %%From row%, %%To row%, %%From column%, %%To column% determine the part of the table that you want to analyse. %Ymin and %Ymax A command to draw a histogram from the rows in the selected @TableOfReal object. The histogram will consist of %groups of bars. The number of groups will be determined by the number of selected columns from the table, while the number of bars within each group will be determined from the number of selected rows. %%Row numbers% and %%Column range%, determine the part of the table that you want to draw. The column range determines the number of bars that you want to draw for each row selected by the %%Row numbers% argument. the drawing boundaries. The following arguments are all relative to the width of a bar in the histogram. %%Horizontal offset% the offset from the left and right margin. %%Distance between bar groups% the distance between each group, i.e., the distance between the right side of the last bar in a group to the left side of the first bar in the next group. %%Distance between bars% the distance between the bars in a group. %%Grey values% the grey values of the bars in a group. Bar positioning If you want to put the labels yourself you will need the following information. The width of a bar is determined as follows: %width = 1 / (%nc \.c %nr + 2 \.c %hoffset + (%nc - 1)\.c %intergroup +%nc\.c(%nr -1)\.c %interbar), where %nc is the number of columns (groups) to draw, %nr is the number of rows to draw (the number of bars within a group), %hoffset is the horizontal offset, %intergroup the distance between each group and %interbar the distance between the bars within a group. The spacing between the bars drawn from a row: %dx = (%intergroup + %nr + (%nr -1) \.c %interbar) *% width The first bar for the %k-th row starts at: %x1 = %hoffset \.c %width + (%k - 1) \.c (1 + %interbar) \.c %width Copy columns from the selected @TableOfReal object to a new TableOfReal object. %Columns defines the indices of the columns to be selected. Ranges can be defined with a colon ":". Columns will be selected in the specified order. %%Row condition specifies a condition for the selection of rows. If the condition evaluates as %true for a particular row, the selected elements in this row will be copied. See @@Matrix: Formula...@ for the kind of expressions that can be used here. Select columns where row... "1 2 3" 1 Select columns where row... "1 : 3" 1 Two alternative expressions to copy the first three columns to a new table with the same number of rows. Select columns where row... "3 : 1" 1 Copy the first three columns to a new table with the same number of rows. The new table will have the 3 columns reversed. Select columns where row... "1:6 9:11" self[row,8]>0 Copy the first six columns and columns 9, 10, and 11 to a new table. Copy only elements from rows where the element in column 8 is greater than zero. Standardizes each column of the selected @TableOfReal. The entries %x__%ij_ in the TableOfReal will change to: (%x__%ij_ \-- %\mu__%j_) / %\si__%j_, where %\mu__%j_ and %\si__%j_ are the mean and the standard deviation as calculated from the %j^^th^ column, respectively. After standardization all column means will equal zero and all column standard deviations will equal one. Calculates a @Configuration based on the @Discriminant scores obtained from the selected @TableOfReal. Row labels in the table indicate group membership. Parameters determines the number of dimensions of the resulting Configuration. First we calculate the Discriminant from the data in the TableOfReal. See @@TableOfReal: To Discriminant@ for details. The eigenvectors of the Discriminant determine the directions that the data in the TableOfReal will be projected unto. Calculates a @Configuration based on the principal components from the selected @TableOfReal. We form principal components without explicitly calculating the covariance matrix #C = #M\'p\.c#M, where #M is the matrix part of the TableOfReal. 1. Make the singular value decomposition of #M. This results in #M = #U\.c#d\.c#V\'p. 2. Sort singular values #d and corresponding row vectors in #V (descending). 3. The principalComponent__%ij_ = \su__%k=1..%numberOfColumns_ %M__%ik_ \.c %V__%jk_. Remark The resulting configuration is unique up to reflections along the new principal directions. A command that creates a (%Pearson) @Correlation object from every selected @TableOfReal object. The correlations are calculated between columns. The linear correlation coefficient %r__%ij_ (also called the %%product moment correlation coefficient% or %%Pearson's correlation coefficient%) between the elements of columns %i and %j is calculated as: %r__%ij_ = \Si__%k_ (%x__%ki_ - %mean__%i_)(%x__%kj_ - %mean__%j_)/(\Vr (\Si__%k_(%x__%ki_ - %mean__%i_)^2) \Vr (\Si__%k_(%x__%kj_ - %mean__%j_)^2)), where %x__%mn_ is the element %m in column %n, and %mean__%n_ is the mean of column %n. A command that creates a (%%Spearman rank-order%) @Correlation object from every selected @TableOfReal object. The correlations are calculated between columns. The Spearman rank-order correlation coefficient %r__%ij_ between the elements of columns %i and %j is calculated as the linear correlation of the ranks: %r__%ij_ = \Si__%k_ (%R__%ki_ - %Rmean__%i_) (%R__%kj_ - %Rmean__%j_) / (\Vr (\Si__%k_(%R__%ki_ - %Rmean__%i_)^2) \Vr (\Si__%k_(%R__%kj_ - %Rmean__%j_)^2)), where %R__%mn_ is the rank of element %m in column %n, and %Rmean__%n_ is the mean of the ranks in column %n. A command that creates a @Covariance object from every selected @TableOfReal object. The covariances are calculated between columns. The covariance coefficients %s__%ij_ between the elements of columns %i and %j are defined as: %s__%ij_ = \Si__%k_ (%x__%ki_ - %mean__%i_)(%x__%kj_ - %mean__%j_)/(%numberOfObservations - %numberOfConstraints), where %x__%ki_ is the element %k in column %i, %mean__%i_ is the mean of column %i, %numberOfObservations equals the number of rows in the table, and %numberOfConstraints equals 1. The actual calculation goes as follows 1. Centralize each column (subtract the mean). 2. Get its @@singular value decomposition@ #U #\Si #V\'p. 3. Form #S = #V #\Si #V\'p. 4. Divide all elements in #S by (%numberOfObservations - 1). A command that creates a @Discriminant object from every selected @TableOfReal object. Row labels in the table indicate group membership. We solve for directions #x that are eigenvectors of the generalized eigenvalue equation: #%B #x - %\la #%W #x = 0, where #%B and #%W are the between-groups and the within-groups sums of squares and cross-products matrices, respectively. Both #%B and #%W are symmetric matrices. Standard formula show that both matrices can also be written as a matrix product. The formula above then transforms to: #%B__1_\'p#%B__1_ #x - %\la #%W__1_\'p#%W__1_ #x = 0 The equation can be solved with the @@generalized singular value decomposition@. This procedure is numerically very stable and can even cope with cases when both matrices are singular. The a priori probabilities in the Discriminant will be calculated from the number of %training vectors %n__%i_ in each group: A command that creates a @PCA object from every selected @TableOfReal object. Calculates Sums of Squares and Cross Products (@SSCP) from the selected @TableOfReal. The sums of squares and cross products %s__%ij_ between the elements of columns %i and %j are calculated as: %s__%ij_ = \Si__%k_ (%x__%ki_ - %mean__%i_)(%x__%kj_ - %mean__%j_), where %x__%mn_ is the element %m in column %n and %mean__%n_ is the mean of column %n. Extracts a @Pattern and a @Categories from the selected @TableOfReal. The selected rows and columns are copied into the Pattern and the corresponding row labels are copied into a Categories. A command that creates a @CCA object from the selected @TableOfReal object. %%Dimension of dependent variate (ny) defines the partition of the table into the two parts whose correlations will be determined. The first %ny columns must be the dependent part, the rest of the columns will be interpreted as the independent part (%nx columns). In general %nx must be larger than or equal to %ny. Calculates canonical correlations between the %dependent and the %independent parts of the table. The corresponding canonical coefficients are also determined. The canonical correlation equations for two data sets #T__%y_ [%n \xx %p] and #T__%x_ [n \xx %q] are: where #S__%yy_ [%p \xx %p] and #S__%xx_ [%q \xx %q] are the covariance matrices of data sets #T__%y_ and #T__%x_, respectively, #S__%yx_ [%p \xx %q] is the matrix of covariances between data sets #T__%y_ and #T__%x_, and the vectors #y and #x are the %%canonical weights% or the %%canonical function coefficients% for the dependent and the independent data, respectively. In terms of the (dependent) data set #T__%y_ and the (independent) data set #T__%x_, these covariances can be written as: #S__%yy_ = #T__%y_\'p #T__%y_, #S__%yx_ = #T__%y_\'p #T__%x_ and #S__%xx_ = #T__%x_\'p #T__%x_. The following @@singular value decomposition@s #T__%y_ = #U__%y_ #D__%y_ #V__%y_\'p and #T__%x_ = #U__%x_ #D__%x_ #V__%x_\'p transform equation (1) above into: (3) (#V__%y_ #D__%y_ #U__%y_\'p#U__%x_ #U__%x_\'p #U__%y_ #D__%y_ #V__%y_\'p - \la #V__%y_ #D__%y_ #D__%y_ #V__%y_\'p)#y = 0 where we used the fact that: #S__%xx_^^-1^ = #V__%x_ #D__%x_^^-2^ #V__%x_\'p. Equation (3) can be simplified by multiplication from the left by #D__%y_^^-1^ #V__%y_' to: (4) ((#U__%x_\'p #U__%y_)\'p (#U__%x_\'p #U__%y_) - \la #I)#D__%y_ #V__%y_\'p #y = #0 This equation can, finally, be solved by a substitution of the s.v.d of #U__%x_\'p #U__%y_ = #U #D #V\'p into (4). This results in (5) (#D^^2^ - \la #I) #V\'p #D__%y_ #V__%y_\'p #y = #0 In an analogous way we can reduce eigenequation (2) to: (6) (#D^^2^ - \la #I) #U\'p #D__%x_ #V__%x_\'p #x = #0 From (5) and (6) we deduce that the eigenvalues in both equations are equal to the squared singular values of the product matrix #U__%x_\'p#U__%y_. These singular values are also called %%canonical correlation coefficients%. The eigenvectors #y and #x can be obtained from the columns of the following matrices #Y and #X: #Y = #V__%y_ #D__%y_^^-1^ #V #X = #V__%x_ #D__%x_^^-1^ #U For example, when the vector #y equals the first column of #Y and the vector #x equals the first column of #X, then the vectors #u = #T__%y_#y and #v = #T__%x_#x are the linear combinations from #T__%y_ and #T__%x_ that have maximum correlation. Their correlation coefficient equals the first canonical correlation coefficient. A command that appears in the ##Multivariate statistics# menu if you select a @@TableOfReal@. It calculates the multivariate means for the different row labels from the selected TableOfReal. Argument %%Expand when %off, then for a table with %n rows and %m different labels (%m\<_%n), the resulting table will have %m rows. When %on, the dimensions of the resulting table will be the same as the originating, and corresponding means substituded in each row. The following commands @@Create TableOfReal (Pols 1973)...@ 0 To TableOfReal (means by row labels)... 0 will result in a new TableOfReal that has 12 rows. Each row will contain the mean F1, F2 and F3 values for a particular vowel. These means were obtained from 50 representations of that vowel. If we had chosen the %expansion: To TableOfReal (means by row labels)... 1 the resulting TableOfReal would have had 600 rows. This representation comes in handy when, for example, you have to calculate deviations from the mean. Extends the domain of the selected @TextGrid object. %%Extend domain by defines the amount of time by which the domain will be extended. %At defines whether starting times or finishing times will be modified. We add an extra (empty) interval into each %%interval tier%. This is necessary to keep original intervals intact. According to the value of the second argument, the new interval will be added at the beginning or at the end of the tier. For %%point tiers% only the domain will be changed. A large American-English speech corpus that resulted from the joint efforts of several American research sites. The TIMIT corpus contains a total of 6300 sentences, 10 sentences spoken by 630 speakers selected from 8 major dialect regions of the USA. 70\% of the speakers are male, 30\% are female. The text corpus design was done by the Massachusetts Institute of Technology (MIT), Stanford Research Institute and Texas Instruments (TI). The speech was recorded at TI, transcribed at MIT, and has been maintained, verified and prepared for CDROM production by the American National Institute of Standards and Technology (NIST) (@@Lamel et al. (1986)@). Z. Bai & J. Demmel (1993), "Computing the generalized singular value decomposition", %%SIAM J. Sci. Comput.% #14, 1464-1486. M.S. Bartlett(1954), "A note on multiplying factors for various chi-squared approximations", %%Joural of the Royal Statistical Society, Series B%, vol. 16, 296-298 A. Boomsma (1977), "Comparing approximations of confidence intervals for the product-moment correlation coefficient", %%Statistica Neerlandica% #31, 179-186. S.B. Davis & P. Mermelstein (1980), "Comparison of parametric representations for monosyllabic word recognition in continuously spoken sentences", %%IEEE Trans. on ASSP% #28, 357-366. B. Efron & R.J. Tibshirani (1993), %%An introduction to the bootstrap%, Chapman & Hall. J.L. Flanagan (1960), "Models for approximating basilar membrane displacement", %%Bell Sys. Tech. J.% #39, 1163-1191. J.E.F. Friedl (1997), %%Mastering Regular Expressions%, O'Reilly & Associates. M.T. Heath, J.A. Laub, C.C. Paige & R.C. Ward (1986), "Computing the singular value decomposition of a product of two matrices", %%SIAM J. Sci. Statist. Comput.% #7, 1147-1159. D.J. Hermes (1988), "Measurement of pitch by subharmonic summation", %%J.Acoust.Soc.Am.% #83, 257-264. T. Irino & R.D. Patterson (1996), "A time-domain, level-dependent auditory filter: The gammachirp", %%J.Acoust.Soc.Am.% #101, 412-419. P.I.M. Johannesma (1972): "The pre-response stimulus ensemble of neurons in the cochlear nucleus", in %%Symposium on Hearing Theory% (IPO, Eindhoven, Holland), 58-69. D.E. Johnson (1998), %%Applied Multivariate methods% L.F. Lamel, R.H. Kassel & S. Sennef (1986): "Speech Database Development: Design and Analysis of the Acoustic-Phonetic Corpus", %%Proc. DARPA Speech Recognition Workshop%", Report No. SAIC-86/1546, 100-19. D.F. Morrison (1990), %%Multivariate Statistical Methods%, McGraw-Hill, New York. G.E. Peterson & H.L. Barney (1952), "Control methods used in a study of the vowels", %%J.Acoust.Soc.Am.% #24, 175-184 L.C.W. Pols, H.R.C. Tromp & R. Plomp (1973), "Frequency analysis of Dutch vowels from 50 male speakers", %%J.Acoust.Soc.Am.% #53, 1093-1101. W.H. Press, S.A. Teukolsky, W.T. Vetterling & B.P. Flannery (1992), %%Numerical Recipes in C: the art of scientific computing%, Second Edition, Cambridge University Press. H. Sakoe & S. Chiba (1978), "Dynamic programming algorithm optimization for spoken word recognition", %%Trans. on ASSP% #26, 43-49. R.N. Shepard (1964), "Circularity in Judgments of Relative Pitch", %%J.Acoust.Soc.Am.% #36, 2346-2353. M. Slaney (1993), "An efficient implementation of the Patterson-Holdsworth auditory filterbank", %%Apple Computer Technical Report% #35, 41 pages. J.M. Tribolet & T.F. Quatieri (1979), "Computation of the Complex Cepstrum", in: %%Programs for Digital Signal Processing%, Digital Signal Processing Committee (eds.), IEEE Press. J.W. Tukey (1977), %%Exploratory data analysis%, Addison-Wesley, Reading, Mass. D.J.P.J. Van Nierop, L.C.W. Pols & R. Plomp (1973), "Frequency analysis of Dutch vowels from 25 female speakers", %%Acustica% #29, 110-118 D.J.M. Weenink (1999), "Formant analysis of Dutch vowels from 10 children", %%Proceedings of the Institute of Phonetic Sciences of the University of Amsterdam% #25, 81-99. D.J.M. Weenink (1985), "Accurate algorithms for performing principal component analysis and discriminant analysis", %%Proceedings of the Institute of Phonetic Sciences of the University of Amsterdam% #19, 45-52. D.J.M. Weenink (1999), "Canonical correlation analysis", %%Proceedings of the Institute of Phonetic Sciences of the University of Amsterdam% #25, 81-99. AffineTransform djmw AffineTransform: Invert Band filtering in the frequency domain Bonferroni correction box plot BarkFilter Bootstrap Categories Categories: Difference Categories: To Confusion Categories: Append Categories: Edit CategoriesEditor CC CCA CCA: Get zero correlation probability... CCA & Correlation: To TableOfReal (loadings) CCA & TableOfReal: To TableOfReal (loadings) CCA & TableOfReal: To TableOfReal (scores)... Canonical correlation analysis CCA & TableOfReal: Predict... Chebyshev polynomials ChebyshevSeries ChebyshevSeries: To Polynomial ClassificationTable concentration ellipse confidence interval confidence level Confusion Confusion: Condense... Confusion: Get fraction correct Confusion: To TableOfReal (marginals) Correlation Correlation: Confidence intervals... Covariance Covariance: Difference Covariance: Get significance of one mean... Covariance: Get fraction variance... Covariance: Get significance of means difference... Covariance: Get significance of one variance... Covariance: Get significance of variance ratio... Covariance: To TableOfReal (random sampling)... Covariance & TableOfReal: Extract quantile range... Create ChebyshevSeries... Create ISpline... Create MSpline... Create Polynomial... Create LegendreSeries... Create Sound from gamma-tone... Create Sound from Shepard tone... Create formant table (Peterson & Barney 1952) Create formant table (Pols & Van Nierop 1973) Create formant table (Weenink 1985) Create TableOfReal (Pols 1973)... Create TableOfReal (Van Nierop 1973)... Create TableOfReal (Weenink 1985)... Discriminant Discriminant analysis Discriminant: Draw sigma ellipses... Discriminant: Extract within-group SSCP... Discriminant: Extract pooled within-groups SSCP Discriminant: Get partial discrimination probability... Discriminant: Get contribution of component... Discriminant: Get Wilks' lambda... Discriminant: Get concentration ellipse area... Discriminant: Get confidence ellipse area... Discriminant & Pattern: To Categories... Discriminant & SSCP: Project Discriminant & TableOfReal: To ClassificationTable... Discriminant & TableOfReal: To Configuration... DTW DTW: Find path (band)... DTW: Find path (slopes)... DTW: Get maximum consecutive steps... DTW: Get time along path... DTW: Swap axes DTW: To Polygon (band)... DTW: To Polygon (slopes)... Eigen Eigen: Draw eigenvalues... Eigen: Draw eigenvector... Eigen: Get contribution of component... Eigen: Get cumulative contribution of components... Eigen: Get eigenvalue... Eigen: Get eigenvector element... Eigen & Matrix: Project... Eigen & SSCP: Project Eigen & TableOfReal: Project... equivalent rectangular bandwidth Excitations Excitations: Append Excitations: To Pattern... FilterBank: Draw filter functions... FilterBank: Draw frequency scales... FilterBank: Get frequency in Hertz... FilterBank: Get frequency in Bark... FilterBank: Get frequency in mel... FormantFilter gamma-tone generalized singular value decomposition invFisherQ fisherQ ISpline Jackknife Legendre polynomials LegendreSeries LegendreSeries: To Polynomial Matrix: Draw distribution... Matrix: Solve equation... MelFilter MelFilter: To MFCC... MSpline Pattern PCA PCA: Get fraction variance accounted for... PCA: Get eigenvalue... PCA: Get eigenvector element... PCA: Get equality of eigenvalues... PCA: Get number of components (VAF)... PCA: To TableOfReal (reconstruct 1)... PCA & Configuration: To TableOfReal (reconstruct) PCA & PCA: Get angle between pc1-pc2 planes PCA & PCA: To Procrustes... PCA & TableOfReal: To Configuration... PCA & TableOfReal: Get fraction variance... Polynomial Polynomial: Get area... Polynomial: Get function value... Polynomial: Get maximum... Polynomial: Get x of maximum... Polynomial: Get minimum... Polynomial: Get x of minimum... Polynomials: Multiply Polynomial: To Polynomial (derivative) Polynomial: To Polynomial (primitive) Polynomial: Scale x... Polynomial: To Roots Polynomial: To Spectrum... Principal component analysis PCA & Covariance: Project PCA & SSCP: Project Regular expressions Regular expressions 1. Special characters Regular expressions 2. Quantifiers Regular expressions 3. Anchors Regular expressions 4. Special constructs with parenthesis Regular expressions 5. Special control characters Regular expressions 6. Convenience escape sequences Regular expressions 7. Octal and hexadecimal escapes Regular expressions 8. Substitution special characters Roots Scree plot singular value decomposition Sound & Pitch: Change gender... Sound: Change gender... Sound: Filter (gammatone)... Sound: To BarkFilter... Sound: To FormantFilter... Sound & Pitch: To FormantFilter... Sound: To MelFilter... Sound: To Pitch (shs)... Spectra: Multiply Spectrum: Conjugate SSCP SSCP: Draw sigma ellipse... SSCP: Get sigma ellipse area... SSCP: Get confidence ellipse area... SSCP: Get diagonality (bartlett)... SSCP: Get fraction variation... SSCP: To CCA... SSCP: To Covariance... SSCP & TableOfReal: Extract quantile range... T-test TableOfReal: Change row labels... TableOfReal: Change column labels... TableOfReal: Draw biplot... TableOfReal: Draw box plots... TableOfReal: Draw rows as histogram... TableOfReal: Select columns where row... TableOfReal: Standardize columns TableOfReal: To Configuration (lda)... TableOfReal: To Configuration (pca)... TableOfReal: To Correlation TableOfReal: To Correlation (rank) TableOfReal: To Covariance TableOfReal: To Discriminant TableOfReal: To PCA TableOfReal: To SSCP... TableOfReal: To Pattern and Categories... TableOfReal: To CCA... TableOfReal: To TableOfReal (means by row labels)... TextGrid: Extend time... TIMIT acoustic-phonetic speech corpus Bai & Demmel (1993) Bartlett (1954) Boomsma (1977) Davis & Mermelstein (1980) Efron & Tibshirani (1993) Flanagan (1960) Friedl (1997) Heath et al. (1986) Hermes (1988) Irino & Patterson (1996) Johannesma (1972) Johnson (1998) Lamel et al. (1986) Morrison (1990) Peterson & Barney (1952) Pols et al. (1973) Press et al. (1992) Sakoe & Chiba (1978) Shepard (1964) Slaney (1993) Tribolet et al. (1979) Tukey (1977) Van Nierop et al. (1973) Weenink (1985) Weenink (2003) Ta a a a Query - Convert - Draw - Modify - Extract - Analyse - To Configuration - TabelOfReal_sort2: we want at least 6 rows!! TabelOfReal_sort2: rowtoindex <= 2 TabelOfReal: Sort and index 1 Row to index Create letter R example... Create letter R example For the monotone transformation on the distances 32.5 Noise range Create INDSCAL Carroll & Wish example... 0.0 Noise standard deviation Create Configuration... Create Configuration uniform Name 10 Number of points 2 Number of dimensions Formula: randomUniform(-1.5, 1.5) formula spline Draw splines left Horizontal range 1.0 right Horizontal range left Vertical range 20.0 right Vertical range Spline type M-spline I-spline 3 Order 0.3 0.5 0.6 Interior knots Garnish required: xmin < xmax and ymin < ymax %s AffineTransform %s_inverse Procrustes AffineTransform: Get transformation element Row number Column number Row number must not exceed number of rows. Column number must not exceed number of columns. AffineTransform: Get translation element Index Index must not exceed number of elements. Configuration Horizontal dimension Vertical dimension Configuration: Draw... Configuration: Draw 12 Label size Use row labels + Label Configuration: Draw sigma ellipses... Configuration: Draw sigma ellipses Number of sigmas Configuration: Draw one sigma ellipse Configuration: Draw confidence ellipses 0.95 Confidence level (0-1) Confidence level Configuration: Draw one confidence ellipse Configuration: Normalize... Configuration: Normalize Sum of squares On (INDSCAL), Off (Kruskal) Each dimension separately Configuration: Rotate... Configuration: Rotate Dimension 1 Dimension 2 60.0 Angle (degrees) Angle Configuration: Invert dimension... Configuration: Invert dimension Dimension Configuration: To Configuration (varimax)... Configuration: To Configuration (varimax) Normalize rows Quartimax 50 Maximum number of iterations 1e-6 Tolerance congruence Configuration & Configuration: To Procrustes... Configuration & Configuration: To Procrustes Orthogonal transform %s_to_%s Configurations: To AffineTransform (congruence)... Configurations: To AffineTransform (congruence) Confusion: To Dissimilarity (pdf)... Confusion: To Dissimilarity (pdf) 0.5 Minimum confusion level %s_pdf Confusion: To Similarity... Confusion: To Similarity Normalize Symmetrization No symmetrization Average (s[i][j] = (c[i][j]+c[j][i])/2) Houtgast (s[i][j]= sum (min(c[i][k],c[j][k]))) untitled_sum ContingencyTable: To Configuration (ca)... ContingencyTable: To Configuration (ca) Scaling of final configuration Row points in centre of gravity of column points Column points in centre of gravity of row points Row points and column points symmetric %.17g Correlation: To Configuration Similarity Similarity: To Dissimilarity... Similarity: To Dissimilarity 0.0 (=from data) Maximum dissimilarity Minimization parameters 1e-5 50 (= each repetition) Number of repetitions Stress measure Normalized Kruskal's stress-1 Kruskal's stress-2 Raw left Proximity range right Proximity range left Distance range right Distance range Mark size (mm) Mark string (+xo.) Dissimilarity Dissimilarity & Configuration: To Configuration (kruskal)... Dissimilarity & Configuration: To Configuration (kruskal) Handling of ties Primary approach Secondary approach Stress calculation Formula1 (sqrt (SUM((dist[k]-fit[k])^2) / SUM((dist[k])^2)) Formula2 (sqrt (SUM((dist[k]-fit[k])^2) / SUM((dist[k]-dbar)^2)) %s_s_kruskal Dissimilarity & Configuration: To Configuration (absolute mds)... Dissimilarity & Configuration: To Configuration (absolute mds) %s_s_absolute Dissimilarity & Configuration: To Configuration (ratio mds)... Dissimilarity & Configuration: To Configuration (ratio mds) %s_s_ratio Dissimilarity & Configuration: To Configuration (interval mds)... Dissimilarity & Configuration: To Configuration (interval mds) %s_s_interval Dissimilarity & Configuration: To Configuration (monotone mds)... Dissimilarity & Configuration: To Configuration (monotone mds) %s_s_monotone Dissimilarity & Configuration: To Configuration (i-spline mds)... Dissimilarity & Configuration: To Configuration (i-spline mds) Spline smoothing Number of interior knots Order of I-spline %s_s_ispline Dissimilarity & Configuration & Weight: To Configuration... Dissimilarity & Configuration & Weight: To Configuration (absolute mds) %s_sw_absolute Dissimilarity & Configuration & Weight: To Configuration (ratio mds) %s_sw_ratio Dissimilarity & Configuration & Weight: To Configuration (interval mds) %s_sw_interval Dissimilarity & Configuration & Weight: To Configuration (monotone mds) %s_sw_monotone Dissimilarity & Configuration & Weight: To Configuration (i-spline mds) %s_sw_ispline Dissimilarity & Configuration: get stress Dissimilarity & Configuration: Get stress Dissimilarity & Configuration: Get stress (absolute mds)... Dissimilarity & Configuration: Get stress (absolute mds) Dissimilarity & Configuration: Get stress (ratio mds)... Dissimilarity & Configuration: Get stress (ratio mds) Dissimilarity & Configuration: Get stress (interval mds)... Dissimilarity & Configuration: Get stress (interval mds) Dissimilarity & Configuration: Get stress (monotone mds)... Dissimilarity & Configuration: Get stress (monotone mds) Dissimilarity & Configuration: Get stress (i-spline mds)... Dissimilarity & Configuration: Get stress (i-spline mds) Dissimilarity & Configuration & Weight: Get stress (absolute mds)... Dissimilarity & Configuration & Weight: Get stress (absolute mds) Dissimilarity & Configuration & Weight: Get stress (ratio mds)... Dissimilarity & Configuration & Weight: Get stress (ratio mds) Dissimilarity & Configuration & Weight: Get stress (interval mds)... Dissimilarity & Configuration & Weight: Get stress (interval mds) Dissimilarity & Configuration & Weight: Get stress (monotone mds)... Dissimilarity & Configuration & Weight: Get stress (monotone mds) Primary approach) Dissimilarity & Configuration & Weight: Get stress (i-spline mds)... Dissimilarity & Configuration & Weight: Get stress (i-spline mds) Dissimilarity & Configuration: Draw Shepard diagram... Dissimilarity & Configuration: Draw Shepard diagram Mark string Mark size Dissimilarity & Configuration: Draw regression (absolute mds)... Dissimilarity & Configuration: Draw regression (absolute mds) Dissimilarity & Configuration: Draw regression (ratio mds)... Dissimilarity & Configuration: Draw regression (ratio mds) Dissimilarity & Configuration: Draw regression (interval mds)... Dissimilarity & Configuration: Draw regression (interval mds) Dissimilarity & Configuration: Draw regression (monotone mds)... Dissimilarity & Configuration: Draw regression (monotone mds) Dissimilarity & Configuration: Draw regression (i-spline mds)... Dissimilarity & Configuration: Draw regression (i-spline mds) Dissimilarity: To Configuration (kruskal)... Dissimilarity: To Configuration (kruskal) 2 (=Euclidean) Distance metric Dissimilarity: To Configuration (absolute mds)... Dissimilarity: To Configuration (absolute mds) %s_absolute Dissimilarity: To Configuration (ratio mds)... Dissimilarity: To Configuration (ratio mds) %s_ratio Dissimilarity: To Configuration (interval mds)... Dissimilarity: To Configuration (interval mds) %s_interval Dissimilarity: To Configuration (monotone mds)... Dissimilarity: To Configuration (monotone mds) %s_monotone Dissimilarity: To Configuration (i-spline mds)... Dissimilarity: To Configuration (i-spline mds) Order-zero spline must at least have 1 interior knot. %s_ispline Dissimilarity & Weight: To Configuration (i-spline mds)... Dissimilarity & Weight: To Configuration (i-spline mds) Dissimilarity & Weight: To Configuration (absolute mds)... Dissimilarity & Weight: To Configuration (absolute mds) Dissimilarity & Weight: To Configuration (ratio mds)... Dissimilarity & Weight: To Configuration (ratio mds) Dissimilarity & Weight: To Configuration (interval mds)... Dissimilarity & Weight: To Configuration (interval mds) Dissimilarity & Weight: To Configuration (monotone mds)... Dissimilarity & Weight: To Configuration (monotone mds) Dissimilarity: To Distance... Dissimilarity: To Distance Scale (additive constant) Scale Distance: To ScalarProduct... Distance: To ScalarProduct Make sum of squares equal 1.0 Distance: To Configuration (indscal)... Distance: To Configuration (indscal) Normalize scalar products 100 (= each repetition) indscal Distance & Configuration: Draw scatter diagram... Distance & Configuration: Draw scatter diagram Minimum x-distance Maximum x-distance Minimum y-distance Maximum y-distance Distance & Configuration: To Configuration (indscal)... Distance & Configuration: To Configuration (indscal) Distance & Configuration: Get VAF... Distance & Configuration: Get VAF Distance & Configuration & Salience: Get VAF... Distance & Configuration & Salience: Get VAF Dissimilarity & Configuration & Salience: Get VAF... Dissimilarity & Configuration & Salience: Get VAF Distance & Configuration & Salience: To Configuration (indscal)... Distance & Configuration & Salience: To Configuration (indscal) 100 Distance: To Configuration (ytl)... Distance: To Configuration (ytl) Salience object Dissimilarity & Distance: Monotone regression Distance & Dissimilarity: Draw Shepard diagram Minimum dissimilarity Multidimensional scaling Salience: Draw Covariance: To Configuration TableOfReal: Normalize table... TableOfReal: Normalize table Norm TableOfReal: Normalize rows... TableOfReal: Normalize rows TableOfReal: Normalize columns... TableOfReal: Normalize columns Get transformation element... Get translation element... Invert To Configuration Get value... -- get additional -- Get table norm Set column label (label)... -- set additional -- Normalize rows... Normalize columns... Normalize table... Standardize rows Standardize columns Test sorting... Procrustus New Objects MDS tutorial -- MDS -- Create INDSCAL Carroll Wish example... Draw splines... Draw MDS class relations AffineTransform help Configuration help Insert column (index)... Remove column (index)... Append Draw... Draw sigma ellipses... Draw one sigma ellipse... Draw confidence ellipses... Draw one confidence ellipse... Randomize Normalize... Centralize -- set rotations & reflections -- Rotate... Rotate (pc) Invert dimension... Analyse To Distance To Configuration (varimax)... To Similarity (cc) Match configurations - To Procrustes... To AffineTransform (congruence)... To Matrix To ContingencyTable To Proximity - To Dissimilarity (pdf)... To Similarity... Synthesize - Sum -- statistics -- Get chi squared probability Get Cramer's statistic Get contingency coefficient To Configuration (ca)... To Configuration... Dissimilarity help Get additive constant To Configuration (monotone mds)... To Configuration (i-spline mds)... To Configuration (interval mds)... To Configuration (ratio mds)... To Configuration (absolute mds)... To Configuration (kruskal)... To Distance... To Weight To Configuration (indscal)... -- linear scaling -- To Configuration (ytl)... To Dissimilarity To ScalarProduct... Procrustes help Get scale Extract transformation matrix Extract translation vector Similarity help To Dissimilarity... Centre rows Centre columns Double centre Cast - To Confusion To Similarity To Salience To ScalarProduct Draw Shepard diagram... -- draw regressions -- Draw monotone regression... Draw i-spline regression... Draw interval regression... Draw ratio regression... Draw absolute regression... Get stress... Get stress (monotone mds)... Get stress (i-spline mds)... Get stress (interval mds)... Get stress (ratio mds)... Get stress (absolute mds)... Draw scatter diagram... Get VAF... 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In the analysis of the INDSCAL three-way data matrix (%numberOfPoints \xx %numberOfDimensions \xx %numberOfSources) we seek to minimize the function: %f(%X, %W__1_,..., %W__%numberOfSources_) = \su__%i=1..%numberOfSources_ | %S__%i_ \-- %X%W__%i_%X\'p |^2 where %S__%i_ is a known symmetric %numberOfPoints \xx %numberOfPoints matrix with scalar products of distances for source %i, %X is the unknown configuration %numberOfPoints \xx %numberOfDimensions matrix, %X\'p its transpose, and, %W__%i_ is the diagonal %numberOfDimensions \xx %numberOfDimensions weight matrix for source %i. The function above has no analytical solution for %X and the %W__%i_. It can be solved, however, by an iterative procedure which Carroll & Chang have christened CANDECOMP (CANonical DECOMPosition). This method minimizes, instead of the function given above, the following function: %g(%X, %Y, %W__1_,..., %W__%numberOfSources_) = \su__%i=1..%numberOfSources_ | %S__%i_ \-- %X%W__%i_%Y\'p |^2 where %X and %Y are both %numberOfPoints \xx %numberOfDimensions configuration matrices. The algorithm proceeds as follows: 1. Initialize the $W matrices and the configuration matrix %X. This can for example be done according to a procedure given in @@Young, Takane & Lewyckyj (1978)@. 2. An alternating least squares minimization process is started as described that sequentially updates %Y, %X an %W (@@Carroll & Chang (1970)@): 2.1. Solve for a new %Y given %X and the %W__%i_ 2.2. Solve for a new %X given the %W__%i_ and the new %Y. 2.3. Solve for the %W__%i_ given the new %X and %Y. Evaluate the goodness-of-fit criterion and either repeat the minimization sequence (2.1\--2.3) or continue. 3. Done: make %Y equal to %X and solve a last time for the %W__%i_. Note: during the minimization the following constraints are effective: The configuration must be centered. The sum of squared coordinates in the configuration space is one for each dimension, i.e., the configuration always has unit variance in each dimension. One of the @@types of objects@ in P\s{RAAT}. An object of type Configuration represents the positions of a number of labelled points in a multidimensional space. How to create a Configuration From the New menu: \bu @@Create Configuration... By multidimensional scaling: \bu @@Dissimilarity: To Configuration (monotone mds)... \bu @@Dissimilarity: To Configuration (i-spline mds)... \bu @@Dissimilarity: To Configuration (interval mds)... \bu @@Dissimilarity: To Configuration (ratio mds)... \bu @@Dissimilarity: To Configuration (absolute mds)... By multidimensional scaling with weights (@@Dissimilarity & Weight: To Configuration...@): \bu ##Dissimilarity & Weight: To Configuration (monotone mds)... \bu ##Dissimilarity & Weight: To Configuration (i-spline mds)... \bu ##Dissimilarity & Weight: To Configuration (interval mds)... \bu ##Dissimilarity & Weight: To Configuration (ratio mds)... \bu ##Dissimilarity & Weight: To Configuration (absolute mds)... By multidimensional scaling with a start Configuration: \bu @@Dissimilarity & Configuration: To Configuration (monotone mds)... \bu @@Dissimilarity & Configuration: To Configuration (i-spline mds)... \bu @@Dissimilarity & Configuration: To Configuration (interval mds)... \bu @@Dissimilarity & Configuration: To Configuration (ratio mds)... \bu @@Dissimilarity & Configuration: To Configuration (absolute mds)... By transforming an existing Configuration: \bu @@Configuration: To Configuration (varimax)... \bu @@Configuration & AffineTransform: To Configuration \bu @@Configuration & Procrustes: To Configuration From @@Principal component analysis@: \bu @@TableOfReal: To Configuration (pca)... \bu @@PCA & TableOfReal: To Configuration... From @@Discriminant analysis@: @@TableOfReal: To Configuration (lda)... \bu @@Discriminant & TableOfReal: To Configuration... How to draw a Configuration \bu @@Configuration: Draw... \bu ##Configuration: Draw as numbers... \bu ##Configuration: Draw as squares... How to modify a Configuration \bu @@Configuration: Randomize \bu @@Configuration: Rotate (pc)@ (to principal directions) \bu @@Configuration: Rotate...@ (in a plane around the origin) \bu @@Configuration: Invert dimension... \bu @@Configuration: Normalize... Inside a Configuration With @Inspect you will see the following attributes: %numberOfRows the number of points (%numberOfPoints\>_1). %numberOfColumns the dimension of the space (%numberOfDimensions\>_1). %rowLabels the names associated with the points. %columnLabels the names for the dimensions. %data [1..%numberOfPoints][1..%numberOfDimensions] the coordinates of the points. %metric determines the way distances between points are measured. In general the distance between points #x__%i_ and #x__%j_ is: %d__%ij_ = (\su__%k=1..%numberOfDimensions_ %w__%k_ |%x__%ik_ \-- %x__%jk_|^^%metric^))^^1/%metric^ For Euclidean distances %metric is 2. %w [1..%numberOfDimensions] weight given to each dimension in the distance calculation. Makes the centre of the selected @Configuration equal to the origin. Draws a projection of the selected @Configuration on a coordinate plane. Settings %%X-coordinate%, %%Y-coordinate% control the dimensions that will show in the plot. %xmin, %xmax; %ymin, %ymax range for horizontal and vertical axes, respectively. %garnish when on, draws a bounding box with decoration. Inverts one dimension of a @Configuration. %%Dimension the dimensions that has to be inverted. Behaviour For all points %i=1..%numberOfPoints: if %j == %dimension then %x__%ij_ = \--%x__%ij_. Normalizes the selected @Configuration. %%Sum of squares% (default: 0.0) The desired value for the variance. %%Each dimension separately When on, the sum of squares in each dimension (column) will be scaled to %sumOfSquares When off, the sum of squares of all the matrix elements will equal %sumOfSquares. With the default value (0.0) for %sumOfSquares, and %eachDimensionSeparately chosen, an INDSCAL-like normalization is applied: the sum of squares for each column is scaled to equal 1.0. When %eachDimensionSeparately is off, a Kruskal-like normalization is applied: the sum of squares of the whole matrix is scaled equal to %numberOfRows. Before the normalization will be applied, however, we first translate the centre of the configuration to the origin by subtracting the mean for each dimension. The sum of squares than equals variance. Changes all coordinates of the points #%x__%i_ in the @Configuration according to: %x__%ij_ = randomUniform (-1, 1) Rotates the @Configuration in a plane around the origin. %%Dimension 1%, %%Dimension 2% the dimensions that span the plane. %Angle the clockwise rotation angle in degrees w.r.t. the direction vector of the lowest of the two dimensions. Rotates the @Configuration to principal directions. The principal directions correspond to the principal components. A command that transforms the second selected @Configuration object to match the first selected Configuration object as closely as possible.This problem of fitting one configuration (testee) to another (target) as closely as possible is called the Procrustes problem. We use a special @@Procrustes transform@ algorithm that does not mutilate or distort the testee configuration. Both Configuration objects must have the same dimensions. A command that rotates the selected @Configuration object to a new Configuration object whose coordinates have maximum %squared variance. %%Normalize rows when selected, the distances of all points to the origin will be made equal before iteration starts. We remember these scale factors and restore the original distances after the iteration process has stopped. %Quartimax when selected, the sum of fourth powers, normalized or raw, will be maximized. %%Maximum number of iterations sets a limit to the number of iterations. One iteration consists of %numberOfDimensions\.c (%numberOfDimensions\--1)/2 planar rotations of all pairs of dimensions. %%Tolerance also determines when the iteration stops. This happens if |%v__%i_\--%v__%i+1_| < %Tolerance \.c %v__%i_, where %v__%i_ is the squared variance for the %i^^th^ iteration. The iteration process stops when either the %%maximum number of iterations% is reached or the %tolerance criterion is met, which ever one is first. Algorithm The Varimax rotation procedure was first proposed by @@Kaiser (1958)@. Given a %numberOfPoints \xx %numberOfDimensions configuration #A, the procedure tries to find an orthonormal rotation matrix #T such that the sum of variances of the columns of #B*#B is a maximum, where #B = #A#T and * is the element wise (Hadamard) product of matrices. A direct solution for the optimal #T is not available, except for the case when %numberOfDimensions equals two. Kaiser suggested an iterative algorithm based on planar rotations, i.e., alternate rotations of all pairs of columns of #A. However, this procedure is not without problems: the varimax function may have stationary points that are not even local maxima. We have incorporated an algorithm of @@Ten Berge (1995)@ that prevents this unpleasant situation from happening. A command that computes a @Distance object for each selected @Configuration. The distance %d__%ij_ between objects %i and %j is calculated as: %d__%ij_ = %d__%ji_ = (\su__%k=1..%numberOfDimensions_ |%x__%ik_ \-- %x__%jk_|^2)^^1/2^ A command that create one @Similarity object from the selected @Configuration objects. In the Similarity object entry %s__%ij_ equals the @@congruence coefficient@ for the %i-th and %j-th selected Configuration object. All Configuration objects must have the same number of points and the same dimensions. A command that transforms the selected @Configuration to a new Configuration object according to the specifications in the selected @AffineTransform object. A command that transforms the selected @Configuration to a new Configuration object according to the specifications in the selected @Procrustes object. A command that creates an @AffineTransform object from two selected @Configuration objects. We calculate the affine transform that transforms the second selected Configuration object to match the first selected Configuration object as closely as possible. The degree of proportionality is the congruence between corresponding dimensions. sets a limit to the number of iterations. also determines when the iteration stops. This happens if |%f(#T__%i_)\--%f(#T__%i+1_)| < %Tolerance \.c %f(#T__%i_), where %f(#T__%i_) is the sum of the congruences for the %i^^th^ iteration (see below). Sometimes the criterion used in a @@Procrustes transform@ is too restrictive for comparing two configurations. This criterion is only zero when the positions in the rotated configuration (#A#T) equal the positions in the other configuration (#B). @@Brokken (1983)@ proposed an algorithm to maximize instead the sum of congruences between corresponding dimensions of #AT and #B. Specifically he proposed to maximize %f(#T) = \su__%i=1..%numberOfDimensions_ #t\'p__%i_#A\'p#b__%i_ / ((#t\'p__%i_#A\'p#A#t__%i_)^^1/2^(#b\'p__%i_#b__%i_)^^1/2^), where #t\'p__%i_ and #b\'p__%i_ are the %i^^th^ column of #T and #B, respectively. A direct solution for #T is not available, it can only be obtained by an iterative procedure. The implemented algorithm is from @@Kiers & Groenen (1996)@ and shows excellent convergence properties. A command that creates a @Procrustes object from two selected @Configuration objects. Argument %%Orthogonal transform% determines whether or not a translation and a scaling are allowed in the transform. We calculate the @@Procrustes transform@ that transforms the second selected Configuration object to match the first selected Configuration object as closely as possible. A command that creates a @Dissimilarity from every selected @Confusion. %Normalize when on, normalize rows by dividing each row element by the row sum. In this way you correct for unequal stimulus numbers. %%No symmetrization%, %Average, %Houtgast determine the symmetrization procedure. See @@Confusion: To Similarity... %%Maximum dissimilarity determines the maximum dissimilarity possible. When the default value, 0.0, is chosen, %maximumDissimilarity is calculated as the maximum element in the Similarity object. We first transform the Confusion to a Similarity. See @@Confusion: To Similarity... To obtain dissimilarities from similarities we "reverse" the latter: %%dissimilarity__%ij_ = %maximumDissimilarity \-- %similarity__%ij_ %%Symmetrize first when on, the confusion matrix is symmetrized before we calculate dissimilarities. %%Maximum dissimilarity% (units of sigma) specifies the dissimilarity from confusion matrix elements that are zero. 1. Normalize rows by dividing each row element by the row sum (optional). 2. Symmetrize the matrix by averaging %f__%ij_ and %f__%ji_. 3. Transformation of the confusion measure which is a sort of %similarity measure to the %dissimilarity measure. Similarity and dissimilarity have an inverse relationship: the greater the similarity, the smaller the dissimilarity and vice versa. Both have a monotonic relationship with distance. The most simple way to transform the similarities %f__%ij_ into dissimilarities is: %dissimilarity__%ij_ = %maximumSimilarity \-- %similarity__%ij_ For ordinal analyses like Kruskal this transformation is fine because only order relations are important in this analysis. However, for metrical analyses like INDSCAL this is not optimal. In INDSCAL, distance is a linear function of dissimilarity. This means that, with the transformation above, you ultimately fit an INDSCAL model in which the distance between object %i and %j will be linearly related to the confusion between %i and %j. For the relation between confusion and dissimilarity, the model implemented here, makes the assumption that the amount of confusion between objects %i and %j is related to the amount that their probability density functions, pdf's, overlap. Because we do not know these pdf's we make the assumption that both are normal, have equal %sigma and are one-dimensional. The parameter to be determined is the distance between the centres of both pdf's. According to formula 26.2.23 in @@Abramowitz & Stegun (1970)@, for each fraction %f__%ij_, we have to find an %x that solves: %f__%ij_ = 1 / \Vr(2%\pi) \in__%x_^^\oo^ e^^-%t\.c%t/2^ %dt This %x will be used as the dissimilarity between %i and %j. The relation between %x and %f__%ij_ is monotonic. This means that the results for a Kruskal analysis will not change much. For INDSCAL, in general, you will note a significantly better fit. A command that creates a @Similarity from every selected @Confusion. determine the symmetrization procedure. The %Average procedure averages: %similarity__%ij_= %similarity__%ji_ = (%confusion__%ij_ + %confusion__%ji_) / 2 The %Houtgast procedure as described in the paper by @@Klein, Plomp & Pols (1970)@, expresses similarity between stimuli %i and %j by the number of times that stimulus %i and %j have resulted in the same response, summated over all response categories. We use the following formula to calculate the %Houtgast dissimilarities: %similarity__%ij_ = \su__%k=1..%numberOfColumns_ min (%confusion__%ik_, %confusion__%jk_) which is equivalent to the formula in the Klein et al. paper: %similarity__%ij_ = \su__%k=1..%numberOfColumns_ (%confusion__%ik_ + %confusion__%jk_ \-- |%confusion__%ik_ \-- %confusion__%jk_|) The %%congruence coefficient% is a measure of similarity between two @@Configuration@s. The congruence coefficient %c(#X, #Y) for the configurations #X and #Y is defined as: %c(%X, %Y) = \su__%i<%j_ %w__%ij_ %d__%ij_(#X) %d__%ij_(#Y) / ([\su__%i<%j_ %w__%ij_ %d^2__%ij_(#X)]^^1/2^ [\su__%i<%j_ %w__%ij_ %d^2__%ij_(#Y)]^^1/2^), where %d__%ij_(#X) is the distance between the points %i and %j in configuration #X and %w__%ij_ are nonnegative weights (default: %w__%ij_ = 1). Since distances are nonnegative, the congruence coefficient has a value between 0 and 1. The %%congruence coefficient% is a better measure of the similarity between configurations than the %%correlation coefficient% of the distances. @@Borg & Groenen (1997)@ give a simple example where things go wrong with correlation coefficients: two configurations #X and #Y with three points each, have distances %d__12_(#X) = 1, %d__13_(#X) = 2, %d__23_(#X) = 3 and %d__12_(#Y) = 2, %d__13_(#Y) = 3, %d__23_(#Y) = 4. These distances have a correlation coefficient of 1. However, in #X the three points lie on a straight line and in #Y the points form a triangle. This unwanted situation occurs because in the calculation of the correlation coefficient the mean is subtracted from the distances and the resulting values are no longer distances (they may become negative). In calculating the correlation between the distances we should not subtract the mean. In fact, the congruence coefficient is exactly this correlation coefficient calculated with respect to the origin and not with respect to the centroid position (the "mean"). For further information on how well one number can assess the similarity between two configurations see @@Borg & Groenen (1997)@ section 19.7. In a two-way contingency table, cell %f__%ij_ contains the frequency with which row category %i co-occurs with column category %j. Necessarily, all %f__%ij_ \>_ 0. Commands Creation \bu ##TableOfReal: To ##ContingencyTable Query \bu ##ContingencyTable: Get chi squared probability \bu ##ContingencyTable: Get Cramer's statistic \bu ##ContingencyTable: Get contingency coefficient Analysis \bu @@ContingencyTable: To Configuration (ca)... A command that creates a @Configuration object from the selected @ContingencyTable object by means of @@Correspondence analysis@. %%Number of dimensions The dimensionality of the Configuration. %%Scaling of the final configuration determines whether row points are in the centre of gravity of column points, or, column points are in the centre of gravity of row points, or, whether roes and columns are treated symmetrically. 1. We start with the following transformation of the entries %f__%ij_: %h__%ij_ = %f__%ij_ / \Vr (%f__%i+_%f__+%j_) - \Vr (%f__%i+_%f__+%j_) / %N, where %h__%ij_ is the entry for a cell in the matrix #H with transformed data, %f__%i+_ is the total count for row %i, %f__+%j_ is the total count for column %j and %N is the grand total. This can be written in matrix form as: #H = #R^^\--1/2^#F#C^^\--1/2^ \-- #R^^1/2^#uu\'p#C^^1/2^ / %N, where #R and #C are diagonal matrices with the row and column totals, respectively and #u a column vector with all elements equal to 1. 2. Next the singular value decomposition of matrix #H is performed: #H = #K #\La #L\'p, where #K\'p#K = #I, #L\'p#L = #I, and #\La is a diagonal matrix with singular values. 3. Now the row (#X) and column points (#Y) can be determined. Three normalizations are possible: \bu Scale row points in the centre of gravity of column points #X = \Vr%N #R^^\--1/2^#K#\La #Y = \Vr%N #C^^\--1/2^#L \bu Scale column points in the centre of gravity of row points #X = \Vr%N #R^^\--1/2^#K #Y = \Vr%N #C^^\--1/2^#L#\La \bu Treat row points and column points symmetrically #X = \Vr%N #R^^\--1/2^#K#\La^^\--1/2^ #Y = \Vr%N #C^^\--1/2^#L\La^^\--1/2^ For more details see @@Gifi (1990)@, chapter 8. Correspondence analysis provides a method for representing data in an Euclidean space so that the results can be visually examined for structure. For data in a typical two-way @ContingencyTable both the row variables and the column variables are represented in the same space. This means that one can examine relations not only among row or column variables but also between row and column variables. In correspondence analysis the data matrix is first transformed by dividing each cell by the square root of the corresponding row and column totals. The transformed matrix is then decomposed with singular value decomposition resulting in the singular values (which in this case are canonical correlations) and a set of row vectors and column vectors. Next the row and column vectors are rescaled with the original total frequencies to obtain optimal scores. These optimal scores are weighted by the square root of the singular values and become the coordinates of the points in the @Configuration. Examples can be found in the books by @@Weller & Romney (1990)@ and @@Gifi (1990)@. A command to create a @Configuration with the specified number of points and number of dimensions. The location of the points will be determined by the formula (see @@Formulas@ for more information about possible formulas). Creates eight @Dissimilarity objects that bear names "1" ... "8". These objects contain the interpoint distances for a twodimensional 3\xx3 @Configuration of points, labelled A, B, C, ... I. All Dissimilarity objects are based on the following underlying configuration. The eight sources weigh this configuration in the following manner: For each source, the distances were subjected to the transformation: %dissimilarity__%ij_ = %distance__%ij_ + %noiseRange \.c #u, where #u is a uniform random variable between 0 and 1. Now you can do the following for example: Select all the Dissimilarity objects and choose @@Dissimilarity: To Distance...|To Distance...@. Uncheck scale (add "additive constant"). Select all the Distance objects and choose @@Distance: To Configuration (indscal)...|To Configuration (indscal)...@. and an @@INDSCAL analysis@ will be performed. In order to reproduce the saliences, you have to uncheck the "Normalize scalar products" option. This example was adapted from @@Carroll & Wish (1974)@. Creates a @Dissimilarity object that bears the name %R. The dissimilarities in this object were chosen to be a monotone transformation of the distances between the 32 two-dimensional points that make up the capital letter #R. All 32 \.c (32-1)/2 interpoint distances were subjected to the transformation: %dissimilarity__%ij_^ = %distance__%ij_^2 + 5 + %noiseRange \.c #u, This example was chosen from @@Green, Carmone & Smith (1989)@. The numbers %d\'p__%ij_ that result from applying an admissible transformation %f on the dissimilarities %\de__%ij_, i.e., %d\'p__%ij_ = %f (%\de__%ij_). Disparities have the same dimension as distances. Other names for disparities are %%pseudo distances% and %%target distances%. It represents a one-way table with dissimilarities between "objects". Creating a Dissimilarity from data in a text file Suppose you have three objects A, B and C. In one way or another, you have acquired the following (symmetric) dissimilarities: %\de__%AB_ = 2 (= %\de__%BA_) , %\de__%AC_ = 1 (= %\de__%CA_), and %\de__%BC_ = 1.4 (= %\de__CB_), where %\de__%AB_ represents the dissimilarity between object A and object B. You can create a simple text file like the following: "ooTextFile" ! The line by which Praat can recognize your file "Dissimilarity" ! The line that tells Praat about the contents 3 "A" "B" "C" ! Number of columns, and column labels 3 ! Number of rows "A" 0 2 1 ! Row label (A), A-B value, A-C value "B" 2 0 1.4 ! Row label (B), B-A value, B-C value "C" 1 1.4 0 ! Row label (C), C-A value, C-B value Notice that: \bu the row and column labels are identical. \bu the matrix elements on the diagonal are zero. \bu the matrix is symmetrical. This text file can be read with the @@Read from file...@ command. Since a Dissimilarity object has the data structure of a square symmetrical TableOfReal, you could also start from an appropriate @TableOfReal object and cast it to a Dissimilarity object. \bu @@Confusion: To Dissimilarity... Drawing \bu ##Draw as numbers... \bu ##Draw as squares... \bu ##Get column mean (index)... \bu ##Get column mean (label)... \bu ##Get column stdev (index)... \bu ##Get column stdev (label)... \bu @@Dissimilarity: Get additive constant Modification \bu @@Formula... \bu ##Set value... \bu ##Remove column (index)... \bu ##Insert column (index)... \bu ##Set row label (index)... \bu ##Set row label (label)... \bu ##Set column label (index)... \bu ##Set column label (label)... Multidimensional scaling analysis \bu @@Dissimilarity: To Configuration (monotone mds)... \bu @@Dissimilarity: To Configuration (i-spline mds)... \bu @@Dissimilarity: To Configuration (interval mds)... \bu @@Dissimilarity: To Configuration (ratio mds)... \bu @@Dissimilarity: To Configuration (absolute mds)... \bu @@Dissimilarity: To Configuration (kruskal)... Transformations \bu @@Dissimilarity: To Distance... \bu @@Dissimilarity: To Weight A command that calculates the "additive constant" from the selected @Dissimilarity. Distances %d__%ij_ will be obtained from dissimilarities %\de__%ij_ according to: %distance__%ij_ = %dissimilarity__%ij_ + %additiveConstant We use a procedure by @@Cailliez (1983)@ to solve the "additive constant problem", i.e. find the smallest %additiveConstant such that all %distance__%ij_ in the above equation have a Euclidean representation. A command that creates a @Configuration object from a @Dissimilarity object. The @disparities %d\'p__%ij_ will be obtained from dissimilarities %\de__%ij_ according to: %d\'p__%ij_ = %\de__%ij_ %d\'p__%ij_ = %a + %b \.c %\de__%ij_ Dissimilarities %\de__%ij_ and @disparities %d\'p__%ij_ will be related by a @spline function: %d\'p__%ij_ = \su__%k=1..(%%numberOfInteriorKnots%+%order)_ spline__%k_ (%knots, %order, %\de__%ij_), where spline__%k_ (\.c) is the value of the %k^^th^ I-spline of order %order and knot sequence %knot evaluated at %\de__%ij_. determines the dimensionality of the configuration. %%Number of interior knots% determines the number of segment boundaries. Each interior knot is the boundary between two segments. The splines in each segment will be joined as continuously as possible. %%Order of I-spline The order of the polynomial basis of the I-spline. Finding the optimal Configuration involves a minimization process: %Tolerance When successive values for the stress differ by less than %Tolerance, the minimization process stops. %%Maximum number of iterations% Minimization stops after this number of iterations has been reached. %%Number of repetitions If chosen larger than 1, the minimization process will be repeated, each time with another random start configuration. The configuration that results in minimum stress, will be saved. Hints If %numberOfInteriorKnots is zero, polynomial regression will be performed. Therefore , the combination %numberOfInteriorKnots = 0 and %order = 1 also gives interval scaling (in fact, it is the implementation in this program). In the limit when %order = 0 and %numberOfInteriorKnots = %numberOfDissimilarities, monotone regression is performed. %%Number of dimensions% (default: 2) %%Distance metric% (default: 2, i.e. Euclidean) the general distance between points #x__%i_ and #x__%j_ (%i,%j = 1..%numberOfPoints) is: (\su__%k=1..%numberOfDimensions_ |%x__%ik_ \--%x__%jk_|^^%metric^)^^1/%metric^ %%Sort distances determines the handling of ties in the data. When off, whenever two or more dissimilarities are equal we do not care whether the fitted distances are equal or not. Consequently, no constraints are imposed on the fitted distances. When on, however, we impose the constaint that the fitted distances be equal whenever the dissimilarities are equal. For the calculation of stress: %Formula1 (default) %stress = \Vr(\su(%distance__%k_ \-- %fittedDistance__%k_)^2 / \su %distance__%k_^2) %%Formula2% %stress = \Vr(\su(%distance__%k_ \-- %fittedDistance__%k_)^2 / \su (%distance__%k_ \-- %averageDistance)^2) Note that values of stress 2 are generally more than double those of stress 1 for the same degree of fit. When successive values for the stress differ less than %Tolerance the minimization process stops. When chosen larger than 1, the minimalization process will be repeated, each time with another random start configuration. The configuration that results in minimum stress will be saved. Precautions When there are few objects it is impossible to recover many dimensions. A rough rule of thumb is that there should be at least twice as many number of observations, i.e. the %numberOfPoints \.c (%numberOfPoints - 1) / 2 (dis)similarities, than parameters to be estimated, i.e. the %numberOfPoints \.c %numberOfDimensions position coordinates. A practical guide is: for %numberOfDimensions = 1 you need \>_ 5 objects for %numberOfDimensions = 2 you need \>_ 9 objects for %numberOfDimensions = 3 you need \>_ 13 objects There is no feasible way to be certain that you have found the true global minimum. However, by using a great number of different random starting configurations to scale the same data it is often possible to obtain practical certainty. Although the procedure for obtaining an initial configuration is based on a %linear relation between distance and (dis)similarity, it gives a very good approximation of the optimal #Configuration and the #Minimizer practically always finds the global minimum from it (I guess...). A way to find out is to try the %numberOfRepetitions parameter which gives you the possibility to fit many times and each time start with another random initial configuration. 1. The Dissimilarity object is converted to a Distance object in the same way as in @@Dissimilarity: To Distance...@.) 2. From the Distance object an initial Configuration is found by first transforming the Distance object to a matrix with scalar products of distances and subsequently solving for the first %numberOfDimensions eigenvectors of this matrix. 3. A minimalization algorithm is started that tries to minimize a function. In this function: \bu 3.1 We normalize the current Configuration from the minimizer \bu 3.2 Calculate a new Distance object from the configuration \bu 3.3 Do a monotone regression of this Distance on the Dissimilarity. This results in a new Distance object. \bu 3.4 Calculate stress from this Distance and the Distance obtained from Dissimilarity. The optimization process is ccontrolledby a conjugate gradient minimization algorithm that tries to minimize the %stress function. In @@Kruskal (1964)@, a steepest descent algorithm is used wwhichis less efficient. Dissimilarities %\de__%ij_ and @disparities %d\'p__%ij_ are related by: %d\'p__%ij_ \<_ %d\'p__%kl_ if %\de__%ij_ \<_ %\de__%kl_ determines the dimension of the configuration. %Primary or %secondary% approach to ties When dissimilarities are equal, i.e., %\de__%ij_ = %\de__%kl_, the primary approach imposes no conditions on the corresponding @disparities %d\'p__%ij_ and %d\'p__%kl_, while the %secondary approach demands that also %d\'p__%ij_ = %d\'p__%kl_. %d\'p__%ij_ = %b \.c %\de__%ij_ A command that creates a @Distance object from a selected @Dissimilarity object. %Scale when on, the @@Dissimilarity: Get additive constant|additiveConstant@ is determined, when off the %additiveConstant = 0. dissimilarities are transformed to distances according to: %distance__%ij_ = %dissimilarity__%ij_ + %additiveConstant. Creates an object of type @Weight for each selected @Dissimilarity object. The values in the weight matrix will be: %w__%ii_ = 0 %w__%ij_ = 1 if %\de__%ij_ > 0 Draws a scatterplot of the dissimilarities %\de__%ij_ from the selected @Dissimilarity object versus @disparities %d\'p__%ij_ obtained from the "regression" of distances %d__%ij_ from @Configuration on the dissimilarities %\de__%ij_. %%Minimum proximity%, %%Maximum proximity% minimum and maximum values for the proximities (horizontal axis). %%Minimum distance%, %%Maximum distance% minimum and maximum values for the distances (vertical axis). %%Mark size (mm)%, %%Mark string% size and kind of the marks in the plot. Draws a scatterplot of the dissimilarities %\de__%ij_ from the selected @Dissimilarity versus @disparities %d\'p__%ij_ obtained from the regression of distances %d__%ij_ from @Configuration on the dissimilarities %\de__%ij_. %d\'p__%ij_ = %a + %b \.c %\de__%ij_, where the values of %a and %b are determined by regression. Draws a scatterplot of the dissimilarities %\de__%ij_ from the selected @Dissimilarity versus @disparities %d\'p__%ij_ obtained from the regression of distances %d__%ij_ from @Configuration on the @spline transformed dissimilarities %\de__%ij_. %%Number of interior knots determines the number of segments. Order of I-spline Draws a scatterplot of the dissimilarities %\de__%ij_ from the selected @Dissimilarity versus @disparities %d\'p__%ij_ obtained from the monotone regression of distances %d__%ij_ from @Configuration on the dissimilarities %\de__%ij_. When dissimilarities are equal, i.e., %\de__%ij_ = %\de__%kl_ the primary approach imposes no conditions on the corresponding distances %d__%ij_ and %d__%kl_, while the %secondary approach demands that also %d__%ij_ = %d__%kl_. Draws a scatterplot of the dissimilarities %\de__%ij_ from the selected @Dissimilarity versus @disparities %d\'p__%ij_ obtained from the "regression" of distances %d__%ij_ from @Configuration on the dissimilarities %\de__%ij_. %d\'p__%ij_ = %b \.c %\de__%ij_, where the value of %b is determined by regression. Draws the Shepard diagram. This is a scatterplot of the dissimilarities from the @Dissimilarity object versus distances (as calculated from the @Configuration). A command to obtain the @stress value for the selected @Dissimilarity and @Configuration object. Stress formula's are #dependent of the scale of the Configuration: you will get #another stress value if you had pre-multiplied the selected Configuration with any number greater than zero. We use stress formula's that are independent of the scale of the Configuration: you would have got the same stress value if you had pre-multiplied the selected Configuration with any number greater than zero. A command that creates a @Configuration object from a @Dissimilarity object. The selected Configuration object serves as a starting configuration for the minimization process. A command to fit an optimal @Configuration for the selected @Dissimilarity object. The selected @Configuration will be used as the starting configuration in the kruskal analysis. A command that calculates the @stress between distances %d__%ij_ derived from the selected @Configuration object and @disparities %d\'p__%ij_ derived from the selected @Dissimilarity object. With the selected @Weight object the evaluation of the influence of each dissimilarity on stress can be influenced. %%Normalized stress%, %%Kruskal's stress-1%, %%Kruskal's stress-2% or %Raw stress% Except for %absolute %mds, we us stress formula's that are independent of the scale of the Configuration (see @stress): you would have got the same stress value if you had pre-multiplied the selected Configuration with any number greater than zero. A command that creates a @Configuration object from a @Dissimilarity object. With the selected @Weight object the influence of each dissimilarity on @stress can be influenced. The selected Configuration object serves as a starting configuration for the minimization process. A command that creates a @Configuration object from a @Dissimilarity object. With the selected @Weight object the influence of each dissimilarity on @stress can be influenced. May be different and depend on the representation function, i.e. the scale of measurement. An object of type Distance represents distances between objects in a metrical space. \bu @@Confusion: To Dissimilarity (pdf)... Perform an @@INDSCAL analysis@ on the selected object(s) of type @Distance that results in a @Configuration and a @Salience object. A command that creates one @Configuration and one @Salience object from a collection of one or more @Distance objects. This Configuration and Salience object normally serve as starting points for an @@individual difference scaling@ such as an @@INDSCAL analysis@. The algorithm is ddescribedin @@Young, Takane & Lewyckyj (1978)@. A command that creates a @ScalarProduct for each selected @Distance. %%Make sum of squares equal 1.0 when selected, the elements in the resulting matrix part will be scaled such that the sum of all the squared elements in the matrix equals 1.0. ScalarProduct entries %b__%ij_ are created from distances %d__%ij_ bij double centering the matrix with elements \--1/2 %d__%ij_^2, i.e., %b__%ij_= \--1/2(%d__%ij_^2 \-- %d__%\.cj_^2 \-- %d__%i\.c_^2 + %d__%\.c\.c_^2), where the dot (\.c) means averaging over that dimension. Calculates the "%%variance accounted for%" from the selected collection of @Distance objects and the selected @Configuration. The optimal @Salience necessary for the calculation will be inferred from the selected Distance and Configuration objects. Performs an @@INDSCAL analysis@ on the selected objects of type @Distance and calculates a @Configuration from them. Uses the selected Configuration object as the initial Configuration in the iteration process. Calculates the "variance accounted for" from the selected collection of @Distance objects, the selected @Configuration and the selected #Salience. A command that creates a new @Configuration from the selected collection of @Distance objects, the selected @Configuration and the selected #Salience. The selected Configuration and Salience serve as start values for the @@INDSCAL analysis@. The purpose of individual difference scaling is to represent objects, whose dissimilarities are given, as points in a metrical space. The distances in the space should be in accordance with the dissimilarities as well as is possible. Besides the configuration a @Salience matrix is calculated. The basic Euclidean model is: %\de__%ijk_ \~~ (\su__%s=1..%r_ %w__%ks_(%x__%is_ \-- %x__%js_)^2)^^1/2^ Here \de__%ijk_ is the (known) dissimilarity between %objects %i and %j, as measured on %data %source %k. The %x's are the %coordinates of the objects in an %r-dimensional space and the %w's are weights or saliences. Because straight minimization of the expression above is difficult, one applies transformations on this expression. Squaring both sides gives the model: %\de^2__%ijk_ \~~ \su__%s=1..%r_ %w__%ks_(%x__%is_ \-- %x__%js_)^2 and the corresponding least squares loss function: \su__%k=1..%numberOfSources_ \su__%i=1..%numberOfPoints_ \su__%j=1..%numberOfPoints_ (%\de^2__%ijk_ \-- %d^2__%ijk_)^2 This loss function is minimized in the (ratio scale option of the) #ALSCAL program of @@Takane, Young & de Leeuw (1976)@. The transformation used by @@Carroll & Chang (1970)@ in the INDSCAL model, transforms the data from each source into scalar products of vectors. For the dissimilarities: %\be__%ijk_ = \--{ %\de^2__%ijk_ \-- %\de^2__%i.%k_ \-- %\de^2__.%jk_ + %\de^2__..%k_ } / 2, where dots replacing indices indicate averaging over the range of that index. In the same way for the distances: %z__%ijk_ = \--{ %d^2__%ijk_ \-- %d^2__%i.%k_ \-- %d^2__%.%jk_ + %d^2__%..%k_ } / 2. %\be__%ijk_ \~~ %z__%ijk_ = \su__%s=1..%numberOfDimensions_ %w__%ks_ %x__%is_ %x__%js_ Translated into matrix algebra, the equation above translates to: %B__%k_ \~~ %Z__%k_ = %X %W__%k_ %X\'p, where %X is a %numberOfPoints \xx %numberOfDimensions configuration matrix, %W__%k_, a non-negative %numberOfDimensions \xx %numberOfDimensions matrix with weights, and %B__%k_ the %k^^th^ slab of %\be__%ijk_. This translates to the following INDSCAL loss function: %f(%X, %W__1_,..., %W__%numberOfSources_) = \su__%k=1..%numberOfSources_ | %B__%k_ \-- %X%W__%k_%X\'p |^2 A method for @@individual difference scaling@ analysis in P\s{RAAT}. An INDSCAL analysis can be performed on objects of type Distance. If you start with @Dissimilarity objects you first have to transform them to Distance objects. \bu @@Dissimilarity: To Distance...@ If you start with a @Confusion you can use: \bu @@Confusion: To Dissimilarity (pdf)...@ Examples \bu @@Distance: To Configuration (indscal)...@ Perform an INDSCAL analysis on one or more objects of type @Distance to calculate a @Configuration. \bu @@Distance & Configuration: To Configuration (indscal)...@ Perform an INDSCAL analysis on one or more objects of type @Distance to calculate a @Configuration. Use the selected Configuration object as the initial Configuration in the iteration process. The function to be minimized in INDSCAL is the following: %f(%X, %W__1_,..., %W__%numberOfSources_) = \su__%i=1..%numberOfSources_ |%S__%i_ \-- %XW__%i_%X\'p|^2 where %X an unknown %numberOfPoints x %numberOfDimensions configuration matrix, the %W__%i_ are %numberOfSources unknown diagonal %numberOfDimensions x %numberOfDimensions matrices with weights, often called saliences, and the %S__%i_ are known symmetric matrices with scalar products of dimension %numberOfPoints x %numberOfPoints. In the absence of an algorithm that minimizes %f, @@Carroll & Chang (1970)@ resorted to the @CANDECOMP algorithm, which instead of the function given above minimizes the following function: %g(%X, %Y, %W__1_,..., %W__%numberOfSources_) = \su__%i=1..%numberOfSources_ |%S__%i_ \-- %XW__%i_%Y\'p|^2. Carroll & Chang claimed that for most practical circumstances %X and %Y converge to matrices that will be columnwise proportional. However, INDSCAL does not only require symmetry of the solution, but also non-negativity of the weights. Both these aspects can not be guaranteed with the CANDECOMP algorithm. @@Ten Berge, Kiers & Krijnen (1993)@ describe an algorithm that automatically satisfies symmetry because it solves %f directly, and, also, can guarantee non-negativity of the weights. This algorithm proceeds as follows: Let #%x__%h_ be the %h-th column of %X. We then write the function %f above as: %f(#%x__%h_, %w__1%h_, ..., %w__%numberOfSources %h_) = \su__%i=1..%numberOfSources_ |%S__%ih_ \-- #%x__%h_%w__%ih_#%x\'p__%h_|^2, with %S__%ih_ defined as: %S__%ih_ = (%S__%i_ - \su__%j\=/%h, %j=1..%numberOfDimensions_ #%x__%j_%w__%ij_#%x\'p__%j_). Without loss of generality we may require that #%x\'p__%h_#%x__%h_ = 1 Minimizing %f over #%x__%h_ is equivalent to minimizing \su__%i=1..%numberOfSources_ |%S__%ih_|^2 \-- 2tr \su %S__%ih_#%x__%h_%w__%ih_#%x\'p__%h_ + \su %w^2__%ih_ This amounts to maximizing %g(#%x__%h_) = #%x\'p__%h_(\su %w__%ih_%S__%ih_)#%x__%h_ subject to #%x\'p__%h_#%x__%h_ = 1. The solution for #%x__%h_ is the dominant eigenvector of (\su %w__%ih_%S__%ih_), which can be determined with the power method (see @@Golub & van Loan (1996)@). The optimal value for the %w__%ih_, given that all other parameters are fixed: %w__%ih_ = #%x\'p__%h_%S__%ih_#%x__%h_ In an alternating least squares procedure we may update columns of %X and the diagonals of the %W matrices in any sensible order. One of the @@MDS models@ in P\s{RAAT}. You can perform a Kruskal-type multidimensional scaling only on objects of type @Dissimilarity. Objects of other types first have to be converted to objects of Dissimilarity type. Example Convert a @Dissimilarity object into a @Configuration object. \bu @@Dissimilarity: To Configuration (monotone mds)...@ choose appropriate parameters \bu @@Dissimilarity & Configuration: Get stress (monotone mds)...@ choose stress-1 to obtain the value for the @stress according to Kruskal. How to get started You can create an example @Dissimilarity object with the @@Create letter R example...@ button which you can find under the ##Multidimensional scaling# option in the #New menu. Multidimensional scaling (MDS) models are defined by specifying how given @Dissimilarity data, %\de__%ij_, are mapped into distances of an %m-dimensional MDS @Configuration %#X. The mapping is specified by a %%representation function%, %f : %\de__%ij_ \-> %d__%ij_(#X), which specifies how dissimilarities should be related to the distances. The MDS analysis tries to find the configuration (in a given dimensionality) whose distances satisfy %f as closely as possible. This closeness is quantified by a badness-of-fit measure which is often called @stress. Representation functions In the application of MDS we try to find a configuration #X such that the following relations are sasatisfieds well as possible: %f(%\de__%ij_) \~~ %d__%ij_(#X) The numbers that result from applying %f on %\de__%ij_ are sometimes called @disparities %d\d'__%ij_. In most applications of MDS, besides the configuration #X, also the function %f is not completely specified, i.e., the exact parameters of %f are unknown and must also be estimated during the analysis. If no particular %f can be derived from a theoretical model, one often restricts %f to a particular class of functions on the basis of the scale level of the dissimilarity data. If the disparities are related to the proximities by a specific parametric function we speak of %metric MDS otherwise we speak of %ordinal or %%non-metric% MDS. \bu %absolute mds: %d\'p__%ij_ = \de__%ij_ No parameters need to be estimated. \bu %ratio mds: %d\'p__%ij_ = %b \.c \de__%ij_, where the value of %b can be estimated by a linear regression of %d__%ij_ on %\de__%ij_. \bu %interval mds: %d\'p__%ij_ = %a + %b \.c %\de__%ij_, where the values of %a and %b can be estimated by a linear regression of %d__%ij_ on %\de__%ij_. \bu i-spline mds: %d\'p__%ij_ = %i-spline(%\de__%ij_), where %i-spline(\.c) is a smooth monotonically increasing @spline curve. The conceptual idea is that it is not possible to map all dissimilarities into disparities by one simple function. \bu %monotone mds: %d\'p__%ij_ = %monotone(\de__%ij_), where %monotone(\.c) is restricted to be a monotonic function that preserves the order of the dissimilarities: if %\de__%ij_ < %\de__%kl_, then %d__%ij_(#X) < %d__%kl_(#X) If %\de__%ij_ = %\de__%kl_ and no particular constraint is involved for %d__%ij_(#X) and %d__%kl_(#X) this is referred to as the %%primary approach% to ties. The %%secondary approach% to ties requires that if %\de__%ij_ = %\de__%kl_, then also %d__%ij_(#X) = %d__%kl_(#X). More information on all aspects of multidimensional scaling can be found in: @@Borg & Groenen (1997)@ and @@Ramsay (1988)@. The most important types and the conversions between them are shown in the following figure. According to the measurement theory of @@Stevens (1951)@, there are four measurement levels, namely #Nominal, #Ordinal, #Interval and #Ratio. In the light of multidimensional scaling, the first two levels, Nominal and Ordinal, are often called %non-%metric. The last two are %metric. This tutorial describes how you can use P\s{RAAT} to perform ##M#ulti##D#imensional ##S#caling (MDS) analysis. MDS helps us to represent %dissimilarities between objects as %distances in a %%Euclidean space%. In effect, the more dissimilar two objects are, the larger the distance between the objects in the Euclidean space should be. The data types in P\s{RAAT} that incorporate these notions are @Dissimilarity, @Distance and @Configuration. In essence, an MDS-analysis is performed when you select a Dissimilarity object and choose one of the ##To Configuration (xxx)...# commands to obtain a Configuration object. In the above, method (xxx) represents on of the possible @@MDS models|multidimensional scaling models@. MDS-analysis Let us first create a Dissimilarity object. You can for example @@Dissimilarity|create a Dissimilarity object from a file@. Here we will the use the Dissimilarity object from @@Create letter R example...|the letter R example@. We have chchosenhe default value (32.5) for the (uniform) noise range. Note that this may result in substantial distortions between the dissimilarities and the distances. Now you can do the following, for example: Select the Dissimilarity and choose @@Dissimilarity: To Configuration (monotone mds)...|To Configuration (monotone mds)...@, and you perform a @@Kruskal analysis|kruskal@-like multidimensional scaling which results in a new Configuration object. (This Configuration could subsequently be used as the starting Configuration for a new MDS-analysis!). Select the Configuration and choose @@Configuration: Draw...|Draw...@ and the following picture will result The following script summarizes: Create letter R example... 32.5 select Dissimilarity R To Configuration (monotone mds)... 2 "Primary approach" 0.00001 50 1 Draw... 1 2 -0.8 1.2 -0.8 0.7 yes Obtaining the stress value Select the Dissimilarity and the Configuration together and query for the @stress value with: @@Dissimilarity & Configuration: Get stress (monotone mds)...|Get stress (monotone mds)...@. plus Configuration R_monotone Get stress (monotone mds)... "Primary approach" "Kruskals's stress-1") The Shepard diagram Select the Dissimilarity and the Configuration together to @@Dissimilarity & Configuration: Draw Shepard diagram...|draw the Shepard diagram@. Draw Shepard diagram...0 200 0 2.2 1 + yes The (monotone) regression Select the Dissimilarity and the Configuration together to @@Dissimilarity & Configuration: Draw regression (monotone mds)...|draw the monotone regression@ of distances on dissimilarities. Draw monotone regresion... "Primary approach" 0 200 0 2.2 1 + yes When you enter %noiseRange = 0 in the form for the letter #R, perfect reconstruction is possible. The Shepard diagram then will show a perfectly smooth monotonically increasing function. Weighing the dissimilarities When you can't have equal confidence in all the number in the Dissimilarity object, you can give different weights to these numbers by associating a @Weight object with the Dissimilarity object. An easy way to do this is to select the Dissimilarity object and first choose @@Dissimilarity: To Weight|To Weight@. Then you might change the individual weights in the Weight object with the @@TableOfReal: Set value...| Set value...@ command (remember: make %w__%ij_ = %w__%ji_). To Weight ! Change [i][j] and [j][i] cells in the Weight object Set value... i j val Set value... j i val ... ! now we can do a weighed analysis. plus Weight R You can also query the @stress values with three objects selected. The following script summarizes: plus Configuration R_s_monotone Using a start Configuration You could also use a Configuration object as a starting configuration in the minimization process. Lets assume that you are not satisfied with the stress value from the Configuration object that you obtained in the previous analysis. You can than use this Configuration object as a starting point for further analysis: Multiple Dissimilarity's (INDSCAL) When you have multiple Dissimilarity objects you can also perform @@individual difference scaling@ (often called @@INDSCAL analysis@). As an example we can use an @@Create INDSCAL Carroll & Wish example...| example taken from Carrol & Wish@. Because INDSCAL only works on metrical data, we can not use Dissimilarity objects directly. We have to transform them first @@Dissimilarity: To Distance...|to Distance@ objects. This type of analysis on multiple objects results in two new objects: a Configuration and a @Salience. An object of type Procrustes represents the special @@AffineTransform|affine transform@ that consists of a combination of a translation, a shape preserving transformation and a scaling (this scaling is often called %dilation). Because the transformation has to be shape preserving, only a combination of a rotation and a reflection is allowed. A configuration matrix #%X is transformed in the following way to a new configuration matrix #%Y: #%Y = %s #%X #%T+ #1#%t', where %s is the scaling factor, #%T is the shape preserving transformation matrix, #%t is the translation vector, and #1 is the vector with only ones as its elements. For more information about the Procrustes transform and its algorithm see chapter 19 in @@Borg & Groenen (1997)@. A transformation that only uses a combination of a translation, a scaling and a rigid transformation to transform one Configuration such that it matches as closely as possible another Configuration. We speak of %%orthogonal Procrustes transform% when only the rigid transformation is allowed but no scaling or translation. An object of type #Proximity represents proximities between objects. Inside a Proximity %numberOfRows, %numberOfColumns the number of objects (%numberOfRows and %numberOfColumns are equal and \>_1). %rowLabels, %columnLabels the names associated with the objects (%rowLabels and %columnLabels are equal. %data [1..%numberOfRows][1..%numberOfColumns] the proximities between the objects. Elements %s__%ij_ in the Salience matrix represent the importance of dimension %j (in the @Configuration) for data source %i. Creation, as a by-product of: \bu @@Distance: To Configuration (indscal)... \bu @@Distance: To Configuration (ytl)... An object of type ScalarProduct represents scalar products %b__%ij_ between objects %i and %j in a metrical space. %b__%ij_ = \su__%k=1..%numberOfDimensions_ %x__%ik_%x__%jk_, where %x__%ik_ and %x__%jk_ are the coordinates of the %k-th dimension of points %i and %j, respectively. From this definition one can see that scalar products, in contrast to distances, do change when the origin is shifted. \bu @@Distance: To ScalarProduct...@ An object of type Similarity represent a one-way table of similarities between "objects". \bu @@Confusion: To Similarity... \bu ##Formula... \bu @@Similarity: To Dissimilarity... A command that creates a @Dissimilarity from every selected @Similarity. determines the maximum dissimilarity possible. When the default value, 0.0, is chchosen%maximumDissimilarity is calculated as the maximum element in the Similarity object. To obtain dissimilarities we 'reverse' similarities: In this way the order of dissimilarities is the reverse of the order of the similarities. Scaling by Majorizing a Complicated Function, the iterative algorithm to find an optimal Configuration. 1. Initialize 1.a. Get initial Configuration #Z 1.b. Set stress %\si__%n_^^[0]^ to a very large value. 1.c. Set iteration counter %k = 0 2. Increase iteration counter by one: %k = %k + 1 3. Calculate distances %d__%ij_(#Z). 4. Transform dissimilarities %\de__%ij_ into disparities %d\'p__%ij_. 5. Standardize the disparities so that %\et__%d\'p_^2 = %n(%n\--1)/2. 6. Compute the Guttman transform #X^^[%k]^ of #Z. 7. Compute new distances %d__%ij_(#X^^[%k]^). 8. Compute normalized stress %\si__%n_ (#d\'p, #X^^[%k]^) 9. If |%\si__%n_^^[%k]^ \-- %\si__%n_^^[%k\--1]^| / %\si__%n_^^[%k\--1]^ < %\ep or %k > %maximumNumberOfIterations, then stop 10. Set #Z = #X^^[%k]^, and go to 2. This algorithm goes back to @@De Leeuw (1977)@. A spline function %f is a piecewise polynomial function defined on an interval [%x__%min_, %x__%max_] with specified continuity constraints, i.e., when the interval [%x__%min_, %x__%max_] is subdivided by points \xi__%i_ such that %x__%min_ = \xi__%1_ < ... < \xi__%q_ = %%x__%max_, then within each subinterval [\xi__%j_, \xi__%j+1_) the function is a polynomial %P__%j_ of specified order %k. A %%knot sequence% %t = {%t__1_, ..., %t__%n+%k_}, where %n is the number of free parameters that specify the spline function, is derived from the \xi__%i_ by placing knots at the boundary values \xi__%i_ according to the order of continuity at that boundary. The most common continuity chcharacteristicsmposed on %f request that for adjacent polynomials the derivatives up to order %k\--2 match. For example, the knot sequence of a spline of order %k for a partition of [%x__%min_, %%x__%max_] into three intervals (%q = 4) will be %t__1_ = ... = %t__%k_ = %x__%min_ (=\xi__1_), %t__%k+1_ = \xi__2_, %t__%k+2_ = \xi__3_ , %t__%k+3_ = ... = %t__%k+%k+2_ = %x__%max_ (= \xi__4_). This is called a %simple knot sequence, because all interior knots are simple. The number of free parameters %n for this case obeys a simple formula: %n = %numberOfInteriorKnots + %order. With suitable basis functions, for example, the M-spline family %M__%i_(%x|%k, %t), %i=1..%n, we can write any spline %f in the form: %f = \su__%i=1..%n_ %a__%i_%M__%i_, where the %M__%i_ are defined by the following recursive formulas: %M__%i_(%x|1,%t) = 1 / (%t__%i+1_ \-- %t__%i_), %t__%i_ \<_ %x < %t__%i+1_, 0 otherwise %M__%i_(%x|%k,%t) = %k [(%x\--%t__%i_)%M__%i_(%x|%k\--1,%t) + (%t__%i+%k_\--%x)%M__%i+1_(%x|%k\--1,%t)] / ((%k\--1)(%t__%i+%k_\--%t__%i_)) These %M__%i_ are localized because %M__%i_(%x|%k,%t) > 0 only when %t__%i_ \<_ %x < %t__%i+%k_ and zero otherwise. Also, we have \in M__%i_(%x)%dx = 1. Because of this localization a change in coefficient %a__%i_ will only effect %f within this interval. The following picture shows an M-spline of order 3 on the interval [0, 1], with three interior knots at 0.3, 0.5 and 0.6. Because the M-splines are nonnegative, %monotone splines% can be derived from them by %integration: %I__%i_(%x|%k,%t) = \in__%xmin_^%x %M__%i_(%u|%k,%t) %du Because each %M__%i_(%x|%k, %t) is a piecewise polynomial of degree %k\--1, each %I__%i_ will be of degree %k. Now we can write: %f = \su__%i=1..%n_ %b__%i_%I__%i_(%x|%k,%t) We can use an M-spline of order %k+1 with a simple knot sequence %t, for which %t__%j_ \<_ x < %t__%j+1_, to put the I-spline of order %k into a more convenient form: %I__%i_(%x|%k,%t) = 0, %i > %j %I__%i_(%x|%k,%t) = \su__%m=%i+1..%j_ (%t__%m+%k+1_\--%t__%m_)%M__%m_(%x|%k+1,%t)/(%k+1), %j\--%k \<_ %i \<_ %j %I__%i_(%x|%k,%t) = 1, %i < %j\--%k The following figure shows the I-splines that were derived from the M-splines above. These spline formula's were taken from @@Ramsay (1988)@ and the errors in his I-spline formulas were corrected. A badness-of-fit measure for the entire MDS representation. Several measures exist. Raw stress %\si__%r_ (#d\'p, #X) = \su__%i<%j_ %w__%ij_(%d\'p__%ij_ \-- %d__%ij_(#X))^2 = \su__%i<%j_ %w__%ij_%d\'p__%ij_^2 + \su__%i<%j_ %w__%ij_%d__%ij_^2(#X) \-- 2 \su__%i<%j_ %w__%ij_%d\'p__%ij_%d__%ij_(#X) = %\et__%d\'p_^2 + %\et^2(#X) \-- 2%\ro(#d\'p, #X) where the %d\'p__%ij_ are the @disparities that are the result from the transformation of the dissimilarities, i.e., %f(%\de__%ij_). Raw stress can be misleading because it is dependent on the normalization of the disparities. The following measure tries to circumvent this inconvenience. Normalized stress %\si__%n_ = \si__%r_ / %\et__%d\'p_^2 This is the stress function that we minimize by iterative majorization. It goes back to @@De Leeuw (1977)@. Kruskal's stress-1 %\si__1_ = \Vr (\su__%i<%j_ %w__%ij_(%d\'p__%ij_ \-- %d__%ij_(#X))^2 / \su__%i<%j_ %w__%ij_%d__%ij_^2(#X))^^1/2^ In this measure, which is due to @@Kruskal (1964)@, stress is expressed in relation to the size of #X. Kruskal's stress-2 %\si__2_ = \Vr (\su__%i<%j_ %w__%ij_(%d\'p__%ij_ \-- %d__%ij_(#X))^2 / \su__%i<%j_ %w__%ij_(%d__%ij_(#X) - %averageDistance)^2)^^1/2^. In general, this measure results in a stress value that is approximately twice the value for stress-1. Relation between %\si__1_ and %\si__n_ When we have calculated %\si__%n_ for Configuration #X, disparities #d\'p and Weight #W we cannot directly use #X, #d\'p and #W to calculate %\si__1_ because the scale of #X is not necessarily optimal for %\si__1_. We allow therefore a scale factor %b > 0 and try to calculate %\si__1_ (#d\'p, %b #X). We minimize the resulting expression for %b and substitute the result back into the formula for stress, i.e., %\si__1_^2 (#d\'p, %b #X) = (%\et__%d\'p_^2 + %b^2 %\et^2(#X) \-- 2 %b %\ro(#d\'p, #X)) / %b^2 %\et^2(#X) d%\si__1_^2 (%b) / d%b == 0, gives %b = %\et__%d\'p_^2 / %\ro %\si__1_^2 = (1 - %\ro^2 / (%\et__%d\'p_^2\.c%\et^2(#X))) This means that %\si__1_ = \Vr %\si__%n_. Relation between %\si__2_ and %\si__n_ We can do the same trick as before for %\si__2_: %\si__2_^2 (#d\'p, %b #X) = (%\et__%d\'p_^2 + %b^2 %\et^2(#X) \-- 2 %b %\ro(#d\'p, #X)) / (%b^2 \su__%i<%j_ %w__%ij_(%d__%ij_(#X) - %averageDistance)^2) From which we derive: %\si__2_ = \Vr ((%\et__%d\'p_^2 \.c %\et^2(#X) - %\ro^2(#d\'p, #X)) / (%\et__%d\'p_^2 \.c \su__%i<%j_ %w__%ij_(%d__%ij_(#X) - %averageDistance)^2)) A command that centres the columns in the selected @TableOfReal objects. The new values in the table, %x\'p__%ij_, will be: %x\'p__%ij_ = %x__%ij_ \-- %x__\.c%j_, where %x__\.c%j_ = \su__%i=1..%numberOfRows_ %x__%ij_ / %numberOfRows, the average of column %j. A command that centres the rows in the selected @TableOfReal objects. %x\'p__%ij_ = %x__%ij_ \-- %x__%i\.c_, %x__%i\.c_ = \su__%j=1..%numberOfColumns_ %x__%ij_ / %numberOfColumns, the average of row %i. A command that returns the norm of the selected @TableOfReal object. Returns: sqrt (\su__%i=1..%numberOfRows_ \su__%j=1..%numberOfColumns_ %x__%ij_^2). A command that normalizes the columns in the selected @TableOfReal objects. %Norm determines the sum of the squared elements in each column after normalization. All elements %x__%ij_ in each column %j=1..%numberOfColumns will be multiplied by sqrt (%norm / \su__%i=1..%numberOfRows_ %x__%ij_^2). A command that normalizes the rows in the selected @TableOfReal objects. determines the sum of the squared elements in each row after normalization. All elements %x__%ij_ in each row %i=1..%numberOfRows will be multiplied by sqrt (%norm / \su__%j=1..%numberOfColumns_ %x__%ij_^2). A command that normalizes the elements in the selected @TableOfReal objects. determines the sum of the squared elements after normalization. All elements %x__%ij_ will be multiplied by sqrt (%norm / \su__%i=1..%numberOfRows_ \su__%j=1..%numberOfColumns_ %x__%ij_^2. An object of type Weight represents a matrix with weights %w__%ij_. An object of type Weight selected together with an onject of type @Dissimilarity can be used to make distinctions in the importance of the contribution of each individual dissimilarity %\de__%ij_ to @stress and therefore to the final configuration. Weights can be used for instance to code for missing values, i.e., take %w__%ij_ = 0 if dissimilarity %\de__%ij_ is missing and %w__%ij_ = 1 if %\de__%ij_ is known. See @@Dissimilarity & Weight: To Configuration...@ for help on the following analysis items: \bu ##Dissimilarity & Weight: To Configuration (monotone mds)... \bu ##Dissimilarity & Weight: To Configuration (i-spline mds)... \bu ##Dissimilarity & Weight: To Configuration (interval mds)... \bu ##Dissimilarity & Weight: To Configuration (ratio mds)... \bu ##Dissimilarity & Weight: To Configuration (absolute mds)... See @@Dissimilarity & Configuration & Weight: Get stress...@ for help on the following query items: \bu ##Dissimilarity & Configuration & Weight: Get stress (monotone mds)... \bu ##Dissimilarity & Configuration & Weight: Get stress (i-spline mds)... \bu ##Dissimilarity & Configuration & Weight: Get stress (interval mds)... \bu ##Dissimilarity & Configuration & Weight: Get stress (ratio mds)... \bu ##Dissimilarity & Configuration & Weight: Get stress (absolute mds)... M. Abramowitz & I. Stegun (1970), %%Handbook of Mathematical Functions%, Dover Publications, Inc., New York. I. Borg & P. Groenen (1997), %%Modern Multidimensional Scaling: Theory and Applications%, Springer. F.B. Brokken (1983), "Orthogonal Procrustes rotation maximizing congruence", %Psychometrika #48, 343-352. F. Cailliez (1983), "The analytical solution of the additive constant problem", %Psychometrika #48, 305-308. J.D. Carroll & J.-J. Chang, (1970): "Analysis of Individual Differences in Multidimensional scaling via an N-way generalization of "Eckart-Young" Decomposition", %Psychometrika #35, 283-319. J.D. Carroll & M. Wish, (1974): "Models and methods for three-way multidimensional scaling", in D.H. Krantz, R.C. Atkinson, R.D. Luce & P. Suppes (Eds.), %%Contemporary developments in mathematical psychology: Vol. 2 Measurement, psychophysics, and neural information processing%, 283-319, New York, Academic Press. J. de Leeuw (1977), "Applications of convex analysis to multidimensional scaling", In J.R. Barra, F. Brodeau, G. Romier & B. van Cutsem (eds.), %% Recent developments in statistics%, Amsterdam, The Netherlands: North-Holland, 133-145. J. de Leeuw & S. Pruzansky (1978), "A new computational method to fit the weighted Euclidean distance model", %Psychometrika , 479-490. A. Gifi (1990), %%Nonlinear Multivariate Analysis%, John Wiley & Sons Ltd., reprint 1996 G. Golub & C. van Loan (1996), %%Matrix computations%, third edition, The Johns Hopkins University Press, London P. Green, F. Carmone, S. Smith (1989): %%Multidimensional scaling: concepts and applications%, section 3. Allyn and Bacon. H.F. Kaiser (1958), "The varimax criterion for analytic rotation in factor analysis", %Psychometrika #23, 187-200. H.A.L. Kiers & P. Groenen (1996), "A monotonically convergent algorithm for orthogonal congruence rotation", %Psychometrika #61, 375-389. W. Klein, R. Plomp, & L.C.W. Pols (1970), "Vowel Spectra, Vowel Spaces, and Vowel Identification", JASA 48, 999-1009. J.B. Kruskal (1964), "Nonmetric multidimensional scaling: a numerical method", %Psychometrika #29, 115-129. J.O. Ramsay (1988), "Monotone Regression Splines in Action", %%Statistical Science% #3, 425-461. S.S. Stevens (1951), "Mathematics, measurement, and psychophysics", in S.S. Stevens (Ed.), %%Handbook of experimental Psychology%, New York: Wiley. Y. Takane, F. Young, J. de Leeuw (1976), "Non-metric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features", %Psychometrika #42, 7-67. J.M.F. ten Berge (1995), "Suppressing permutations or rigid planar rotations: A remedy against nonoptimal varimax rotations", %Psychometrika #60, 437-446. J.M.F. ten Berge, H.A.L. Kiers & W.P. Krijnen (1993), "Computational Solutions for the Problem of Negative Saliences and Nonsymmetry in INDSCAL", %Journal of Classification #10, 115-124. W.S. Torgerson (1958), %%Theory and methods of scaling%, New York: Wiley. F.W. Young, Y. Takane & R. Lewyckyj (1978), "Three notes on ALSCAL", %Psychometrika #43, 433-435. S.C. Weller & A.K. Romney (1990) %%Metric Scaling: Correspondence Analysis%, Sage University Paper Series on Quantitative Applications in the Social Sciences 07-075, Newbury Park, CA: Sage. CANDECOMP djmw Configuration Configuration: Centralize Configuration: Draw... Configuration: Invert dimension... Configuration: Normalize... Configuration: Randomize Configuration: Rotate... Configuration: Rotate (pc) Configuration: To Configuration (procrustes) Configuration: To Configuration (varimax)... Configuration: To Distance Configuration: To Similarity (cc) Configuration & AffineTransform: To Configuration Configuration & Procrustes: To Configuration Configurations: To AffineTransform (congruence)... Configuration & Configuration: To Procrustes... Confusion: To Dissimilarity... Confusion: To Dissimilarity (pdf)... Confusion: To Similarity... congruence coefficient ContingencyTable ContingencyTable: To Configuration (ca)... Correspondence analysis Create Configuration... Create INDSCAL Carroll & Wish example... Create letter R example... disparities Dissimilarity Dissimilarity: Get additive constant Dissimilarity: To Configuration (absolute mds)... Dissimilarity: To Configuration (interval mds)... Dissimilarity: To Configuration (i-spline mds)... Dissimilarity: To Configuration (kruskal)... Dissimilarity: To Configuration (monotone mds)... Dissimilarity: To Configuration (ratio mds)... Dissimilarity: To Distance... Dissimilarity: To Weight Dissimilarity & Configuration: Draw regression (absolute mds)... Dissimilarity & Configuration: Draw regression (interval mds)... Dissimilarity & Configuration: Draw regression (i-spline mds)... Dissimilarity & Configuration: Draw regression (monotone mds)... Dissimilarity & Configuration: Draw regression (ratio mds)... Dissimilarity & Configuration: Draw Shepard diagram... Dissimilarity & Configuration: Get stress (absolute mds)... Dissimilarity & Configuration: Get stress (interval mds)... Dissimilarity & Configuration: Get stress (i-spline mds)... Dissimilarity & Configuration: Get stress (monotone mds)... Dissimilarity & Configuration: Get stress (ratio mds)... Dissimilarity & Configuration: To Configuration (absolute mds)... Dissimilarity & Configuration: To Configuration (interval mds)... Dissimilarity & Configuration: To Configuration (i-spline mds)... Dissimilarity & Configuration: To Configuration (kruskal)... Dissimilarity & Configuration: To Configuration (monotone mds)... Dissimilarity & Configuration: To Configuration (ratio mds)... Dissimilarity & Configuration & Weight: Get stress... Dissimilarity & Configuration & Weight: To Configuration... Dissimilarity & Weight: To Configuration... Distance Distance: To Configuration (indscal)... Distance: To Configuration (ytl)... Distance: To ScalarProduct... Distance & Configuration: Draw scatter diagram... Distance & Configuration: Get VAF... Distance & Configuration: To Configuration (indscal)... Distance & Configuration & Salience: Get VAF... Distance & Configuration & Salience: To Configuration (indscal)... individual difference scaling INDSCAL analysis Kruskal analysis MDS models Measurement levels Multidimensional scaling Procrustes Procrustes transform Proximity Salience ScalarProduct Similarity Similarity: To Dissimilarity... smacof spline stress TableOfReal: Centre columns TableOfReal: Centre rows TableOfReal: Get table norm TableOfReal: Normalize columns... TableOfReal: Normalize rows... TableOfReal: Normalize table... Weight Abramowitz & Stegun (1970) Borg & Groenen (1997) Brokken (1983) Cailliez (1983) Carroll & Chang (1970) Carroll & Wish (1974) De Leeuw (1977) De Leeuw & Pruzansky (1978) Gifi (1990) Golub & van Loan (1996) Green, Carmone & Smith (1989) Kaiser (1958) Kiers & Groenen (1996) Klein, Plomp & Pols (1970) Kruskal (1964) Ramsay (1988) Stevens (1951) Takane, Young & de Leeuw (1976) Ten Berge (1995) Ten Berge, Kiers & Krijnen (1993) Torgerson (1958) Young, Takane & Lewyckyj (1978) Weller & Romney (1990) b eC b -c $ b C 6b b $ b C Tb b $ Ԥb uC sb b $ b ŪC b b $ b C b b $ @b JC b 'j db (empty) CategoriesEditor CategoriesEditor.c min >= 1 && max <= my size && (newpos <= min || newpos >= max) CategoriesEditorCommand Insert CategoriesEditorInsert Remove CategoriesEditorRemove Replace CategoriesEditorReplace Move up CategoriesEditorMoveUp Move down CategoriesEditorMoveDown %d selection(s) out of view nothing Undo `%.40s' Redo `%.40s' %6d %.*s CategoriesEditor help Help Positions: Values: listWindow list Value: Text Insert at end Undo Redo Move selection up Move selection down C pb i ` b ? ?Activation C 1b +c |b size item [%ld]: Categories C ܩb i <b ClassificationTable *b $ *b i b b 8b C *b i $ b ? f@ @-DT! @ @ ? ? @ @ @ @ ? ? @ @ ? @ @ @ @ @ @ @ @ @ @ @ ? mBjR?te|?yk?QW? k?ĉR?? >$k j5 ɿAGf1BtYoIg'-~ 0ܷu*t0vGWy /w :k)K俄/x4"#ր\C-?|6p?'u?Ou]L?Dͨ?_x?4r?/E?Dpw4?8Y7?&"?]%? ?eB?E ?Ѫ?4u? ?M!z"?P5S?R> ?n?N?M4?A?2>q?W"-nƿҿlA 5ݿͽ h?MYc}y߿Ϻw@̿)(顿1<Q ?m??ÿƷzӿeABֿԁ@俴S ? ? ? ? ? ? Yb Zb \b ^b `b bb db fb hb jb xC lb hj hb metric w Trying to read "%s". Configuration my numberOfColumns Number of points = %ld Number of dimensions = %ld Metric = %ld dimension Configuration.c nr > 0 && nc > 0 Configuration_draw: %d from %d labels are not visible because they are empty or they contain only spaces or they contain only non-printable characters R_fit R %d A B C D E F G H I Configurations C ״b i |b +eG?KH9 @ ? $@@? Y@ ? fff? ?fff? ? ? ? I have %ld rows and %ld columns. Entropies (y is row variable): %.17g :total %.17g :y %.17g :x %.17g :y given x %.17g :x given y %.17g :dependency of y on x %.17g :dependency of x on y %.17g :symmetrical dependency %d :total number of entries -- undefined -- :fraction correct %.17g :fraction correct Confusion Categories_to_Confusion: dimensions do not agree. Confusion_addConfusion: stimulus or response not valid. Pointer Confusion_Matrix_draw: number of positions. Confusion_difference: dimensions not equal. Confusion_condense: no row or column labels. b , b b ȷb b !b 0 c b 'b H c b $ ,b b ( ,b ,b #C b b , b ? ?numberOfGroups groups total aprioriProbabilities costs Trying to read "%s". Discriminant SSCPs SSCP my numberOfGroups Number of groups = %ld Number of variables = %ld Number of discriminant functions = %ld Number of observations (total) = %ld Discriminant_setAprioriProbability: group (%d) must be in interval [1, %d]. Discriminant_setAprioriProbability: probability must be in interval [0,1] Discriminant_setGroupLabels: The number of strings must equal the number of groups. constant function_ Discriminant_extractWithinGroupSSCP: index must be in interval [1,%d] Discriminant_drawConcentrationEllipses: Nothing drawn because there is only one dimension in the discriminant space. function %d TableOfReal_to_Discriminant %s: table contains infinities. %s: At least one of the rows has no label. c %s: There were no column labels. We could not set them either. %s: number of groups must be greater than one. Eigenvector Discriminant_and_TableOfReal_to_ClassificationTable: the number of columns does not agree with the dimension of the discriminant. Discriminant_and_TableOfReal_to_ClassificationTable: %d groups use pooled covariance matrix. ? b b b p b @i b ` b h b l b Db b X D b i p b ? +? ? @ @ $@v~v~ @@ @ ?x y weightedDistance pathLength (empty) path []: %s path [%ld]: Trying to read "%s". DTW path DTW_State my pathLength DTW info Name: %s Domain prototype: from %.8g to %.8g Domain candidate: from %.8g to %.8g Number of frames prototype: %ld Number of frames candidate: %ld Path length %ld (frames) Global warped distance: %.8g Distance along diagonal: %.8g %s: There is a conflict between the chosen parameters. We cannot 'Match end positions' because the sum of the durations of the shortest object and the adjustment window is shorter than the duration of the longest object and you have not chosen to include the end point in the adjustment window. Suggestions: 1. Include end point in adjustment window, or, 2. Uncheck 'Match end positions'. %s: The slope constraints cannot be satisfied. Hint: To follow the the shortest path diagonal, the quotient 'Non-diagonal steps'/'Diagonal steps' is %.4g. Find path Er direction == DTW_UNREACHABLE, x %d, y %d Calculate time warp: frame %ld from %ld %d cells from %d had no valid direction assigned. DTW_pathfinder: Path stops at (x, y) = (%d, %d). DTW.c pathIndex > 1 && y > 0 DTW_pathFinder_band DTW_pathFinder_slopes DTW_findPath: Invalid slope constraint. DTW_findPath: There is a conflict between the chosen slope constraint and the relative duration. The duration ratio of the longest and the shortest object is %.17g. This implies that the largest slope in the constraint must have a value greater or equal to this ratio. DTW_findPath: illegal path pathIndex > 1 && ipos > 0 DTW_to_Polygon_band DTW_to_Polygon_slopes distance Spectrograms_to_DTW: #frequencies and/or frequency ranges do not match. Calculate distances: column %ld from %ld b b j 8b Lb Vb b bb b b ? $@ @ ? f@-DT! @,D b lj b numberOfEigenvalues dimension eigenvalues eigenvectors Trying to read "%s". Eigen my numberOfEigenvalues my dimension Eigen_initFromSquareRootPair %: Returned status code from NUMlapack_dggsvd: %d %s: No eigenvectors can be found. Matrix too singular. Cumulative fractional eigenvalue Fractional eigenvalue Cumulative eigenvalue Eigenvalue Index Element number Eigens_alignEigenvectors: The dimension of the eigenvectors must be equal (Object %d offending). The eigenvectors must have the same dimension. Eigenvector range too large. J>D b hj Pb Excitations Excitations.c my size > 0 Excitations_to_Pattern:number of rows is not a multiple of join. Matrix_and_Categories_to_TableOfReal: number of rows and number of categories must be equal. ? ffffff? @ ?Od@< ?Matrix_scale: choice must be >= 0 && < 3. Matrix_scale: extremum == 0, (part of) matrix unscaled. number/bin Matrix_solveEquation: there must be at least 2 columns in the matrix. Matrix_solveEquation: solution is not unique (fewer equations than unknowns). @ zo ?ư> ? +eG?KH9 ? +=-C 6? !? @ 8@? @?333333??333333???p= ףp? Q?????XD b n b ZD b b b [D 'b b @b _D ~b b ( hb -aD b i b JnD rb i 0b nD yb i b qD b lj pb sD b b b :tD b b b tD b i Xb uD b c b buD b q b xD "b b <b yD 2b q b D Vb c b D b n , $b ?ʡE?9v? ?? ?-?? ? ?9v?ʡE? ??-? ?b tb vb xb zb |b ~b b b ??ffffff??ffffff?? ?333333?333333?333333?333333? b Rb \b 2b xb b b Distances_to_Similarity_cc: All matrices must have the same dimensions. Transformator Transformator_transform: Dimensions do not agree. RatioTransformator MonotoneTransformator classISplineTransformator_transform: I-spline[%d], data[%d] = %f ISplineTransformator Number of rows: %ld Number of columns: %ld Entropies (y is row variable): %.17g :total %.17g :y %.17g :x %.17g :y given x %.17g :x given y %.17g :dependency of y on x %.17g :dependency of x on y %.17g :symmetrical dependency %.17g :chi squared %d :degrees of freedom %.17g : probability ContingencyTable ContingencyTable_to_Configuration_ca: Dimension too high. ContingencyTable_to_Configuration_ca: Empty row (%d). ContingencyTable_to_Configuration_ca: Empty column (%d). TableOfReal_to_Dissimilarity: TableOfReal must be a square matrix. TableOfReal_to_Similarity: TableOfReal must be a square matrix. TableOfReal_to_Distance: TableOfReal must be a square matrix. TableOfReal_to_ScalarProduct: TableOfReal must be a square matrix. Weight Salience dimension %d MDSVec MDSVecs Preference Confusions Distances ScalarProduct ScalarProducts Dissimilarity Dissimilarity_getAdditiveConstant: Matrix part is empty. Dissimilarities Similarity Confusion_to_Similarity: Confusion must be a square matrix. Similarity_to_Dissimilarity: Your maximumDissimilarity is smaller than the maximum similarity. Some data may be lost. Dissimilarity_to_Distance: could not determine "additive constant", the average dissimilarity was used as its value. Confusion_to_Dissimilarity_pdf: Must be a square matrix. MDS.c minimumConfusionLevel > 0 Distance_to_Configuration_torsca: number of dimensions too high. Proximity_Distance_drawScatterDiagram: dimensions and labels must be the same. Distance Proximities ytl i, j, a[i][j] %ld %ld %g untitled Dissimilarity_Configuration_Weight_Transformator_smacof: dimensions!!! MDS analysis kruskal: stress %f mds many times %ld from %ld Kruskal Dissimilarity_Configuration_kruskal: the number of data must be larger than number of parameters in the model. INDSCAL analysis indscal: vaf %f indscal **************** INDSCAL results on Distances ******************* %s, number of object(s): %d %s s WARNING: %d zero weight%s! Variance Accounted For = %.17g The optimal configuration was reached in %d iterations indscal_mr **************** INDSCAL with monotone regression ******************* %s, number of object(s): %d Variance Accounted For = %.17g Based on MONOTONE REGRESSION The optimal configuration was reached in %d iterations Indscal many times Distances_Configuration_Salience_vaf: dimensions must conform. ScalarProducts_Configuration_Salience_vaf: dimensions of input objects must conform. ScalarProducts_Configuration_Salience_vaf: ScalarProduct %d does not match Configuration. R 1 2 3 4 5 6 7 8 CarrollWish , drawSplines: knots must be in interval (%f, %f) drawSplines: too many knots (101) \s{M}\--spline \s{I}\--spline t__1_ {t__1_, t__2_} {t__1_..t__%d_} t__%d_ {t__%d_, t__%d_} {t__%d_..t__%d_} Confusion Dissimilarity %\de__%%ij%_ Distance %d__%%ij%_, %d\'p__%%ij%_ Configuration pdf average houtgast %d\'p__%%ij%_ = %\de__%%ij%_ absolute %d\'p__%%ij%_ = %b\.c%\de__%%ij%_ ratio %d\'p__%%ij%_ = %b\.c%\de__%%ij%_+%a interval %d\'p__%%ij%_ = \s{I}-spline (%\de__%%ij%_) %d\'p__%%ij%_ = monotone (%\de__%%ij%_) monotone \s{TORSCA} \s{YTL} \s{INDSCAL} ? ? ? @? "@>D b n P b ,D b b h 0b D b b 8 `b Dimension of search space: %6ld Iterations: %ld, Function calls: %ld, Cost: %f Minimization interrupted after %ld iterations. Minimizer Starting... Minimizer_minimize: minimum %f reached after %ld iterations and %ld function calls. Minimize many times Current %ld: minimum = %.17g %ld from %ld Number of iterations SteepestDescentMinimizer VDSmagtMinimizer LineMinimizer D b i ` b ? ? ?Pattern Matrix_to_Pattern:number of rows is not a multiple of join. *b $ *b b b b .b b .b D *b b $ b numberOfObservations (empty) labels []: %s labels [%ld] centroid Trying to read "%s". labels Trying to read element %ld of "%s". PCA my dimension Number of components = %d Number of dimensions = %d Number of observations = %d TableOfReal_to_PCA %s: There is not enough data to perform a PCA. Your table has less than 2 rows. %s: The number of rows in your table is less than the number of columns. %s: All values in your table are zero. pc PCA_and_Configuration_to_TableOfReal: The dimension of the Configuration must be less equal the dimension of the PCA. *G ? ? ?~b ~b ji ,b Ab b b 0 b b Nb Ub $ cb ( b ? 8@ @ ư>-DT! @=E ~b ji b pE Wb b b "E b b pb E b 5c <b ? V(E b b b -E b b 0 b 3E jb b 0 b 55E b b 0 \b numberOfCoefficients coefficients degree numberOfKnots knots Trying to read "%s". FunctionTerms my numberOfCoefficients Spline my numberOfKnots Polynomial.c degree > 1 FunctionTerms_setCoefficient: index out of range [1, %d]. FunctionTerms_setCoefficient: you cannot remove the highest degree term. Polynomial xmin < xmax Polynomial2_multiply: domains do not overlap. LegendreSeries Roots 0 Imaginary part Real part Not implemented yet Roots_setRoot: index must be in interval [1, %d]. Roots_to_Spectrum: numberOfFrequencies must be greater or equal 2. Roots_getRoot: root index out of range. Polynomial_to_Spectrum: numberOfFrequencies must be greater or equal 2. ChebyshevSeries FunctionTerms_and_RealTier_fit: not enough data points. FunctionTerms_and_RealTier_fit: not enough data points in fit interval. numberOfPoints > 2 && order > 0 && index > 0 Spline_init: degree must be <= 20. Spline_initKnotsfromString: knots must be inside domain. MSpline_createFromStrings: numberOfCoefficients must equal %d t__1_ {t__1_, t__2_} {t__1_..t__%d_} t__%d_ {t__%d_, t__%d_} {t__%d_..t__%d_} MSpline MSpline_createFromStrings: degree must be <= 20. ISpline ISpline_createFromStrings: degree must be <= 20. b X b j b b b b b ( b 0 b 8 b @ b H b P ? ?v:E b lj X b xmin xmax nx dx x1 ymin ymax ny dy y1 Sampled2 (Sampled2::readAscii:) xmin should <= xmax and ymin <= ymax. (Sampled2::readAscii:) nx should >= 1 and ny >= 1. (Sampled2::readAscii:) dx should > 0 and dy > 0. C ? B `@ ? C @ ? G F @ G A A A @Y@ Y@fffffU@ @@ 9 -DT! ( H-DT!@q= ףp?HzG? @#?-DT! @ @ @ @ (@ 0@ @@ B@ I@ @ 4@ $@ {@+eG? )@UUUUUU|= ??%s%s%s -i -r -s %s: %ld from %ld samples have been clipped. Advice: you could scale the amplitudes or write to a binary file. rb Sound_readFromCmuAudioFile: incorrect header size. Sound_readFromCmuAudioFile: incorrect number of channels. Sound_readFromCmuAudioFile: multi channel, cannot read. Sound_readFromCmuAudioFile: incorrect sampling frequency. Sound_readFromCmuAudioFile: incorrect number of samples. Sound_readFromCmuAudioFile: not completed. Sound_readFromCmuAudioFile: Reading from file "%s" not performed. integer float Sound_readFromRawFile: number of bytes per sample should be 1, 2 or 4. Sound_readFromRawFile: no samples left to read Sound_readFromRawFile: no memory for Sound. Sound_readFromRawFile: not completed. Sound_readFromRawFile: Reading from file "%s" not performed wb Sound_readWriteToRawFile: cannot open. number of bytes per sample should be 1, 2 or 4. Sound_writeToRawAudioFile Sound_writeToRawFile: not completed Sound_writeToRawFile: writing to file "%s" not performed. Sound_readFromDialogicADPCMFile %s: File is empty %s: File too long Sound_createSimpleToneComplex: frequency of (some) components too high. Sound_createMistunedHarmonicComplex: frequency of (some) components too high. Sound_createMistunedHarmonicComplex:mistuned component too high. Sound_extensions.c n > 0 && centre_frequency > 0 && bandwidth >= 0 && samplingFrequency > 0 --gammatonefilter4-- F = %s, B = %s, T = %s Gain = %s a[%d] = %s b[%d] = %s Sound_createShepardToneComplex %s: The highest frequency you want to generate is above the Nyquist frequency. Choose a larger value for "Sampling frequency", or lower values for "Number of components" or "Lowest frequency". %s: Octave offset fraction must be greater or equal zero and smaller than one. Sound_createShepardTone: lowest frequency too high. Sound_createShepardTone: frequency of highest component too high. Sound_createPattersonWightmanTone: frequency of one or more components too large. Sound_createPlompTone: frequency of one or more components too large. Sound_overwritePart %s: Sample rates must be equal. %s: Times of part to be overwritten must be within the sound. %s: Not enough samples to be copied %s: Sound_changeGender %s: The Pitch and the Sound object must have the same starting times and finishing times. %s: There were no voiced segments found. @ @?+eG? ? ? @-DT! @ꌠ9Y>)F @p= ף?333333??333333?Sound_to_Pitch2.c frame->nx >= nx hamming->nx == nx spec->nx == nfft2 Sound_to_Pitch_shs: not performed. ? @:\i!>* 3h?Q <@QP@ @@iW @R Q??SPINET analysis SPINET: filter %ld from %ld Sound_to_SPINET: not performed. c x c (b c X c ` c h c p c $ c c t c $ c zE c b x c @ ?gamma excitationErbProportion inhibitionErbProportion y s Trying to read "%s". SPINET my ny my nx Extrema power: %.8g %.8g rectified: %.8g %.8g Time (s) Frequency (ERB) Cooperative interaction output Gammatone filterbank output strength ?+eG? H@ꌠ9Y>)F @ @ @?SPINET_to_Pitch: frequency range too small. SPINET_to_Pitch: ceiling is smaller than centre frequency of lowest filter. SPINET_to_Pitch: not performed. Gc 0 Gc i c )c ( Lc E Gc i 0 H c @'? -DT! @ ? ? @ @E c hj 0 c E Qc H c 0 c ̟E \c H c 0 tc numberOfObservations centroid Trying to read "%s". SSCP my numberOfRows SSCP_and_TableOfReal_to_MahalanobisDistance %s:The number of columns (%d) in the TableOfReal must equal the dimension (%d) of the SSCP-object. %s:The row selection in the TableOfReal is not valid. TableOfReal_to_SSCP: The SSCP will not have full dimensionality. This may be a problem in following analysis steps. (The number of data points (%d) was less than the number of variables (%d).) Covariance_and_TableOfReal_extractQuantileRange %s: 0 <= lowerQuantile < higherQuantile <= 1. %s: dimensions %s: Not enough data in quantile interval. ? TableOfReal_to_SSCPs_byLabel: %d row labels out of %d are unique. We can't determine SSCP-objects for these rows. SSCP_to_CCA %s %s: The leading minor of order %d is not positive definite, and the factorization of Syy could not be completed. %s: The leading minor of order %d is not positive definite, and the factorization of Sxx could not be completed. %s: Error in inverse for Sxx. %s: Error in inverse for R. SSCPs SSCPs_sum: unequal dimensions (%d). Dimension %d Covariance Correlation SSCP.c numberOfConstraints >= 0 Covariance_difference: matrices don't have equal dimensions. Covariance_difference: number of observations of matrices do not agree. The minimum size (%ld) of the two is used. Covariance_difference: number of observations too small. %s: Index must be in interval [1 - %d]. %s: Indices must be different. Covariance_getSignificanceOfOneMean Covariance_getSignificanceOfTwoMeans Covariance_getSignificanceOfOneVariance Covariance_getSignificanceOfRatioOfTwoVariances Correlation_getConfidenceIntervals: Confidence level must be in interval (0 - 1). Correlation_getConfidenceIntervals: number of observations must be greater than 4. Correlation_getConfidenceIntervals: "number of tests" cannot be less than zero. Correlation_getConfidenceIntervals: "number of tests" exceeds the number of elements in the Correlation object. Correlation_testDiagonality_bartlett: number of constraints can not exceed the number of observations. 33@ `@33?L>̜@ @@33?L>ff@L@ff?L>33@ffF@ ?L> @fff@33?L>̬@y@?>33@Y@33?> @Y@ ?L>̌@9@33?L>̜@ffF@ ?=̬@l@ ?L>@Y@?L>@ @@33?=@ @@̌?=@ @?L>ff@̌@ ?>̬@y@ff?>33@ `@33?>ff@33s@?>33@33s@ ?>̬@Y@?L>33@l@ ?>33@fff@ ?L>33@33S@? ?@Y@33?L> @ @@?L> @Y@?>ff@ `@ ?L>ff@Y@33?L>ff@L@?L>@ffF@?L>̬@Y@ ?>ff@33@ ?= @ff@33?L>̜@ffF@ ?L> @L@?L> @ `@ff?L>̜@fff@33?=̌@ @@ff?L>33@Y@ ?L> @ `@ff?> @33@ff?>̌@L@ff?L> @ `@??33@33s@33?>@ @@33?>33@33s@?L>33@L@33?L>@l@ ?L> @33S@33?L> @L@ff@33?@L@ @ ?@ffF@̜@ ? @33@ @ff? @333@33@ ?ff@333@ @ff?@33S@ff@?̜@@33S@ ?33@9@33@ff?ff@,@y@33? @ @ `@ ?̼@ @@ff@ ? @ @ @ ?33@9@ff@33?33@9@fff@ff?ff@ffF@̌@33?33@ @@ @ ?@,@33@ ?ff@ @ @ ?33@ @y@̌?̼@L@@ff?33@333@ @ff?@ @̜@ ?33@333@ff@?@9@@ff?33@ @@̌@33?@333@@33?ff@ @@ @? @9@ @ ?ff@ff&@ `@ ? @@33s@̌? @@l@ ?@,@y@? @,@33@?̬@ @@ @ ? @Y@ @?ff@ffF@ff@ ?@33@̌@ff?33@ @@33@ff? @ @ @ff? @ff&@̌@?33@ @@33@33?@ff&@ @? @33@33S@ ?33@,@ff@ff?ff@ @@ff@?ff@9@ff@ff?ff@9@@ff?33@ @ @@̌?ff@333@33@ff?@33S@ @ @@,@33@33?33@ @@̼@ff@@9@33@ff? @ @@@ @33@ @@33@ff@̜@ @ @?@9@@ff?ff@ @@ff?ff@fff@33@ @ @L@33@ @@,@@33?@ @@ @ff@ff@ @ @ @@333@33@@@L@@33@ @ @@ @ff?ff@33s@ff@ @ff@ff&@@33@ @ @ @ ?@L@ff@33@33@333@̜@ @ff@333@ff@ @@,@̜@ff?ff@33S@ff@ff@ff@L@ @ff?ff@333@@ff?33@ @@̜@ff?@333@33@ff@ff@ @@@?@333@33@33?@33s@@ @@333@33@ @@333@33@ ?33@ff&@33@33?ff@ @@33@33@@Y@33@@@ffF@ @ff? @ @@@ff?@ffF@̬@ff@ff@ffF@33@@@ffF@33@33@@,@33@33?@L@̼@33@ff@33S@ff@ @ff@ @@ff@33@@ @ @33? @ @@ff@ @ff@Y@̬@33@̼@ @@33@ff? ? @ ? ? ? @ ???wE ^$c hj c sl sw pl pw 1 2 3 iris ? TableOfReal_split: illegal row selection. TableOfReal_split: illegal col selection. TableOfReal_getColumnExtrema: not a valid column. TableOfReal_drawRowsAsHistogram %s: Invalid columns %s: No rows! %s: Invalid row (%d) %s: No greys! TableOfReal_drawBiplot: There must be at least two (independent) columns in the table. ?__r_ ?__c_ TableOfReal_extensions.c r > 0 && w > 0 o * rowLabels || columnLabels my numberOfRows == thy size my numberOfColumns == thy size TableOfReal_and_Categories_swap: unequal number of items. All matrix entries should be positive! Column %d + TableOfReal_drawScatterPlot: %d from %d labels are not visible because they are empty or they contain only spaces or non-printable characters TablesOfReal TablesOfReal_sum: dimensions or labels of items 1 and %d differ TableOfReal_drawVectors %s: The index in the "From" column(s) must be in range [1, %d]. %s: The index in the "To" column(s) must be in range [1, %d]. TableOfReal_sortRowsByIndex: one or more indices out of range [1, %d]. TableOfReal_setSequentialColumnLabels: wrong column indices. TableOfReal_setSequentialRowLabels: wrong row indices. TableOfReal_choleskyDecomposition %s: Must be a square symmetric matrix. TableOfReal_appendColumns %s: The number of rows must be equal. %s: %d row labels differed. Cannot add zero tables. Numbers of rows do not match. ncol == his numberOfColumns (c (c (c (c (c (c (c (c (c (c )c )c )c )c )c )c )c )c )c ")c &)c ))c -)c 0)c 7)c :)c <)c ?)c C)c F)c H)c K)c O)c R)c Y)c \)c `)c c)c g)c k)c o)c t)c {)c {)c })c })c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c )c *c *c *c *c *c *c *c *c *c *c *c *c *c (c *c (c *c (c *c *c *c *c "*c h# @ Mb? iy i ih \ic eh \ep ey e ae \ae aa \as aw a\hs ay a\ic ah \vt ao \ct oy \ct\ic ow o uh \hs uw u ux \u" er \er\hr ax \sw ix \i- axr \sr ax-h \sw\ov l r w y j hh h hv \hh el l\|v m n ng \ng em m\|v en n\|v eng \ng\|v nx n^\fh s sh \sh z zh \zh f th \te v dh \dh jh d\zh ch t\sh b d g p t k dx \fh q ? pau epi h# 1 2 h\# %ld%ld%s%n %ld%ld%s TextGrid_readFromTIMITLabelFile %s: cannot open file. wrd %ld%ld%s %s: incorrect number of items. %s: incorrect time at line %ld. %s: file "%s":Start time set to previous end time for label at line %ld %s: Empty TextGrid ipa phn %s: Reading from file "%s" not performed. TextGrid_renameTier: Tier number (%d) should not be larger than the number of tiers (%d). |E ,c hj +c The number of elements are not equal. %ld strings. %ld unique categories. OrderedOfString OrderedOfString_selectUniqueItems: not performed OrderedOfString_difference: the number of items differ %ld mE -c n -c E -c hj 8-c Command Command.c execute && undo CommandHistory my current > 0 && my current <= my size data && (Thing_member (data, my itemClass) || my itemClass == NULL) -DT!@ ?)Ǻ? @ ?ư>h㈵> obHN&nU?Ēr9?! ?>]ݱ&? O?A|` @65~ eA@ @@ F@ $@ @ @(\:@(\?HzG:@ @ P@ L@ @ WH? *@tV? ? ?K?Q ?J +?ffffff? -DT! @䜹(F @ @ ? ^-!r? , %d %s=[ , %.12g%s , %s ; ]; NUM2.c norm > 0 nr > 0 && nc > 0 && icol > 0 && icol <= nc icol1 > 0 && icol1 <= nc && icol2 > 0 && icol2 <= nc NUMstatistics_huber: scale is zero. index > 0 numberOfComponents > 0 && numberOfComponents <= ncols NUMProcrustes: degenerate configuration(s). nSplines > 0 NUMnrbis: root must be bracketed. NUMnrbis: maximum number of iterations (%d) exceeded. NUMridders: root must be bracketed. d < 0 in ridders; x1=%.17g, x2=%.17g, x3=%.17g, f1=%.17g, f2=%.17g, f3=%.17g, iter=%ld NUMridders: maximum number of iterations (%ld) exceeded. %ld root=%.17g x1=%.17g x2=%.17g x3=%.17g x4=%.17g f1=%.17g f2=%.17g f3=%.17g f4=%.17g d=%.17g ref > 0 && factor > 0 && rb <= re && cb <= ce NUMdmatrix_to_dBs: all matrix elements must be positive. 0 < first && first <= last && npoints > 1 NUMsplint_f: bad input value NUMsplint_d: bad input value Too many intersections. cospsi>= -1 && cospsi <= 1 x1 < x2 && x3 < x4 tol > 0 && a < b NUMminimize_brent: maximum number of iterations (%d) exceeded. ? @? ? @ Base Number of digits in mantissa Minimum exponent Largest exponent Rounding mode Precision Epsilon Underflow threshold Safe minimum Overflow threshold 6c 6c j T6c X6c \6c 6c 6c 8F 6c lj 5c min max v Trying to read "%s". DoubleVector my min my max ComplexVector OT learning OTGrammar Create metrics grammar Initial ranking Equal Foot form high WSP high Trochaicity constraint FtNonfinal Trochaic Include FootBimoraic Include FootBisyllabic Include Peripheral Nonfinality constraint Nonfinal MainNonfinal HeadNonfinal Overt forms have secondary stress Include *Clash and *Lapse Include codas NoCoda assimilation Create tongue-root grammar... Create tongue-root grammar Constraint set Five Nine Ranking Random Infant Wolof Draw tableau Input string Cannot edit from batch. OTGrammar: Evaluate 2.0 Evaluation noise OTGrammar: Generate inputs... Generate inputs 1000 Number of trials %s_in Get candidate 1 Tableau Candidate 'Tableau' should not exceed number of tableaus. %s 'Candidate' should not exceed number of candidates. Get constraint name Constraint number 'Constraint number' should not exceed number of constraints. Get disharmony Get input OTGrammar: Interpretive parse Partial output Best input = %ld: %s Best output = %ld: %s Get number of candidates %ld Get number of optimal candidates Get number of violations Tableau number Candidate number 'Tableau number' should not exceed number of tableaus. 'Candidate number' should not exceed number of candidates for this tableau. Get ranking value Get winner OTGrammar: Input to output... OTGrammar: Input to output Input form OTGrammar: Input to outputs... OTGrammar: Input to outputs Trials %s_out OTGrammar: Inputs to outputs... OTGrammar: Inputs to outputs Is candidate grammatical? Is candidate singly grammatical? Is partial output grammatical? Is partial output singly grammatical? OTGrammar & 2 Strings: Learn... OTGrammar: Learn Reranking strategy Demotion only Symmetric one Symmetric all Weighted uncancelled Weighted all EDCD 0.1 Plasticity Rel. plasticity spreading Honour local rankings Number of chews OTGrammar: Learn from partial adult outputs 0 Store history every OTGrammar: Learn one... OTGrammar: Learn one Underlying form: Adult surface form: Output string OTGrammar: Learn one from partial adult output Partial adult surface form (e.g. overt form): OTGrammar: Remove constraint Constraint name OTGrammar: Remove harmonically bounded candidates Singly OTGrammar: Reset all rankings 100.0 OTGrammar: Set ranking Constraint Disharmony OTGrammar & Distributions: Get fraction correct... Column number 100000 Replications OT learning 6. Shortcut to OT learning OTGrammar & Distributions: Learn from partial outputs 1.0 Initial plasticity Replications per plasticity Plasticity decrement 4 Number of plasticities OTGrammar & PairDistribution: Get fraction correct... OTGrammar & PairDistribution: Learn OTGrammar: To output Distributions... OTGrammar: Compute output distributions Trials per input Write OTGrammar to spreadsheet txt Partial form 1 Partial form 2 'Candidate number' should not exceed number of candidates. OTMulti: Get winner OTMulti: Generate optimal form OTMulti: Generate optimal forms OTMulti: Learn one Learn forward backward bidirectionally OTMulti: Remove constraint OTMulti: Reset all rankings OTMulti: Set ranking OTMulti: Compute output distribution OTMulti & PairDistribution: Learn OTCase -- new optimality -- New Objects Optimality Theory OT learning tutorial -- tableau grammars -- Create NoCoda grammar Create place assimilation grammar Create place assimilation distribution Create metrics grammar... OTGrammar help Edit Draw tableau... Write to headerless spreadsheet file... Query - Get number of constraints Get constraint... Get ranking value... Get disharmony... Get number of tableaus Get input... Get number of candidates... Get candidate... Get number of violations... -- parse -- Get winner... Get number of optimal candidates... Is candidate grammatical... Is candidate singly grammatical... Get interpretive parse... Is partial output grammatical... Is partial output singly grammatical... Generate inputs... Get inputs Measure typology Evaluate Evaluate... Input to output... Input to outputs... To output Distributions... To PairDistribution... Modify ranking Set ranking... Reset all rankings... Learn one... Learn one from partial output... Modify structure - Remove constraint... Remove harmonically bounded candidates... Get output... Get outputs... To output Distribution... Learn from partial outputs... Get fraction correct... List obligatory rankings... Learn... List obligatory rankings Inputs to outputs... kuc vc vc wc Uxc xc xc xc xc xc xc yc !yc byc nyc yc yc zc zc Tzc kzc zc zc d{c |c |c |c |c Y}c e}c }c }c H~c T~c ~c c c |c c c @c jc c Bc c Ӆc ;c c ܆c c Pc c c 6c yc c c c ͉c c cc c ފc uc c c ԏc c c Cc c c Ӆc ;c c ܆c c Pc c c 6c ҕc c c ٗc ۗc c 4c ٗc \c @@ ?F @@333?/F c c c Λc c c ٗc Мc ޜc c ٗc @c ٗc Qc \c oc c c c ʝc ؞c Ic c c c c c :c Uc tc c ϡc c ,c `c jc c c c :c c c c c `c c c c )c c ۗc c 4c +c ۗc #c Rc zc ۗc ~c c zc ۗc ըc c +c mc ۗc %c Sc zc ۗc {c c zc ۗc ҫc c (c @@ ?ZF c 8c c c ۗc uc c @@ ?F ϰc ۗc c c @@ ?ZF Dc Jc ۗc c c @@ ?ZF c ۗc c c @@ ?F 9c c c ڶc c c ,c @c Qc Nc Xc fc tc ~c c c ۗc &c Zc c @ ?F @ ?F c ۗc ^c c ƹc @ ?CF @ ?F c ںc ټc c Vc Dc c c c c Sc ]c gc sc c c c c c c c Oc \c ic kc c c c c c c c Ic c c c c Ac Tc \c qc c c c c c 3c Pc ~c ۗc c c c <c jc c c qc c c @ ?F c @ ?F <c @ ?IF c @ ?zF c c !c c c Ac c c c c c c ۗc c c c >c lc c @ ?F c c \c c c c ۗc c c c Cc qc c c c ۗc c Bc wc c c c ;c ۗc wc c c c 0c ^c ۗc Uc c c c c <c ۗc c ;c ic c c c d ۗc ud d d d 2d \d d d Md ۗc d d 3d gd ۗc @d td d d Yd sd d d d ۗc d $ d O d d d d d d 5 d ۗc E d y d d d d d 5 d P d j d 3 d Td ~d d d bd ^d d d d d d Hd d d d d d d Nd ? d f d ; d k d d e#d X)d +d #+d -d .d c /d /d /d /d 0d 0d 0d '0d 30d @0d M0d Z0d g0d t0d 0d 0d 0d 0d 0d 0d 0d 0d 0d 1d 1d "1d 11d @1d O1d ^1d m1d |1d 1d 2d 5d 6d 6d R6d _6d 6d 6d 6d 6d /7d ;7d 7d 7d C8d K8d 8d 8d 9d 9d W9d ^9d 9d :d C:d K:d ;d ;d Q<d d<d =d %=d k=d =d =d >d ,>d Y>d t>d >d >d ?d @d @d @d q@d @d ,Ad 6Ad CAd Ad Bd Bd =Cd ,Ad Cd Cd Ad Cd 6Ad sDd Ed &Fd Fd WGd ,Ad Gd Gd #Hd Hd Hd Id .Jd \Jd bJd !Kd ZLd Md oMd pat pa an+pa at+ma \ict\ic it\ep et\ep \swt\sw \swt\ic In @@Optimality Theory@, the `rules' that an output form has to satisfy. Since there can be many constraints and these constraints can conflict with each other, the constraints are %violable and the highest-ranked constraints have the largest say in determining the optimal output. See the @@OT learning@ tutorial for many examples. A command in the @@New menu@ for creating an @OTGrammar object with a tongue-root-harmony grammar. These OTGrammar grammars only accept inputs of the form V__1_tV__2_, where V__1_ and V__2_ are chosen from the six front vowels i, \ic, e, \ep, \sw, and a. In a text field, these vowels should be typed as $$##i#$, $$##\bsic#$, $$##e#$, $$##\bsep#$, $$##\bssw#$, and $$##a#$, respectively (see @@Special symbols@). The following phonological features are relevant: ATR RTR high i \ic mid e \ep low \sw a Constraints The resulting OTGrammar will usually contain at least the following five constraints: *[rtr / hi] "do not implement [retracted tongue root] if the vowel is high." *[atr / lo] "do not implement [advanced tongue root] if the vowel is low." P\s{ARSE} (rtr) "make an underlying [retracted tongue root] specification surface." P\s{ARSE} (atr) "make an underlying [advanced tongue root] specification surface." *G\s{ESTURE} (contour) "do not go from advanced to retracted tongue root, nor the other way around, within a word." This set of constraints thus comprises: \bu two %%##grounding conditions#% (@@Archangeli & Pulleyblank (1994)@), which we can see as gestural constraints; \bu two %%##faithfulness constraints#%, which favour the similarity between input and output, and can be seen as implementing the principle of maximization of perceptual contrast; \bu a %%##harmony constraint#%, which, if crucially ranked higher than at least one faithfulness constraint, forces %%##tongue-root harmony#%. In addition, there may be the following four constraints: *[rtr / mid] "do not implement [retracted tongue root] if the vowel is mid; universally ranked lower than *[rtr / hi]." *[rtr / lo] "do not implement [retracted tongue root] if the vowel is low; universally ranked lower than *[rtr / mid]." *[atr / mid] "do not implement [advanced tongue root] if the vowel is mid; universally ranked lower than *[atr / lo]." *[atr / hi] "do not implement [advanced tongue root] if the vowel is high; universally ranked lower than *[atr / mid]." The universal rankings referred to are due to the %%##local-ranking principle#% (@@Boersma (1997a)@). A learning algorithm may enforce this principle, e.g., if *[rtr / hi] falls down the ranking scale, *[rtr / mid] may be pushed along. For information on learning these tongue-root grammars, see @@OT learning@ and @@Boersma (2000)@. Bruce P. Hayes & Margaret MacEachern (1998): "Quatrain form in English folk verse", %Language #74: 473\--507. John J. McCarthy & Alan Prince (1995): Faithfulness and reduplicative identity. In Jill Beckman, Laura Walsh Dickey & Suzanne Urbanczyk (eds.), %%Papers in Optimality Theory%. %%University of Massachusetts Occasional Papers% #18. Amherst, Mass.: Graduate Linguistic Student Association. pp. 249384. [Rutgers Optimality Archive #60, http://roa.rutgers.edu] A framework for transferring one linguistic representation into another, e.g. transferring an underlying form into a surface form. Before @@Prince & Smolensky (1993)@, phonologists tended to this with a sequentially ordered set of rules, each of which transferred a representation into another. With @OT (that's the abbreviation), there are no intermediate steps in the derivation, but a set of ranked @constraints chooses the optimal output form from a set of candidates. In P\s{RAAT}, you can draw Optimality-Theoretic tableaus and simulate Optimality-Theoretic learning. See the @@OT learning@ tutorial. An abbreviation for @@Optimality Theory@. This tutorial describes how you can draw Optimality-Theoretic tableaus and simulate Optimality-Theoretic learning with P\s{RAAT}. You can read this tutorial sequentially with the help of the "< 1" and "1 >" buttons. 1. @@OT learning 1. Kinds of OT grammars|Kinds of OT grammars@ (ordinal and stochastic, @OTGrammar) 2. @@OT learning 2. The grammar|The grammar@ 2.1. @@OT learning 2.1. Viewing a grammar|Viewing a grammar@ (N\s{O}C\s{ODA} example, @OTGrammarEditor) 2.2. @@OT learning 2.2. Inside the grammar|Inside the grammar@ (saving, inspecting) 2.3. @@OT learning 2.3. Defining your own grammar|Defining your own grammar@ 2.4. @@OT learning 2.4. Evaluation|Evaluation@ (noise) 2.5. @@OT learning 2.5. Editing a grammar|Editing a grammar@ 2.6. @@OT learning 2.6. Variable output|Variable output@ (place assimilation example) 2.7. @@OT learning 2.7. Tableau pictures|Tableau pictures@ (printing, EPS) 2.8. @@OT learning 2.8. Asking for one output|Asking for one output@ 2.9. @@OT learning 2.9. Output distributions|Output distributions@ 3. @@OT learning 3. Generating language data|Generating language data@ 3.1. @@OT learning 3.1. Data from a pair distribution|Data from a pair distribution@ 3.2. @@OT learning 3.2. Data from another grammar|Data from another grammar@ (tongue-root-harmony example) 4. @@OT learning 4. Learning an ordinal grammar|Learning an ordinal grammar@ 5. @@OT learning 5. Learning a stochastic grammar|Learning a stochastic grammar@ 6. @@OT learning 6. Shortcut to OT learning|Shortcut to OT learning@ 7. @@OT learning 7. Learning from overt forms|Learning from overt forms@ This is chapter 1 of the @@OT learning@ tutorial. According to @@Prince & Smolensky (1993)@, an @@Optimality Theory|Optimality-Theoretic@ (@OT) grammar consists of a number of ranked @constraints. For every possible input (usually an underlying form), GEN (the generator) generates a (possibly very large) number of %%##output candidates%#, and the ranking order of the constraints determines the winning candidate, which becomes the single optimal output. In OT, ranking is %#strict, i.e., if a constraint %A is ranked higher than the constraints %B, %C, and %D, a candidate that violates only constraint %A will always be beaten by any candidate that respects %A (and any higher constraints), even if it violates %B, %C, and %D. Ordinal OT grammars Because only the ranking order of the constraints plays a role in evaluating the output candidates, Prince & Smolensky took the grammar to contain no absolute ranking values, i.e., they accepted only an ordinal relation between the constraint rankings. For such a grammar, @@Tesar & Smolensky (1998)@ devised a learning algorithm (Error-Driven Constraint Demotion, EDCD) that changes the ranking order whenever the form produced by the learner is different from the adult form. Such a learning step can sometimes lead to a large change in the behaviour of the grammar. Stochastic OT grammars The EDCD algorithm is fast and convergent. As a model of language acquisition, however, its drawbacks are that it is extremely sensitive to errors in the learning data and that it does not show realistic gradual learning curves. For these reasons, @@Boersma (1997b)@ / @@Boersma (1998)@ / @@Boersma (2000)@ proposed stochastic constraint grammars in which every constraint has a %%##ranking value%# along a continuous ranking scale, and a small amount of %#noise is added to this ranking value at evaluation time. The associated error-driven learning algorithm (Gradual Learning Algorithm, GLA) effects small changes in the ranking values of the constraints with every learning step. An added virtue of the GLA is that it can learn languages with optionality and variation, which was something that EDCD could not do. Ordinal OT grammars can be seen as a special case of the more general stochastic OT grammars: they have integer ranking values (%#strata) and zero evaluation noise. In P\s{RAAT}, therefore, every constraint is taken to have a ranking value, so that you can do stochastic as well as ordinal OT. An OT grammar is implemented as an @OTGrammar object. In an OTGrammar object, you specify all the constraints, all the possible inputs and all their possible outputs. This is chapter 2 of the @@OT learning@ tutorial. We can ask the grammar to produce an output form for any input form that is in its list of tableaus. 2.7. @@OT learning 2.7. Tableau pictures|Tableau pictures@ (printing, EPS files) Consider a language where the underlying form /pat/ leads to the surface form [pa], presumably because the structural constraint N\s{O}C\s{ODA} outranks the faithfulness constraint P\s{ARSE}. To create such a grammar in P\s{RAAT}, choose ##Create NoCoda grammar# from the Optimality Theory submenu of the @@New menu@. An @OTGrammar object will then appear in the list of objects. If you click Edit, an @OTGrammarEditor will show up, containing: 1. the constraint list, sorted by %#disharmony (= ranking value + noise): %%ranking value %disharmony ##N\s{O}C\s{ODA}# 100.000 100.000 ##P\s{ARSE}# 90.000 90.000 2. the tableaus for the two possible inputs /pat/ and /pa/: From the first tableau, we see that the underlying form /pat/ will surface as [pa], because the alternative [pat] violates a constraint (namely, N\s{O}C\s{ODA}) with a higher disharmony than does [pa], which only violates P\s{ARSE}, which has a lower disharmony. Note the standard OT tableau layout: asterisks (*) showing violations, exclamation marks (!) showing crucial violations, greying of cells that do not contribute to determining the winning candidate, and a finger (\pf) pointing to the winner (this may look like a plus sign (+) if you don't have the Zapf Dingbats font installed on your computer or printer). The second tableau shows that /pa/ always surfaces as [pa], which is no wonder since this is the only candidate. All cells are grey because none of them contributes to the determination of the winner. You can write an @OTGrammar grammar into a text file by choosing @@Write to text file...@ from the Write menu of the Objects window. For the N\s{O}C\s{ODA} example, the contents of the file will look like: File type = "ooTextFile" Object class = "OTGrammar" 2 constraints constraint [1]: "N\bss{O}C\bss{ODA}" 100 100 ! NOCODA constraint [2]: "P\bss{ARSE}" 90 90 ! PARSE 0 fixed rankings 2 tableaus input [1]: "pat" 2 candidate [1]: "pa" 0 1 candidate [2]: "pat" 1 0 input [2]: "pa" 1 candidate [1]: "pa" 0 0 To understand more about this data structure, consult the @OTGrammar class description or click #Inspect after selecting the OTGrammar object. The $$"\bss{...}"$ braces ensure that the constraint names show up with their traditional small capitals (see @@Text styles@). You can read this text file into Praat again with @@Read from file...@ from the Read menu in the Objects window. By editing a text file created from an example in the @@New menu@, you can define your own OT grammars. As explained at @@Write to text file...@, Praat is quite resilient about its text file formats. As long as the strings and numbers appear in the correct order, you can redistribute the data across the lines, add all kinds of comments, or leave the comments out. For the N\s{O}C\s{ODA} example, the text file could also have looked like: "ooTextFile" "OTGrammar" 2 "N\bss{O}C\bss{ODA}" 100 100 "P\bss{ARSE}" 90 90 0 ! number of fixed rankings 2 ! number of accepted inputs "pat" 2 ! input form with number of output candidates "pa" 0 1 ! first candidate with violations "pat" 1 0 ! second candidate with violations "pa" 1 ! input form with number of candidates "pa" 0 0 To define your own grammar, you just provide a number of constraints and their rankings, and all the possible input forms with all their output candidates, and all the constraint violations for each candidate. The order in which you specify the constraints is free (you don't have to specify the highest-ranked first), as long as the violations are in the same order; you could also have reversed the order of the two input forms, as long as the corresponding candidates follow them; and, you could also have reversed the order of the candidates within the /pat/ tableau, as long as the violations follow the output forms. Thus, you could just as well have written: 0 "pa" 1 "pat" 2 "pat" 0 1 "pa" 1 0 In an Optimality-Theoretic model of grammar, %#evaluation refers to the determination of the winning candidate on the basis of the constraint ranking. In an ordinal OT model of grammar, repeated evaluations will yield the same winner again and again. We can simulate this behaviour with our N\s{O}C\s{ODA} example. In the editor, you can choose ##Evaluate (zero noise)# or use its keyboard shortcut Command-0 (= Command-zero). Repeated evaluations (keep Command-0 pressed) will always yield the following grammar: In a stochastic OT model of grammar, repeated evaluations will yield different disharmonies each time. To see this, choose ##Evaluate (noise 2.0)# or use its keyboard shortcut Command-2. Repeated evaluations will yield grammars like the following: ##N\s{O}C\s{ODA}# 100.000 100.427 ##P\s{ARSE}# 90.000 87.502 and ##N\s{O}C\s{ODA}# 100.000 101.041 ##P\s{ARSE}# 90.000 90.930 ##N\s{O}C\s{ODA}# 100.000 96.398 ##P\s{ARSE}# 90.000 89.482 The disharmonies vary around the ranking values, according to a Gaussian distribution with a standard deviation of 2.0. The winner will still be [pa] in almost all cases, because the probability of bridging the gap between the two ranking values is very low, namely 0.02 per cent according to @@Boersma (1998)@, page 332. With a noise much higher than 2.0, the chances of P\s{ARSE} outranking N\s{O}C\s{ODA} will rise. To see this, choose ##Evaluate...# and supply 5.0 for the noise. Typical outcomes are: ##N\s{O}C\s{ODA}# 100.000 92.634 ##P\s{ARSE}# 90.000 86.931 ##N\s{O}C\s{ODA}# 100.000 101.162 ##P\s{ARSE}# 90.000 85.311 ##P\s{ARSE}# 90.000 99.778 ##N\s{O}C\s{ODA}# 100.000 98.711 In the last case, the order of the constraints has been reversed. You will see that [pat] has become the winning candidate: However, in the remaining part of this tutorial, we wil stick with a noise with a standard deviation of 2.0. This specific number ensures that we can model fairly rigid rankings by giving the constraints a ranking difference of 10, a nice round number. Also, the learning algorithm will separate many constraints in such a way that the differences between their ranking values are in the vicinity of 10. In the N\s{O}C\s{ODA} example, the winning candidate for the input /pat/ was always [pa]. To make [pat] the winner instead, N\s{O}C\s{ODA} should be ranked lower than P\s{ARSE}. To achieve this even with zero noise, go to the editor and select the N\s{O}C\s{ODA} constraint by clicking on it (a spade symbol \sp will mark the selected constraint), and choose ##Edit ranking...# from the Edit menu, or use the keyboard shortcut Command-E. In the resulting dialog, we lower the ranking of the constraint from 100 to 80, and click OK. This is what you will see in the editor: \sp ##N\s{O}C\s{ODA}# 80.000 103.429 ##P\s{ARSE}# 90.000 88.083 Nothing has happened to the tableau, because the disharmonies still have their old values. So choose ##Evaluate (noise 2.0)# (Command-2) or ##Evaluate (zero noise)# (Command-0). The new disharmonies will centre around the new ranking values, and we see that [pat] becomes the new winner: ##P\s{ARSE}# 90.000 90.743 ##N\s{O}C\s{ODA}# 80.000 81.581 Each time you press Command-2, which invokes the command ##Evaluate (noise 2.0)# from the Edit menu, you will see the disharmonies changing. If the distance between the constraint rankings is 10, however, the winning candidates will very probably stay the same. So starting from the N\s{O}C\s{ODA} example, we edit the rankings of the constraints again, setting the ranking value of P\s{ARSE} to 88 and that of N\s{O}C\s{ODA} to 85. If we now press Command-2 repeatedly, we will get [pat] in most of the cases, but we will see the finger pointing at [pa] in 14 percent of the cases: ##P\s{ARSE}# 88.000 87.421 ##N\s{O}C\s{ODA}# 85.000 85.585 but ##N\s{O}C\s{ODA}# 85.000 87.128 ##P\s{ARSE}# 88.000 85.076 As a more functionally oriented example, we consider nasal place assimilation. Suppose that the underlying sequence /an+pa/ surfaces as the assimilated [ampa] in 80 percent of the cases, and as the faithful [anpa] in the remaining 20 percent, while the non-nasal stop /t/ never assimilates. This can be achieved by having the articulatory constraint *G\s{ESTURE} ranked at a short distance above *R\s{EPLACE} (n, m): 3 constraints "*G\bss{ESTURE}" 102.7 0 "*R\bss{EPLACE} (n, m)" 100.0 0 "*R\bss{EPLACE} (t, p)" 112.0 0 "an+pa" 2 "anpa" 1 0 0 "ampa" 0 1 0 "at+ma" 2 "atma" 1 0 0 "apma" 0 0 1 You can create this grammar with ##Create place assimilation grammar# from the @@New menu@. In the editor, it will often look like follows: ##*R\s{EPLACE} (t, p)# 112.000 109.806 ##*G\s{ESTURE}# 102.700 102.742 ##*R\s{EPLACE} (n, m)# 100.000 101.044 If you keep the Command-2 keys pressed, however, you will see that the tableaus change into something like the following in approximately 20 percent of the cases: ##*R\s{EPLACE} (t, p)# 112.000 113.395 ##*R\s{EPLACE} (n, m)# 100.000 103.324 ##*G\s{ESTURE}# 102.700 101.722 We see that /at+ma/ always surfaces at [atma], because *R\s{EPLACE} (t, p) is ranked much higher than the other two, and that the output of /an+pa/ is variable because of the close rankings of *G\s{ESTURE} and *R\s{EPLACE} (n, m). To show a tableau in the @@Picture window@ instead of in the editor, you select an @OTGrammar object and click ##Draw tableau...#. After you specify the input form, a tableau is drawn with the current font and size at the location of the current selection (%viewport) in the Picture window. The top left corner of the tableau is aligned with the top left corner of the selection. You can draw more than one object into the Picture window, whose menus also allow you to add a lot of graphics of your own design. Besides printing the entire picture (with @@Print...@), you can save a part of it to an EPS file for inclusion into your favourite word processor (with @@Write to EPS file...@). For the latter to succeed, make sure that the selection includes at least your tableau; otherwise, some part of your tableau may end up truncated. To ask the grammar to produce a single output for a specified input form, you can choose @@OTGrammar: Input to output...@. The dialog will ask you to provide an input form and the strength of the noise (the standard value is 2.0 again). This will perform an evaluation and write the result into the Info window. If you are viewing the grammar in the @OTGrammarEditor, you will see the disharmonies change, and if the grammar allows variation, you will see that the winner in the tableau in the editor varies with the winner shown in the Info window. Since the editor shows more information than the Info window, this command is not very useful except for purposes of scripting. See the following page for some related but more useful commands. To ask the grammar to produce %many outputs for a specified input form, and collect them in a @Strings object, you select an @OTGrammar and choose @@OTGrammar: Input to outputs...|Input to outputs...@. For example, select the object "OTGrammar assimilation" from our place assimilation example (@@OT learning 2.6. Variable output|\SS2.6@), and click ##Input to outputs...#. In the resulting dialog, you specify 1000 trials, a noise strength of 2.0, and "an+pa" for the input form. After you click OK, a @Strings object will appear in the list. If you click Info, you will see that it contains 1000 strings. If you click Inspect, you will see that most of the strings are "ampa", but some of them are "anpa". These are the output forms computed from 1000 evaluations for the input /an+pa/. To count how many instances of [ampa] and [anpa] were generated, you select the @Strings object and click @@Strings: To Distributions|To Distributions@. You will see a new @Distributions object appear in the list. If you draw this to the Picture window (with ##Draw as numbers...#), you will see something like: ampa 815 anpa 185 which means that our grammar, when fed with 1000 /an+pa/ inputs, produced [ampa] 815 times, and [anpa] 185 times, which is consistent with our initial guess that a ranking difference of 2.7 would cause approximately an 80\% - 20\% distribution of [ampa] and [anpa]. Checking the distribution hypothesis To see whether the guess of a 2.7 ranking difference is correct, we perform 1,000,000 trials instead of 1000. The output distribution (if you have enough memory in your computer) becomes something like (set the %Precision to 7 in the drawing dialog): ampa 830080 anpa 169920 The expected values under the 80\% - 20\% distribution hypothesis are: ampa 800000 anpa 200000 We compute (e.g. with @@Calculator...@) a %\ci^2 of 30080^2/800000 + 30080^2/200000 = 5655.04, which, of course, is much too high for a distribution with a single degree of freedom. So the ranking difference must be smaller. If it is 2.4 (change the ranking of *G\s{ESTURE} to 102.4), the numbers become something like ampa 801974 anpa 198026 which gives a %\ci^2 of 24.35. By using the Calculator with the formula $$chiSquareQ (24.35, 1)$, we find that values larger than this have a probability of 8\.c10^^-7^ under the 80\% - 20\% distribution hypothesis, which must therefore be rejected again. Rather than continuing this iterative procedure to find the correct ranking values for an 80\% - 20\% grammar, we will use the Gradual Learning Algorithm (@@OT learning 5. Learning a stochastic grammar|\SS5@) to determine the rankings automatically, without any memory of past events other than the memory associated with maintaining the ranking values. Measuring all inputs To measure the outcomes of all the possible inputs at once, you select an @OTGrammar and choose @@OTGrammar: To output Distributions...|To output Distributions...@. As an example, try this on our place assimilation grammar. You can supply 1000000 for the number of trials, and the usual 2.0 for the standard deviation of the noise. After you click OK, a @Distributions object will appear in the list. If you draw this to the Picture window, the result will look like: /an+pa/ \-> anpa 169855 /an+pa/ \-> ampa 830145 /at+ma/ \-> atma 999492 /at+ma/ \-> apma 508 We see that the number of [apma] outputs is not zero. This is due to the difference of 9.3 between the rankings of *R\s{EPLACE} (t, p) and *G\s{ESTURE}. If you rank *R\s{EPLACE} (t, p) at 116.0, the number of produced [apma] reduces to about one in a million, as you can easily check with some patience. A learner needs two things: a grammar that she can adjust (@@OT learning 2. The grammar|\SS2@), and language data. If the grammar contains faithfulness constraints, the learner needs pairs of underlying and adult surface forms. For our place assimilation example, she needs a lot of /at+ma/ - [atma] pairs, and four times as many /an+pa/ - [ampa] pairs as /an+pa/ - [anpa] pairs. We can specify this language-data distribution in a @PairDistribution object, which we could simply write into a text file: "PairDistribution" 4 pairs "at+ma" "atma" 100 "at+ma" "apma" 0 "an+pa" "anpa" 20 "an+pa" "ampa" 80 The values appear to represent percentages, but they could also have been 1.0, 0.0, 0.2, and 0.8, or any other values with the same proportions. We could also have left out the second pair and specified "3 pairs" instead of "4 pairs" in the third line. We can create this pair distribution with ##Create place assimilation distribution# from the Optimality Theory submenu of the @@New menu@ in the Objects window. To see that it really contains the above data, you can draw it to the Picture window. To change the values, use Inspect (in which case you should remember to click Change after any change). To generate input-output pairs from the above distribution, select the @PairDistribution and click @@PairDistribution: To Stringses...|To Stringses...@. If you then just click OK, there will appear two @Strings objects in the list, called "input" (underlying forms) and "output" (surface forms). Both contain 1000 strings. If you Inspect them both, you can see that e.g. the 377th string in "input" corresponds to the 377th string in "output", i.e., the two series of strings are aligned. See also the example at @@PairDistribution: To Stringses...@. These two Strings objects are sufficient to help an @OTGrammar grammar to change its constraint rankings in such a way that the output distributions generated by the grammar match the output distributions in the language data. See @@OT learning 5. Learning a stochastic grammar|\SS5@. Instead of generating input-output pairs directly from a @PairDistribution object, you can also generate input forms and their winning outputs from an @OTGrammar grammar. Of course, that's what the language data presented to real children comes from. Our example will be a tongue-root harmony grammar. Choose @@Create tongue-root grammar...@ from the Optimality Theory submenu of the @@New menu@. Set %%Constraint set% to "Five", and %Ranking to "Wolof". Click OK. An object called "OTGrammar Wolof" will appear in the list. Click #Edit. You will see the following grammar appear in the @OTGrammarEditor: ##*[rtr / hi]# 100.000 100.000 ##P\s{ARSE} (rtr)# 50.000 50.000 ##*G\s{ESTURE} (contour)# 30.000 30.000 ##P\s{ARSE} (atr)# 20.000 20.000 ##*[atr / lo]# 10.000 10.000 This simplified Wolof grammar, with five constraints with clearly different rankings, is equivalent to the traditional OT ranking *[rtr / hi] >> P\s{ARSE} (rtr) >> *G\s{ESTURE} (contour) >> P\s{ARSE} (atr) >> *[atr / lo] These constraints are based on a description of Wolof by @@Archangeli & Pulleyblank (1994)|Archangeli & Pulleyblank (1994: 225\--239)@. For the meaning of these constraints, see @@Boersma (1998)|Boersma (1998: 295)@, or the @@Create tongue-root grammar...@ manual page. For each input, there are four output candidates: the vowel heights will be the same as those in the input, but the tongue-root values of V__1_ and V__2_ are varied. For example, for the input [ita] we will have the four candidates [ita], [it\sw], [\icta], and [\ict\sw]. With this way of generating candidates, we see that the five constraints are completely ranked. First, the absolute prohibition on surface [\ic] shows that *[rtr / hi] outranks RTR faithfulness (otherwise, [\ict\ic] would have been the winner): Second, the faithful surfacing of the disharmonic /it\ep/ shows that RTR faithfulness must outrank the harmony (anti-contour) constraint (otherwise, [ite] would have been the winner): Third, the RTR-dominant harmonicization of underlying disharmonic /et\ep/ shows that harmony must outrank ATR faithfulness (otherwise, [et\ep] would have won): Finally, the faithful surfacing of the low ATR vowel /\sw/ even if not forced by harmony, shows that ATR faithfulness outranks *[atr / lo] (otherwise, [ata] would have been the winning candidate): These four ranking arguments clearly establish the crucial rankings of all five constraints. Generating inputs from the grammar According to @@Prince & Smolensky (1993)@, the input to an OT grammar can be %anything. This is the idea of %%##richness of the base%#. When doing a practical investigation, however, we are only interested in the inputs that will illustrate the properties of our partial grammars. In the case of simplified Wolof, this means the 36 possible V__1_tV__2_ sequences where V__1_ and V__2_ are any of the six front vowels i, \ic, e, \ep, \sw, and a (see @@Create tongue-root grammar...@). A set of inputs can be generated from an @OTGrammar object by inspecting the list of tableaus. So select the Wolof tongue-root grammar and choose @@OTGrammar: Generate inputs...|Generate inputs...@. Set %%Number of trials% to 100, and click OK. A @Strings object named "Wolof_in" will appear in the list. Click Inspect and examine the 100 input strings. You will see that they have been randomly chosen from the 36 possible V__1_tV__2_ sequences as described at @@Create tongue-root grammar...@: \epta, et\ep, \epti, it\ep, \ept\ep, iti, \ept\ic, it\ic, \icti, et\ep, ... Thus, when asked to generate a random input, these grammars produce any of the 36 possible V__1_tV__2_ sequences, all with equal probability. Generating outputs from the grammar To compute the outputs for the above set of input forms, select %both the @OTGrammar object %and the input @Strings object, and choose @@OTGrammar & Strings: Inputs to outputs...|Inputs to outputs...@, perhaps specifying zero evaluation noise. A new Strings objects called "Wolof_out" will appear in the list. If you Inspect it, you will see that it contains a string sequence aligned with the original input strings: \epta, \ept\ep, \epti, it\ep, \ept\ep, iti, \epti, iti, iti, \ept\ep, ... In this way, we have created two Strings objects, which together form a series of input-output pairs needed for learning a grammar that contains faithfulness constraints. With the data from a tongue-root-harmony language with five completely ranked constraints, we can have a throw at learning this language, starting with a grammar in which all the constraints are ranked at the same height, or randomly ranked, or with articulatory constraints outranking faithfulness constraints. Let's try the third of these. Create an infant tongue-root grammar by choosing @@Create tongue-root grammar...@ and specifying "Five" for the constraint set and "Infant" for the ranking. The result after a single evaluation will be like: ##*G\s{ESTURE} (contour)# 100.000 100.631 ##*[atr / lo]# 100.000 100.244 ##*[rtr / hi]# 100.000 97.086 ##P\s{ARSE} (rtr)# 50.000 51.736 ##P\s{ARSE} (atr)# 50.000 46.959 Such a grammar produces all kinds of non-adult results. For instance, the input /\swt\ic/ will surface as [at\ic]: The adult form is very different: [\swti]. The cause of the discrepancy is in the order of the constraints *[atr / lo] and *[rtr / hi], which militate against [\sw] and [\ic], respectively. Simply reversing the rankings of these two constraints would solve the problem in this case. More generally, @@Tesar & Smolensky (1998)@ prove that demoting all the constraints that cause the adult form to lose into the stratum just below the highest-ranked constraint violated in the learner's form (here, moving *[atr / lo] just below *[rtr / hi] into the same stratum as P\s{ARSE} (rtr)), will guarantee convergence to the target grammar, %%if there is no variation in the data%. But Tesar & Smolensky's algorithm cannot be used for variable data, since all constraints would be tumbling down, exchanging places and producing wildly different grammars at each learning step. Since language data do tend to be variable, we need a gradual and balanced learning algorithm, and the following algorithm is guaranteed to converge to the target language, if that language can be described by a stochastic OT grammar. The reaction of the learner to hearing the mismatch between the adult [\swti] and her own [at\ic], is simply: 1. to move the constraints violated in her own form, i.e. *[rtr / hi] and P\s{ARSE} (atr), up by a small step along the ranking scale, thus decreasing the probability that her form will be the winner at the next evaluation of the same input; 2. and to move the constraints violated in the adult form, namely *[atr / lo] and P\s{ARSE} (rtr), down along the ranking scale, thus increasing the probability that the adult form will be the learner's winner the next time. If the small reranking step (the %#plasticity) is 0.1, the grammar will become: ##*[atr / lo]# 99.900 100.244 ##*[rtr / hi]# 100.100 97.086 ##P\s{ARSE} (rtr)# 49.900 51.736 ##P\s{ARSE} (atr)# 50.100 46.959 The disharmonies, of course, will be different at the next evaluation, with a probability slightly higher than 50\% that *[rtr / hi] will outrank *[atr / lo]. Thus the relative rankings of these two grounding constraints have moved into the direction of the adult grammar, in which they are ranked at opposite ends of the grammar. Note that the relative rankings of P\s{ARSE} (atr) and P\s{ARSE} (rtr) are now moving in a direction opposite to where they will have to end up in this RTR-dominant language. This does not matter: the procedure will converge nevertheless. We are now going to simulate the infant who learns simplified Wolof. Take an adult Wolof grammar and generate 1000 input strings and the corresponding 1000 output strings following the procedure described in @@OT learning 3.2. Data from another grammar|\SS3.2@. Now select the infant @OTGrammar and both @Strings objects, and choose @@OTGrammar & 2 Strings: Learn...|Learn...@. After you click OK, the learner processes each of the 1000 input-output pairs in succession, gradually changing the constraint ranking in case of a mismatch. The resulting grammar may look like: ##*[rtr / hi]# 100.800 98.644 ##*G\s{ESTURE} (contour)# 89.728 94.774 ##*[atr / lo]# 89.544 86.442 ##P\s{ARSE} (rtr)# 66.123 65.010 ##P\s{ARSE} (atr)# 63.553 64.622 We already see some features of the target grammar, namely the top ranking of *[rtr / hi] and RTR dominance (the mutual ranking of the P\s{ARSE} constraints). The steps have not been exactly 0.1, because we also specified a relative plasticity spreading of 0.1, thus giving steps typically in the range of 0.7 to 1.3. After learning once more with the same data, the result is: ##*[rtr / hi]# 100.800 104.320 ##P\s{ARSE} (rtr)# 81.429 82.684 ##*[atr / lo]# 79.966 78.764 ##*G\s{ESTURE} (contour)# 81.316 78.166 ##P\s{ARSE} (atr)# 77.991 77.875 This grammar now sometimes produces faithful disharmonic utterances, because the P\s{ARSE} now often outrank the gestural constraints at evaluation time. But there is still a lot of variation produced. Learning once more with the same data gives: ##*[rtr / hi]# 100.800 100.835 ##P\s{ARSE} (rtr)# 86.392 82.937 ##*G\s{ESTURE} (contour)# 81.855 81.018 ##*[atr / lo]# 78.447 78.457 ##P\s{ARSE} (atr)# 79.409 76.853 By inspecting the first column, you can see that the ranking values are already in the same order as in the target grammar, so that the learner will produce 100 percent correct adult utterances if her evaluation noise is zero. However, with a noise of 2.0, there will still be variation. For instance, the disharmonies above will produce [ata] instead of [\swt\sw] for underlying /\swt\sw/. Learning seven times more with the same data gives a reasonable proficiency: ##*[rtr / hi]# 100.800 99.167 ##P\s{ARSE} (rtr)# 91.580 93.388 ##*G\s{ESTURE} (contour)# 85.487 86.925 ##P\s{ARSE} (atr)# 80.369 78.290 ##*[atr / lo]# 75.407 74.594 No input forms have error rates above 4 percent now, so the child has learned a lot with only 10,000 data, which may be on the order of the number of input data she receives every day. We could have sped up the learning process appreciably by using a plasticity of 1.0 instead of 0.1. This would have given a comparable grammar after only 1000 data. After 10,000 data, we would have ##*[rtr / hi]# 107.013 104.362 ##P\s{ARSE} (rtr)# 97.924 99.984 ##*G\s{ESTURE} (contour)# 89.679 89.473 ##P\s{ARSE} (atr)# 81.479 83.510 ##*[atr / lo]# 73.067 72.633 With this grammar, all the error rates are below 0.2 percent. We see that crucially ranked constraints will become separated after a while by a gap of about 10 along the ranking scale. If we have three constraints obligatorily ranked as A >> B >> C in the adult grammar, with ranking differences of 8 between A and B and between B and C in the learner's grammar (giving an error rate of 0.2\% ), the ranking A >> C has a chance of less than 1 in 100 million to be reversed at evaluation time. This relativity of error rates is an empirical prediction of our stochastic grammar model. Having shown that the algorithm can learn deep obligatory rankings, we will now see that it also performs well in replicating the variation in the language environment. Create a place assimilation grammar as described in @@OT learning 2.6. Variable output|\SS2.6@, and set all its rankings to 100.000: ##*G\s{ESTURE}# 100.000 100.000 ##*R\s{EPLACE} (t, p)# 100.000 100.000 ##*R\s{EPLACE} (n, m)# 100.000 100.000 Create a place assimilation distribution and generate 1000 string pairs (@@OT learning 3.1. Data from a pair distribution|\SS3.1@). Select the grammar and the two @Strings objects, and learn with a plasticity of 0.1: ##*R\s{EPLACE} (t, p)# 104.540 103.140 ##*R\s{EPLACE} (n, m)# 96.214 99.321 ##*G\s{ESTURE}# 99.246 97.861 The output distributions are now (using @@OTGrammar: To output Distributions...@, see @@OT learning 2.9. Output distributions|\SS2.9@): /an+pa/ \-> anpa 14.3\% /an+pa/ \-> ampa 85.7\% /at+ma/ \-> atma 96.9\% /at+ma/ \-> apma 3.1\% After another 10,000 new string pairs, we have: ##*R\s{EPLACE} (t, p)# 106.764 107.154 ##*G\s{ESTURE}# 97.899 97.161 ##*R\s{EPLACE} (n, m)# 95.337 96.848 With the following output distributions (measured with a million draws): /an+pa/ \-> anpa 18.31\% /an+pa/ \-> ampa 81.69\% /at+ma/ \-> atma 99.91\% /at+ma/ \-> apma 0.09\% The error rate is acceptably low, but the accuracy in reproducing the 80\% - 20\% distribution could be better. This is because the relatively high plasticity of 0.1 can only give a coarse approximation. So we lower the plasticity to 0.001, and supply 100,000 new data: ##*R\s{EPLACE} (t, p)# 106.810 107.184 ##*G\s{ESTURE}# 97.782 99.682 ##*R\s{EPLACE} (n, m)# 95.407 98.760 With the following output distributions: /an+pa/ \-> anpa 20.08\% /an+pa/ \-> ampa 79.92\% /at+ma/ \-> atma 99.94\% /at+ma/ \-> apma 0.06\% So besides learning obligatory rankings like a child does, the algorithm can also replicate very well the probabilities of the environment. This means that a GLA learner can learn stochastic grammars. Once you have mastered the tedious procedures of making Praat learn stochastic grammars, as described in the previous chapters of this tutorial, you can try a faster procedure, which simply involves selecting an @OTGrammar object together with a @PairDistribution object, and clicking ##Learn...#. Once you click OK, Praat will feed the selected grammar with input/output pairs drawn from the selected distribution, and the grammar will be modified every time its output is different from the given output. Here is the meaning of the arguments: %%Evaluation noise% (standard value: 2.0) the standard deviation of the noise added to the ranking of each constraint at evaluation time. %%Strategy% (standard value: Symmetric all) what to do when the learner's output is different from the given output. Possibilities: Demotion only: lower the ranking of every constraint that is violated more in the correct output than in the learner's output. This algorithm crashes if there is variation in the data, i.e. if some inputs can have more than one possible adult outputs. Symmetric one: lower the ranking of the highest-ranked constraint that is violated more in the adult output than in the learner's output, and raise the ranking of the highest-ranked constraint that is violated more in the learner's output than in the adult output. This is the "minimal" algorithm described and refuted in @@Boersma (1998)@, chapters 14-15. Symmetric all: lower the ranking of all constraints that are violated more in the adult output than in the learner's output, and raise the ranking of all constraints that are violated more in the learner's output than in the adult output. This is the algorithm described in @@Boersma & Hayes (2001)@. Weighted uncancelled: the same as "Symmetric all", but the size of the learning step is divided by the number of moving constraints. This makes sure that the average ranking of all the constraints is constant. Weighted all: the "Symmetric all" strategy can reworded as follows: "lower the ranking of all constraints that are violated in the adult output, and raise the ranking of all constraints that are violated in the learner's output". Do that, but divide the size of the learning step by the number of moving constraints. EDCD: Error-Driven Constraint Demotion, the algorithm described by @@Tesar & Smolensky (1998)@. All constraints that prefer the adult form and are ranked above the highest-ranked constraint that prefers the learner's form, are demoted to the ranking of that last constraint minus 1.0. %%Initial plasticity% (standard value: 1.0) %%Replications per plasticity% (standard value: 100000) %%Plasticity decrement% (standard value: 0.1) %%Number of plasticities% (standard value: 4) these four arguments determine the %%learning scheme%, i.e. the number of times the grammar will receive data at a certain plasticity. With the standard values, there will be 100000 data while the plasticity is 1.0 (the initial plasticity), 100000 data while the plasticity is 0.1, 100000 data while the plasticity is 0.01, and 100000 data while the plasticity is 0.001. If you want learning at a constant plasticity, set the %%number of plasticities% to 1. %%Rel. plasticity spreading% (standard value: 0.1) if this is not 0, the size of the learning step will vary randomly. For instance, if the plasticity is set to 0.01, and the relative plasticity spreading is 0.1, you will get actual learning steps that could be anywhere between 0.007 and 0.013, according to a Gaussian distribution with mean 0.01 and standard deviation 0.001. %%Honour local rankings% (standard value: on) if this is on, the fixed rankings that you supplied in the grammar will be maintained during learning: if a constraint falls below a constraint that is supposed to be universally lower-ranked, this second constraint will be demoted as well. %%Number of chews% (standard value: 1) the number of times that each input-output pair is fed to the grammar. Setting this number to 20 will give a slightly different (perhaps more accurate) result than simply raising the plasticity by a factor of 20. In order to be able to learn phonological production, both EDCD and GLA require pairs of underlying form and surface form. However, the language-learning child hears neither of these forms: she only hears ##%%overt forms%#, with less structural information than the underlying and surface forms contain. Interpretive parsing The language-learning child has to construct both the surface form and the underlying form from the overt form that she hears. @@Tesar & Smolensky (1998)@ proposed that the child computes a surface form from the overt form by using the same constraint ranking as in production. For instance, the overt form [\si \si\'^ \si], which is a sequence of three syllables with stress on the second syllable, will be interpreted as the surface form /(\si \si\'^) \si/ in iambic left-aligning languages (I\s{AMBIC} >> T\s{ROCHAIC}, and A\s{LL}F\s{EET}L\s{EFT} >> A\s{LL}F\s{EET}R\s{IGHT}), but as the surface form /\si (\si\'^ \si)/ in trochaic right-aligning languages. Tesar & Smolensky call this procedure @@Robust Interpretive Parsing@, because it works even if the listener's grammar would never produce such a form. For instance, if I\s{AMBIC} >> A\s{LL}F\s{EET}R\s{IGHT} >> T\s{ROCHAIC} >> A\s{LL}F\s{EET}L\s{EFT}, the listener herself would produce the iambic right-aligned /\si (\si \si\'^)/ for any trisyllabic underlying form, though she will still interpret [\si \si\'^ \si] as /(\si \si\'^) \si/, which is illegal in her own grammar. Hearing forms that are illegal in one's own grammar is of course a common situation for language-learning children. In Tesar & Smolensky's view, the underlying form can be trivially computed from the surface form, since the surface form %contains enough information. For instance, the surface form /(\si \si\'^) \si/ must lead to the underlying form \|f\si \si \si\|f if all parentheses and stress marks are removed. Since @@McCarthy & Prince (1995)@, this %containment view of surface representations has been abandoned. In P\s{RAAT}, therefore, the underlying form is not trivially computed from the surface form, but all the tableaus are scanned for the surface form that violates the least high-ranked constraints (in the usual OT sense), as long as it contains the given overt form. For instance, if I\s{AMBIC} >> A\s{LL}F\s{EET}R\s{IGHT} >> T\s{ROCHAIC} >> A\s{LL}F\s{EET}L\s{EFT}, the overt form [\si \si\'^ \si] occurs in two candidates: the surface form /(\si \si\'^) \si/ in the tableau for the underlying form \|f\si \si \si\|f, and the surface form /\si (\si\'^ \si)/ in the tableau for the underlying form \|f\si \si \si\|f. The best candidate is the surface form /(\si \si\'^) \si/ in the tableau for the underlying form \|f\si \si \si\|f. Hence, P\s{RAAT}'s version of Robust Interpretive Parsing will map the overt form [\si \si\'^ \si] to the underlying form \|f\si \si \si\|f (the 'winning tableau') and to the surface form /(\si \si\'^) \si/ (to be sure, this is the same result as in Tesar & Smolensky's version, but crucial differences between the two versions will appear when faithfulness constraints are involved). In P\s{RAAT}, you can do interpretive parsing. For example, create a grammar with ##Create metrics grammar...# from the @@New menu@. Then choose ##Get interpretive parse...# from the #Query submenu and supply "[L1 L L]" for the overt form, which means a sequence of three light syllables with a main stress on the first. The Info window will show you the optimal underlying and surface forms, given the current constraint ranking. Learning from partial forms Now that the learning child can convert an overt form to an underlying-surface pair, she can compare this surface form to the surface form that she herself would have derived from this underlying form. For instance, If I\s{AMBIC} >> A\s{LL}F\s{EET}R\s{IGHT} >> T\s{ROCHAIC} >> A\s{LL}F\s{EET}L\s{EFT}, the winning tableau is \|f\si \si \si\|f, and the perceived adult surface form is /(\si \si\'^) \si/. But from the underlying form \|f\si \si \si\|f, the learner will derive /\si (\si \si\'^)/ as her own surface form. The two surface forms are different, so that the learner can take action by reranking one or more constraints, perhaps with EDCD or GLA. In P\s{RAAT}, you can learn from partial forms. Select the metrics grammar and choose ##Learn from one partial output...#, and supply "[L1 L L]". If you do this several times, you will see that the winner for the tableau "|L L L|" will become one of the two forms with overt part "[L1 L L]". To run a whole simulation, you supply a @Distributions object with one column, perhaps from a text file. The following text file shows the overt forms for Latin, with the bisyllabic forms occurring more often than the trisyllabic forms: "Distributions" 1 column with numeric data "Latin" 28 rows "[L1 L]" 25 "[L1 H]" 25 "[H1 L]" 25 "[H1 H]" 25 "[L1 L L]" 5 "[H1 L L]" 5 "[L H1 L]" 5 "[H H1 L]" 5 "[L1 L H]" 5 "[H1 L H]" 5 "[L H1 H]" 5 "[H H1 H]" 5 "[L L1 L L]" 1 "[L H1 L L]" 1 "[L L H1 L]" 1 "[L H H1 L]" 1 "[L L1 L H]" 1 "[L H1 L H]" 1 "[L L H1 H]" 1 "[L H H1 H]" 1 "[H L1 L L]" 1 "[H H1 L L]" 1 "[H L H1 L]" 1 "[H H H1 L]" 1 "[H L1 L H]" 1 "[H H1 L H]" 1 "[H L H1 H]" 1 "[H H H1 H]" 1 Read this file into P\s{RAAT} with @@Read from file...@. A @Distributions object then appears in the object list. Click @@Distributions: To Strings...|To Strings...@, then OK. A @Strings object containing 1000 strings, drawn randomly from the distribution, with relative frequencies as in the text file, will appear in the list. Click @Inspect to check the contents. You can now select the @OTGrammar together with the @Strings and choose ##Learn from partial outputs...#. A thousand times, P\s{RAAT} will construct a surface form from the overt form by interpretive parsing, and also construct the underlying form in the same way, from which it will construct another surface form by evaluating the tableau. Whenever the two surface forms are not identical, some constraints will be reranked. In the current implementation, the disharmonies for interpretive parsing and for production are the same, i.e., if the evaluation noise is not zero, the disharmonies are randomly renewed before each interpretive parsing but stay the same for the subsequent virtual production. One of the @@types of objects@ in P\s{RAAT}. See the @@OT learning@ tutorial. Inside an OTGrammar With @Inspect, you will see the following attributes: %constraints a list of constraints. Each constraint contains the following attributes: %name the fixed name of the constraint, for instance "P\s{ARSE}". %ranking the continuous ranking value; will change during learning. %disharmony the effective ranking value during stochastic evaluation; with a non-zero evaluation noise, this will be different from %ranking. %fixedRankings an often empty list of locally ranked pairs of constraints. Each local-ranking pair contains the following attributes: %higher the index of the universally higher-ranked of the two constraints, a number between 1 and the number of constraints. %lower the index of the universally lower-ranked of the two constraints. %tableaus a list of tableaus. Each tableau contains the following attributes: %input the input string of the tableau. For production grammaras, the underlying form of the utterance, for example \|fan+pa\|f or \|fb\rt\ic\ng + \s{PAST}\|f. %candidates a list of output candidates. Each output candidate consists of: %output the output string of the tableau. In generative phonology: the surface form of the utterance, for example [anpa] or [ampa] or [b\rt\ct:t] or [b\rt\ae\ng]. In functional phonology: the combination of the articulatory and the perceptual results, for example [anpa]-/anpa/ or [ampa]-/ampa/ or [b\rt\ct:t]-/b\rt\ct:t/ or [b\rt\ae\ng]-/b\rt\ae\ng/. %marks a list of the number of violations of each constraint for this output form. If there are 13 constraints, this list will contain 13 integer numbers for each candidate. OTGrammar creation You can easily create some #OTGrammar examples from the @@New menu@, or type your own grammars into a text file and read the file into Praat. See the @@OT learning@ tutorial. OTGrammar actions You can perform the following actions on selected #OTGrammar objects: @@OTGrammar: Generate inputs...@ @@OTGrammar: Input to output...@ @@OTGrammar: Input to outputs...@ (compute the output distribution for a given input) @@OTGrammar: To output Distributions...@ @@OTGrammar & Strings: Inputs to outputs...@ @@OTGrammar: Learn one...@ @@OTGrammar & 2 Strings: Learn...@ You can view an #OTGrammar in an @OTGrammarEditor. A command to create a @Strings object from a selected @OTGrammar. A practical grammar-specific implementation of the %%richness of the base%: the inputs are drawn at random with equal probabilities from the inputs associated with the tableaus. For an example, see @@OT learning 3.2. Data from another grammar@. Argument %%Number of trials the number of times a string will be drawn from the possible inputs to the grammar. A command to ask the selected @OTGrammar object to evaluate the candidates associated with a specified input form. See @@OT learning 2.8. Asking for one output@ for tutorial information. Arguments %%Input form the input form whose surface form you want to know. If this string is not in the list of the possible inputs of the selected OTGrammar, you will get an error message. %Noise (standard value: 2.0) the standard deviation of the noise added to the ranking value of every constraint during evaluation. See @@OT learning 2.4. Evaluation@. A command to ask the selected @OTGrammar object to evaluate a number of times the candidates associated with a specified input form. The result is a @Distributions object. See @@OT learning 2.9. Output distributions@ for tutorial information and examples. %Trials (standard value: 1000) the number of evaluations that you want to perform. the standard deviation of the noise added to the ranking value of every constraint during the evaluations. See @@OT learning 2.4. Evaluation@. the input form whose surface forms you want to measure. If this string is not in the list of the possible inputs of the selected OTGrammar, you will get an error message. Causes every selected @OTGrammar object to process one input/output pair according to the Gradual Learning Algorithm by @@Boersma (1998)@ and @@Boersma (2000)@. See @@OT learning 4. Learning an ordinal grammar@ and @@OT learning 5. Learning a stochastic grammar@. A command to ask the selected @OTGrammar object to evaluate a number of times the candidates associated with every input form. The result is a @Distributions object. See @@OT learning 2.9. Output distributions@. An action that creates a @Strings object from a selected @OTGrammar and a selected @Strings. The selected Strings object is considered as a list of inputs to the OTGrammar grammar. %%Noise the standard deviation of the noise that will be temporarily added to the ranking value at each evaluation. The resulting Strings object will contain the output string of the grammar for each of the input strings. See @@OT learning 3.2. Data from another grammar@. Causes the selected @OTGrammar object to process a number of input/output pairs according to the Gradual Learning Algorithm by @@Boersma (1998)@ and @@Boersma (2000)@. See @@OT learning 4. Learning an ordinal grammar@ and @@OT learning 5. Learning a stochastic grammar@. One of the @editors in P\s{RAAT}, for viewing and editing the grammar in an @OTGrammar object. See the @@OT learning@ tutorial for examples. Usage The menu command that you will probably use most often if you investigate variation, is the ##Evaluate (noise 2.0)# command, which you can invoke from the Edit menu or by pressing Command-2. This command performs a new evaluation with the current ranking values. Some noise is added to the ranking values, so that the %#disharmonies of the constraint will change. This may cause a change in the ranking order of the constraints, which in its turn may cause a different candidate to win in some tableaus. Alan Prince & Paul Smolensky (1993): %%Optimality Theory: Constraint Interaction in Generative Grammar.% Rutgers University Center for Cognitive Science Technical Report #2. The mapping from overt forms to surface forms in the acquisition model by @@Tesar & Smolensky (1998)@. In P\s{RAAT}, you can do robust interpretive parsing on any @OTGrammar object. See @@OT learning 7. Learning from overt forms@. ppgb Create tongue-root grammar... Hayes & MacEachern (1998) McCarthy & Prince (1995) Optimality Theory OT OT learning OT learning 1. Kinds of OT grammars OT learning 2. The grammar OT learning 2.1. Viewing a grammar OT learning 2.2. Inside the grammar OT learning 2.3. Defining your own grammar OT learning 2.4. Evaluation OT learning 2.5. Editing a grammar OT learning 2.6. Variable output OT learning 2.7. Tableau pictures OT learning 2.8. Asking for one output OT learning 2.9. Output distributions OT learning 3. Generating language data OT learning 3.1. Data from a pair distribution OT learning 3.2. Data from another grammar OT learning 4. Learning an ordinal grammar OT learning 5. Learning a stochastic grammar OT learning 6. Shortcut to OT learning OT learning 7. Learning from overt forms OTGrammar OTGrammar: Generate inputs... OTGrammar: Input to output... OTGrammar: Input to outputs... OTGrammar: Learn one... OTGrammar: To output Distributions... OTGrammar & Strings: Inputs to outputs... OTGrammar & 2 Strings: Learn... OTGrammarEditor Prince & Smolensky (1993) Robust Interpretive Parsing @& .> ? 4@ЛF SUd 0Rj pRd Evaluate 2.0 Noise Evaluate (noise 2.0) Evaluate (tiny noise) Evaluate (zero noise) Edit ranking constraint 100.0 Ranking value Disharmony Select a constraint first. OTGrammar: Learn one... Learn one Underlying form: Input string Adult surface form: Output string Evaluation noise Reranking strategy Demotion only Symmetric one Symmetric all Weighted uncancelled Weighted all EDCD 0.1 Plasticity Rel. plasticity spreading Honour local rankings Learn one from partial adult output Partial adult surface form (e.g. overt form): Partial output 1 Number of chews Learn one from partial output Remove constraint Reset all rankings Ranking OTGrammarEditor OTGrammar OT learning -- edit ot -- Edit Evaluate... Edit ranking... Reset all rankings... Learn one... Learn one from partial output... -- remove ot -- OTGrammarEditor help Help OTGrammar help OT learning tutorial %%ranking value %disharmony \sp %s@@%ld|%s@ %.3f %.3f OTGrammarEditor not created. ]d ]d ]d ]d ]d ]d ]d ]d ]d ]d ]d ^d ^d #^d .^d <Xd A^d W^d $ W^d j ]d a^d m^d Vd ]d ^d ]d ^d ^d ^d Wd ^d ^d ^d ^d Xd _d XF W^d lj $ ([d άF Z`d i [d ? @ (@? ?ffffff9@ R@ ?? @ @ b@ I@ Y@MbP?& .>F cfd lj \d name ranking disharmony tiedToTheLeft tiedToTheRight higher lower output numberOfConstraints marks my numberOfConstraints input numberOfCandidates candidates OTGrammarCandidate my numberOfCandidates OTGrammar constraints OTGrammarConstraint index numberOfFixedRankings fixedRankings OTGrammarFixedRanking my numberOfFixedRankings numberOfTableaus tableaus OTGrammarTableau my numberOfTableaus Number of constraints: %ld Number of tableaus: %ld Number of candidates: %ld Number of violation marks: %ld %ld constraints constraint [%ld]: " " %.17g %.17g ! %ld fixed rankings %ld %ld %ld tableaus input [%ld]: " " %ld candidate [%ld]: " " %d No constraints. No tableaus. No candidates in tableau %ld. OTHistory Input "%s" not in list of tableaus. The partial output "%s" does not match any candidate for any input form. (OTGrammar: Get interpretive parse:) Not performed. This grammar accepts no input "%s". %s \pf * ! No winner (OTGrammar_inputToOutput:) Not performed. (OTGrammar_inputsToOutputs:) Not performed. (OTGrammar_inputToOutputs:) Not performed. Measuring input "%s" %s \-> %s (OTGrammar_measureTypology:) Cannot handle more than 12 constraints. (OTGrammar_step:) Adult form has strict superset violations! EDCD stalls. Underlying form: %s Adult output: %s Winner output: %s (OTGrammar_step:) Loser wins! Can never happen. (OTGrammar_step:) Loser equals correct candidate. Cannot generate adult output "%s". Numbers of strings in input and output do not match. (OTGrammar_learn:) Not completed. Learning with full knowledge... Processing input-output pair %ld out of %ld: %s -> %s Only %ld input-output pairs out of %ld were processed. OTGrammar did not complete learning from input-output pairs. (OTGrammar_setRanking): No constraint %ld. Datum Initial state Final state (OTGrammar_learnFromPartialOutputs:) Not completed. Learning with limited knowledge... Processing partial output %ld out of %ld: %s Only %ld partial outputs out of %ld were processed. OTGrammar did not complete learning from partial outputs. (OTGrammar_PairDistribution_getFractionCorrect:) Not completed. (OTGrammar_Distributions_getFractionCorrect:) Not completed. Cannot remove last constraint. No constraint "%s". OTGrammar.c icand >= 1 icand %ld, ncand %ld OTGrammar_List4 There are no total rankings that generate these input-output pairs. %ld/%ld: Trying ranking %s >> %s >> %ld/%ld OR %s w CONSTRAINTS rankings %f disharmonies INPUT %s loser co-winner winner %s %s = id id I@ r@ @ ? @ {Gz? ? {Gz? 9@ @ ? @ffffff??(\?(\? I@ffffff? ?jt?MbP @ ??333333?dld fsd nsd :OG nnd hvd \hd Hz st ManipulationEditor.pitch.scaling ManipulationEditor.pitch.minimum ManipulationEditor.pitch.maximum ManipulationEditor.pitch.units ManipulationEditor.pitch.draggingStrategy ManipulationEditor.pitch.stylize.frequencyResolution ManipulationEditor.pitch.stylize.useSemitones ManipulationEditor.pitch.interpolateQuadratically.numberOfPointsPerParabola ManipulationEditor.duration.minimum ManipulationEditor.duration.maximum Remove pulse(s) Add pulse 0.0 Position (s) Position Remove pitch point(s) Add pitch point There are no pulses. Time (s) 100.0 Frequency (Hz or st) Time Frequency PitchTier: Stylize... Stylize pitch 2.0 Frequency resolution Units Semitones Interpolate quadratically 4 Number of points per parabola Shift pitch frequencies -20.0 Frequency shift Hertz Mel Erb Multiply pitch frequencies 1.2 Factor The multiplication is always done in Hertz. Set pitch range 300.0 Maximum (Hz or st) Maximum Maximum pitch must be greater than %.4g %s. Set pitch units Pitch units Semitones re 100 Hz Set duration range 0.25 Minimum 3.0 Minimum relative duration must not be greater than 1. Maximum relative duration must not be less than 1. Maximum relative duration must be greater than minimum. Minimum relative duration must not be greater than the minimum value present, which is %.4g. Maximum relative duration must not be less than the maximum value present, which is %.4g. ManipulationEditor Set dragging strategy Dragging strategy All Only horizontal Only vertical Single all, multiple only vertical Remove duration point(s) Add duration point 1.0 Relative duration New duration Manipulation Extract original sound File Extract pulses Extract pitch tier Extract duration tier Publish resynthesis -- close -- Pulse Add pulse at cursor Add pulse at... -- remove pulses -- Pitch Add pitch point at cursor Add pitch point at time slice Add pitch point at... -- remove pitch -- -- pitch prefs -- Set pitch range... Set pitch units... Set pitch dragging strategy... -- modify pitch -- Shift pitch frequencies... Multiply pitch frequencies... All: Stylize pitch... Stylize pitch (2 st) Interpolate quadratically... Interpolate quadratically (4 pts) Dur Add duration point at cursor Add duration point at... -- remove duration -- -- duration prefs -- Set duration range... -- refresh duration -- Forget duration Synth Pulses -- Pulses (hum) -- Pulses & LPC -- ("LPC resynthesis") -- pitch resynth -- -- Pitch -- Pitch (hum) Pulses -- Pitch Pulses -- Pitch (hum) -- full resynth -- Sound & Pulses -- Pitch & Duration ("PSOLA manipulation") LPC -- Pitch ("LPC pitch manipulation") ManipulationEditor help Help Manipulation help %%Sound %%Pulses %.4g %.1f Hz %.2f st %%Pitch manip %%Pitch from pulses (no pitch points) %%Duration manip %.3f (no duration points) %f %.5f Drag pitch points Drag pitch point %.2f Drag duration points Drag duration point SG @ud d 0td DurationTier DurationTier help Help DurationTierEditor Relative duration %5g Set duration range... 0.25 3.0 Minimum duration Maximum duration X T ? eA ?? T@fffff8@ M@ ? &@ ? ? Q@-q=-? @ @{Gz?Gz? @G {d 'j hvd FunctionEditor.c i < maxGroup Preferences Synchronize zoom and scroll 0.05 Arrow scroll step (s) Arrow scroll step Play 0.0 From 1.0 To Select Start of selection End of selection Move cursor to Position Move cursor by Distance Move start of selection by Move end of selection by %.17g %s Zoom Intro Preferences... File -- after prefs -- Query Get start of selection Get begin of selection Get cursor Get end of selection Get selection length View Zoom... Show all Zoom in Zoom out Zoom to selection Scroll page back Scroll page forward -- play -- Audio: Play... Play or stop Play window Interrupt playing Select... Move cursor to start of selection Move cursor to begin of selection Move cursor to end of selection Move cursor to... Move cursor by... Move start of selection by... Move begin of selection by... Move end of selection by... Select earlier Select later Move start of selection left Move begin of selection left Move start of selection right Move begin of selection right Move end of selection left Move end of selection right Help buttons all in out sel scrollBar Group drawingArea text Thing_member (function, classFunction) %f FunctionEditor Time domain: %.3f seconds Total duration %f seconds Visible part %f seconds %f (%.3f / s) XtWindow (my drawingArea) FunctionEditor.shellWidth FunctionEditor.shellHeight FunctionEditor.groupWindow FunctionEditor.arrowScrollStep ƥG }d d |d IntensityTier IntensityTier help Help IntensityTierEditor Intensity (dB) Intensity %4g %4g dB Set intensity range... 50.0 100.0 Minimum intensity (dB) Maximum intensity (dB) Minimum intensity Maximum intensity ? @ ?UUUUUU? ? ? @ @ @ @ @@ @ y@ @ @ $@ A @=G ld hvd ~d Change ceiling 600 Ceiling (Hertz) Ceiling Path finder 0.03 Silence threshold 0.45 Voicing threshold 0.01 Octave cost 0.35 Octave-jump cost 0.14 Voiced/unvoiced cost Pull formants Hertz Octave up Fifth up Fifth down Octave down Unvoice PitchEditor Pitch Change ceiling... Edit Path finder... -- pitch -- Query Get pitch Selection -- up and down -- PitchEditor help Help Pitch help %.2f %ld Hz %d intens Unv Change path yG d d (d PitchTierEditor PitchTier PitchTierEditor help Help PitchTier help Frequency (Hz) Frequency %5g %5g Hz Set frequency range... 50.0 600.0 Minimum frequency (Hz) Maximum frequency (Hz) Minimum frequency Maximum frequency ?{Gz?-C 6?? ? ? ?G 1d hvd @d Selection Make a selection first. Remove point(s) Add point 0.0 Position PointEditor -- query jitter -- Query Get jitter (local) Get jitter (local, absolute) Get jitter (rap) Get jitter (ppq5) Get jitter (ddp) -- query shimmer -- Get shimmer (local) Get shimmer (local, dB) Get shimmer (apq3) Get shimmer (apq5) Get shimmer (apq11) Get shimmer (dda) Point Add point at cursor Add point at... -- remove point -- PointEditor help Help ? ?? -? r? @ @ @ ?G yd hvd d Remove point(s) Add point 0.0 Time (s) Time -- view/realtier -- View Point Add point at cursor Add point at... (no points) %f Drag points Drag point RealTierEditor Y %5g Set range... 1.0 Minimum Maximum RealTierEditor.c data != NULL Thing_member (data, classRealTier) sound == NULL || Thing_member (sound, classSound) ? ? ? @ >@H d hvd ` hd SoundEditor.publish.windowType SoundEditor.publish.relativeWidth SoundEditor.publish.preserveTimes Extract windowed selection slice Name Window 1.0 Relative width Preserve times No samples selected. Write selection to AIFF file %s.aiff Write selection to AIFC file %s.aifc Write selection to WAV file %s.wav Write selection to NeXT/Sun file %s.au Write selection to NIST file %s.nist (SoundEditor_cut:) You cannot cut all of the signal away, because you cannot create a Sound with 0 samples. You could consider using Copy instead. Cut (SoundEditor_paste:) Clipboard is empty; nothing pasted. (SoundEditor_paste:) Cannot paste because sampling frequency of clipboard does not match sampling frequency of edited sound. Paste Set to zero Reverse selection Data class: Data name: seconds Editor start: Editor end: Window start: Window end: Selection start: Selection end: Sound autoscaling: Spectrogram show: Hertz Spectrogram view from: Spectrogram view to: Spectrogram window length: dB Spectrogram dynamic range: Spectrogram number of time steps: Spectrogram number of frequency steps: Fourier Spectrogram method: Spectrogram window shape: Spectrogram autoscaling: dB/Hz Spectrogram maximum: dB/octave Spectrogram pre-emphasis: Spectrogram dynamicCompression: Spectrogram cursor frequency: Pitch show: Pitch floor: Pitch ceiling: Pitch unit: Pitch view from: Pitch view to: Autocorrelation Forward cross-correlation Pitch method: Pitch very accurate: Pitch max. number of candidates: of global peak Pitch silence threshold: (periodic power / total power) Pitch voicing threshold: per octave Pitch octave cost: Pitch octave jump cost: Pitch voiced/unvoiced cost: Intensity show: Intensity view from: Intensity view to: Formant show: Formant maximum formant: Formant number of poles: Formant window length: Formant dynamic range: mm Formant dot size: Burg Formant method: Formant pre-emphasis from: Pulses show: SoundEditor LongSoundEditor Copy to list of objects: File Extract sound selection (preserve times) Extract selection (preserve times) Extract sound selection (time from 0) Extract selection (time from 0) Extract selection Extract windowed sound selection... Extract windowed selection... -- write -- Copy to disk: Write sound selection to WAV file... Write selection to WAV file... Write sound selection to AIFF file... Write selection to AIFF file... Write sound selection to AIFC file... Write selection to AIFC file... Write sound selection to Next/Sun file... Write selection to Next/Sun file... Write sound selection to NIST file... Write selection to NIST file... -- close -- -- cut copy paste -- Edit Copy selection to Sound clipboard Paste after selection -- zero -- Set selection to zero -- move to zero -- Select Move start of selection to nearest zero crossing Move begin of selection to nearest zero crossing Move cursor to nearest zero crossing Move end of selection to nearest zero crossing -- reports -- Query Settings report SoundEditor help Help LongSoundEditor help (window longer than %.7g seconds) (zoom in to see the samples) SoundEditor.c sound != NULL @? @ ? v@ L@ p@ >A @@ $@ @ p@ @@ @ 袻@ @@ @ @@ zD > ?7H ,d 'j X! d SoundRecorder.bufferSize_MB SoundRecorder.coupleSliders SoundRecorder.mac.defaultDevice SoundRecorder.mac.defaultSource %s Error number %d out of range. No sound driver present. Out of memory. Unknown sound error. Audio input not opened. Audio input: cannot prepare header. Quit some other programs or go to "Sound input prefs" in the Preferences menu. Audio input: cannot add buffer. Audio input not started. Audio input not stopped. Audio input not reset. Audio input: cannot unprepare header. Audio input not closed. Cannot stop recording. Cannot record. You can still save to file. SoundRecorder.c w == my leftGainScale w == my rightGainScale Cannot change sampling frequency. column row rc Input source: (use Windows mixer without meters) Meter meter Sampling frequency: fsamp 8000 9800 11025 12000 16000 22050 22254.54545 24000 32000 44100 48000 64000 scale form Record Stop Play Close sep Save to list: Save left channel to list: left sound Save right channel to list: right PpgB Audio file not written. Write to WAV file %s.wav Write to AIFC file %s.aifc Write to NeXT/Sun file %s.au Write to NIST file %s.nist Write left to WAV file Write right to WAV file Write to stereo WAV file stereo.wav Write left to AIFC file Write right to AIFC file Write to stereo AIFC file stereo.aifc Write left to NeXT/Sun file Write right to NeXT/Sun file Write to stereo NeXT/Sun file stereo.au Write left to NIST file Write right to NIST file Write to stereo NIST file stereo.nist SoundRecorder Write to WAV file... File Write to AIFC file... Write to NeXT/Sun file... Write to NIST file... -- write -- Write left channel to WAV file... Write right channel to WAV file... Write to stereo WAV file... -- write wav -- Write left channel to AIFC file... Write right channel to AIFC file... Write to stereo AIFC file... -- write aifc -- Write left channel to NeXT/Sun file... Write right channel to NeXT/Sun file... Write to stereo NeXT/Sun file... -- write next/sun -- Write left channel to NIST file... Write right channel to NIST file... Write to stereo NIST file... -- write nist -- SoundRecorder help Help No sound input devices available. Your computer does not support stereo sound input. XtWindow (my leftMeter) my leftGraphics XtWindow (my rightMeter) my rightGraphics SoundRecorder not created. ? @ N@{Gz?H 7d hvd d %ld Hz SpectrogramEditor Y@ N@ ? HH 5d hvd pd SpectrumEditor.bandSmoothing %.1f dB Spectrum: Filter (pass Hann band)... Filter (pass Hann band) 100.0 Band smoothing (Hz) Band smoothing To apply band-pass filter, first make a selection. Pass band Filter (stop Hann band) To apply band-stop filter, first make a selection. Stop band SpectrumEditor Spectrum Publish band File Publish band-filtered sound -- close -- -- edit band -- Edit Pass band... Stop band... SpectrumEditor help Help Spectrum help Frequency domain: %.0f %.2f Hertz Total bandwidth %.2f Hertz Window %.2f Hertz %.2f Hz any matching string for green colouring ?? @ ?-? ? 333333?333333? ?? @ @? @)\(? >@d ͫd d d d d H խd hvd @ d TextGridEditor.useTextStyles TextGridEditor.fontSize TextGridEditor.alignment TextGridEditor.shiftDragMultiple2 TextGridEditor.showNumberOf TextGridEditor.greenMethod TextGridEditor.greenString To %s, first select a tier by clicking anywhere inside it. TextGridEditor.c my selectedTier >= 1 || my selectedTier <= grid -> tiers -> size tier -> methods == classIntervalTier query the starting point of an interval seconds The selected tier is not an interval tier. query the end point of an interval query the label of an interval %s tier -> methods == classTextTier 18 Font size (points) Text alignment in intervals Left Centre Right The symbols %#_^ in labels are shown as typed mean italic/bold/sub/super With the shift key, you drag a single boundary multiple boundaries Show number of nothing intervals or points non-empty intervals or points Paint intervals green whose label... some text here for green paint ...the text Font size Write to TextGrid text file %s.TextGrid No selection. publish != NULL No samples selected. Write selection to AIFF file %s.aiff Write selection to AIFC file %s.aifc Write selection to WAV file %s.wav Write selection to NeXT/Sun file %s.au Write selection to NIST file %s.nist Genericize Nativize Cannot add a boundary at %f seconds, because there is already a boundary there. Add boundary Cannot add a point at %f seconds, because there is already a point there. Add point remove a point or boundary To remove a boundary, first click on it. Remove boundary %s%s To remove a point, first click on it. Remove point Move boundary to zero crossing Move boundary to B Move boundary to E Move point to zero crossing Move point to B Move point to E move a point or boundary To move a boundary, first click on it. To move a point, first click on it. find a text Find text Text: string check spelling Rename tier Name rename a tier publish a tier remove all text from a tier Remove text from tier Sorry, I refuse to remove the last tier. remove a tier Remove tier Add interval tier 1 (= at top) Position %ld (= at bottom) Add point tier Duplicate tier %ld duplicate a tier TextGridEditor Special symbols Phonetic symbols Text styles Copy to list of objects: File Extract sound selection (preserve times) Extract selection (preserve times) Extract sound selection (time from 0) Extract selection (time from 0) Extract selection -- write -- Copy to disk: Write TextGrid to text file... Write sound selection to WAV file... Write selection to WAV file... Write sound selection to AIFF file... Write selection to AIFF file... Write sound selection to AIFC file... Write selection to AIFC file... Write sound selection to Next/Sun file... Write selection to Next/Sun file... Write sound selection to NIST file... Write selection to NIST file... -- close -- -- cut copy paste -- Edit Cut text Cut Copy text Copy Paste text Paste Erase text Erase -- encoding -- Genericize entire TextGrid Nativize entire TextGrid -- search -- Find... Find again -- move to zero -- Select Move start of selection to nearest zero crossing Move begin of selection to nearest zero crossing Move cursor to nearest zero crossing Move end of selection to nearest zero crossing -- query interval -- Query Get starting point of interval Get end point of interval Get label of interval Interval Add interval on tier 1 Add interval on tier 2 Add interval on tier 3 Add interval on tier 4 Add interval on tier 5 Add interval on tier 6 Add interval on tier 7 Add interval on tier 8 Boundary Move to nearest zero crossing -- insert boundary -- Add on selected tier Add on tier 1 Add on tier 2 Add on tier 3 Add on tier 4 Add on tier 5 Add on tier 6 Add on tier 7 Add on tier 8 Add on all tiers -- remove mark -- Remove Tier Copy tier to list of objects -- add tier -- Add interval tier... Add point tier... Duplicate tier... Rename tier... -- remove tier -- Remove all text from tier Remove entire tier Spell Check spelling in tier Check spelling in interval -- edit lexicon -- Add selected word to user dictionary TextGridEditor help Help About special symbols About text styles \pf %ld (%ld) (##%ld#) %f Drag Cannot drop point on an existing point. ! (intervalTier && ! clickedLeftBoundary) Select previous tier View Select next tier Select previous interval Select next interval Extend-select left Extend-select right -- select interval -- d d d )d :d Td od d ꌠ9Y>)ꌠ9Y>)F Y@ F@ >@ ?left Time range (s) right Time range (s) left Time range right Time range left Frequency range (Hz) right Frequency range (Hz) left Frequency range right Frequency range 0.0 0.0 (= all) Interpolation None Parabolic Cubic Sinc70 Sinc700 0.5 Time (s) Nearest Linear Unit Maximum frequency must be greater than minimum frequency. %s formula Movie movingArea AmplitudeTier: Add point... Add one point 0.8 Sound pressure (Pa) Sound pressure Time Create empty AmplitudeTier empty Name Starting time (s) 1.0 Finishing time (s) Starting time Finishing time Finishing time must be greater than starting time. Cannot edit an AmplitudeTier from batch. AmplitudeTier: Formula... AmplitudeTier: Formula # ncol = the number of points for col from 1 to ncol # x = the time of the colth point, in seconds # self = the value of the colth point, in Pascal self = `formula' endfor - self ; upside down 0.0001 Shortest period (s) 0.02 Longest period (s) 1.6 Maximum amplitude factor AmplitudeTier: Get shimmer (local)... AmplitudeTier: Get shimmer (local) Longest period Shortest period AmplitudeTier: Get shimmer (local, dB)... AmplitudeTier: Get shimmer (local, dB) AmplitudeTier: Get shimmer (apq3)... AmplitudeTier: Get shimmer (apq3) AmplitudeTier: Get shimmer (apq5)... AmplitudeTier: Get shimmer (apq5) AmplitudeTier: Get shimmer (apq11)... AmplitudeTier: Get shimmer (apq11) AmplitudeTier: Get shimmer (dda)... AmplitudeTier: Get shimmer (dda) AmplitudeTier AmplitudeTier: To IntensityTier... AmplitudeTier: To IntensityTier -10000.0 Threshold (dB) Threshold AmplitudeTier: To Sound (pulse train)... AmplitudeTier: To Sound (pulse train) 44100 Sampling frequency (Hz) 2000 Interpolation depth (samples) Interpolation depth Sampling frequency To include a copy of a Sound in your AmplitudeTier editor: select an AmplitudeTier and a Sound, and click "Edit". %s_amp grid Cochleagram difference Hertz (root-mean-square) Cochleagram: Formula... Cochleagram Formula `x' is time in seconds, `y' is place in Bark label y := y1; for row := 1 to nrow do { x := x1; for col := 1 to ncol do { self [row, col] := `formula' ; x := x + dx } y := y + dy } self Cochleagram Cochleagram movie Paint Cochleagram Garnish From Cochleagram to Excitation added Get mean difference 1 Column number Get probability String Distributions To Strings 1000 Number of strings To Strings (exact) To Transition Environment Greedy To Transition (noise) surface DurationTier: Add point... Add one point to DurationTier 1.5 Relative duration Create DurationTier... Create empty DurationTier Cannot edit a DurationTier from batch. DurationTier: Formula... DurationTier: Formula # self = the value of the colth point, in relative units self * 1.5 ; slow down Get target duration seconds DurationTier: Get value at time... Get DurationTier value Duration: Get value at index... 10 Point number DurationTier To include a copy of a Sound in your DurationTier editor: select a DurationTier and a Sound, and click "Edit". Draw Excitation 0 From frequency (Bark) 25.6 To frequency (Bark) Minimum (phon) 100 Maximum (phon) Maximum Minimum To frequency From frequency Excitation: Formula... Excitation Formula `x' is the place in Bark, `col' is the bin number x := 0; for col := 1 to ncol do { self [1, col] := `formula' ; x := x + dx } sones Excitation From Excitation to Formant 20 Maximum number of formants Formant: Draw speckles... Draw Formant 5500.0 Maximum frequency (Hz) 30.0 Dynamic range (dB) Dynamic range Maximum frequency Formant: Draw tracks... Draw formant tracks Formant: Formula (bandwidths)... Formant: Formula (bandwidths) row is formant number, col is frame number: for row from 1 to nrow do for col from 1 to ncol do B (row, col) := self / 2 ; sharpen all peaks Formant: Formula (frequencies)... Formant: Formula (frequencies) row is formant number, col is frame number: for row from 1 to nrow do for col from 1 to ncol do F (row, col) := if row = 2 then self + 200 else self fi Formant: Get bandwidth at time... Formant: Get bandwidth Formant number Hertz Bark Formant: Get maximum... Formant: Get maximum %s (there are at most this many formants in every frame) Formant: Get mean... Formant: Get mean Formant: Get minimum... Formant: Get minimum %s (at least this many formants in every frame) Formant: Get number of formants... Formant: Get number of formants Frame number There is no frame %ld in a Formant with only %ld frames. %d formants Formant: Get quantile 0.50 (= median) Quantile Formant: Get quantile of bandwidth Formant: Get standard deviation Formant: Get time of maximum... Formant: Get time of maximum Formant: Get time of minimum... Formant: Get time of minimum Formant: Get value at time... Formant: Get value Formant Formant: Scatter plot 2 Horizontal formant number 3000 left Horizontal range (Hz) 400 right Horizontal range (Hz) Vertical formant number 1500 left Vertical range (Hz) right Vertical range (Hz) Mark size (mm) + Mark string (+xo.) Mark string Mark size right Vertical range left Vertical range right Horizontal range left Horizontal range From Formant to Matrix Formant: Track... Formant tracker 3 Number of tracks 550 Reference F1 (Hz) 1650 Reference F2 (Hz) 2750 Reference F3 (Hz) 3850 Reference F4 (Hz) 4950 Reference F5 (Hz) Frequency cost (/kHz) Bandwidth cost Transition cost (/octave) Transition cost Frequency cost Reference F5 Reference F4 Reference F3 Reference F2 Reference F1 %s %s %s_filt FormantTier: Add point... Frequencies and bandwidths (Hz): 500 50 1500 100 2500 150 3500 200 4500 300 fb pairs %lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf Number of formant-bandwidth pairs must be at least 1. Create empty FormantTier Down to TableOfReal Include formants Include bandwidths FormantTier: Get bandwidth at time... FormantTier: Get bandwidth FormantTier: Get value at time... FormantTier: Get value FormantTier Draw FormantTier Draw harmonicity 0.0 (= auto) Harmonicity: Formula... Harmonicity Formula x is time for col := 1 to ncol do { self [col] := `formula' ; x := x + dx } Harmonicity: Get maximum... Harmonicity: Get maximum dB Harmonicity: Get mean... Harmonicity: Get mean Harmonicity: Get minimum... Harmonicity: Get minimum Harmonicity: Get standard deviation... Harmonicity: Get standard deviation Harmonicity: Get time of maximum... Harmonicity: Get time of maximum Harmonicity: Get time of minimum... Harmonicity: Get time of minimum Harmonicity: Get value at time... Harmonicity: Get value Harmonicity: Get value in frame... Get value in frame Harmonicity Draw Intensity Minimum (dB) Maximum (dB) Intensity Formula `x' is the time in seconds, `col' is the frame number, `self' is in dB x := x1; for col := 1 to ncol do { self [col] := `formula' ; x := x + dx } Intensity: Get maximum... Intensity: Get maximum Intensity: Get mean... Intensity: Get mean Averaging method energy Intensity: Get minimum... Intensity: Get minimum Intensity: Get quantile 0.50 Quantile (0-1) Intensity: Get standard deviation... Intensity: Get standard deviation Intensity: Get time of maximum... Intensity: Get time of maximum Intensity: Get time of minimum... Intensity: Get time of minimum Intensity: Get value at time... Intensity: Get value Intensity: Get value in frame... Intensity Plot intensity by pitch From frequency (Hertz) To frequency (Hertz) From intensity (dB) 100.0 To intensity (dB) Drawing method Speckles Curve Speckles and curve To intensity From intensity IntensityTier: Add point... 75 Intensity (dB) Create empty IntensityTier Cannot edit an IntensityTier from batch. IntensityTier: Formula... IntensityTier: Formula # self = the value of the colth point, in dB self + 3.0 IntensityTier: Get value at time... Get IntensityTier value IntensityTier: Get value at index... IntensityTier To include a copy of a Sound in your IntensityTier editor: select an IntensityTier and a Sound, and click "Edit". %s_int Sound & IntervalTier: Multiply Scale to 0.9 IntervalTier: Down to TableOfReal Label IntervalTier: Get centre points Text IntervalTier: Get end points IntervalTier: Get starting points IntervalTier IntervalTier & PointProcess: End to centre... From end to centre Phase (0-1) Phase %s %s %ld IntervalTier & PointProcess: Start to centre... From start to centre Read IntervalTier from Xwaves This is an old-style Label object. To turn it into a TextGrid, select it together with a Sound of the appropriate duration, and click "To TextGrid". averaged Ltas: Compute trend line... Ltas: Compute trend line 600.0 4000.0 %s_trend Ltas: Draw -20.0 left Power range (dB/Hz) 80.0 right Power range (dB/Hz) bars right Power range left Power range curve poles speckles Ltas Formula `x' is the frequency in Hertz, `col' is the bin number x := x1; for col := 1 to ncol do { self [1, col] := `formula' ; x := x + dx } Ltas: Get band from frequency... Ltas: Get band from frequency Frequency (Hz) Frequency Ltas: Get frequency from bin number... Ltas: Get frequency from bin number Bin number Ltas: Get frequency of maximum... Ltas: Get frequency of maximum From frequency (Hz) To frequency (Hz) Ltas: Get frequency of minimum... Ltas: Get frequency of minimum From frequency (s) To frequency (s) Ltas: Get local peak height 1700.0 left Environment (Hz) 4200.0 right Environment (Hz) 2400.0 left Peak (Hz) 3200.0 right Peak (Hz) left Environment right Environment left Peak right Peak The beginning of the environment must lie before the peak. The end of the peak must lie after its beginning. The end of the environment must lie after the peak. Ltas: Get maximum... Ltas: Get maximum Ltas: Get mean... Ltas: Get mean Ltas: Get minimum... Ltas: Get minimum %ld bins Ltas: Get slope left Low band (Hz) 1000.0 right Low band (Hz) left High band (Hz) right High band (Hz) right High band left High band right Low band left Low band Ltas: Get standard deviation... Ltas: Get standard deviation Ltas: Get value at frequency... Ltas: Get value Frequency (Hertz) Ltas: Get value in bin... Get value in bin Ltas merged Ltas: Subtract trend line... Ltas: Subtract trend line left Frequency range (Hertz) right Frequency range (Hertz) %s_fit fromManipulationEditor Cannot edit a Manipulation from batch. Manipulation does not contain a DurationTier. Manipulation does not contain a Sound. Manipulation does not contain a PitchTier. Manipulation does not contain a PointProcess. Manipulation Binary file without Sound Text file without Sound To replace the DurationTier in a Manipulation object, select a DurationTier object and a Manipulation object and choose "Replace duration". To replace the PitchTier in a Manipulation object, select a PitchTier object and a Manipulation object and choose "Replace pitch". Manipulation: Replace duration tier Manipulation: Replace pitch tier %s_%s Create Matrix... Create Matrix xy xmin xmax Number of columns dx x1 ymin ymax Number of rows dy y1 Formula: x*y xmax (%.8g) should not be less than xmin (%.8g). ymax (%.8g) should not be less than ymin (%.8g). Create simple Matrix... Create simple Matrix Draw one altitude contour From x = To x = From y = To y = Height Draw altitude contours Draw rows eigenvectors eigenvalues Formula... Matrix Formula %ld Matrix: Get value at xy X Y ) and y = (at x = Matrix: Get value in cell Row number Row number must not exceed number of rows. Column number must not exceed number of columns. Matrix: Get x of column Matrix: Get y of row Matrix Matrix movie Matrix: Paint cells... Matrix: Paint cells with greys Matrix: Paint altitude contours with greys Matrix: Paint grey image Matrix: Paint 3-D surface plot Matrix: Power... Power Read Matrix from raw text file Read Matrix from LVS AP file Matrix: Set value... Matrix: Set value New value Row number must not be greater than number of rows. Column number must not be greater than number of columns. Matrix: To Sound Row (negative values count from last row) Write Matrix to matrix text file mat Write Matrix to spreadsheet txt PairDistribution Generate two Strings objects Number input Name of first Strings output Name of second Strings PairDistribution & Distributions: Get fraction correct Column Draw parametrized curve Tmin Tmax Step Xmin Xmax Ymin Ymax ParamCurve %ld voiced frames Pitch: Draw... Pitch: Draw 500.0 Pitch: Draw erb left Frequency range (ERB) 10.0 right Frequency range (ERB) Pitch: Draw logarithmic 50.0 Pitch: Draw mel left Frequency range (mel) right Frequency range (mel) Pitch: Draw semitones Range in semitones re 100 Hertz: -12.0 left Frequency range (st) right Frequency range (st) Cannot edit a Pitch from batch. Pitch: Formula x = time; col = frame; row = candidate (1 = current path); frequency (time, candidate) := self*2; Example: octave jump up Pitch: Get maximum Pitch: Get mean Pitch: Get mean absolute slope Mel Semitones ERB --undefined-- %.17g %s/s %.17g Semitones/s Pitch: Get minimum Pitch: Get quantile Pitch: Get standard deviation mel logHertz semitones Hz logHz Pitch: Get time of maximum Pitch: Get time of minimum Pitch: Get value at time... Pitch: Get value at time Pitch: Get value in frame... Pitch: Get value in frame Pitch Pitch: Smooth... Pitch: Smooth Bandwidth (Hertz) Bandwidth Pitch: Speckle Pitch: Speckle erb Pitch: Speckle logarithmic Pitch: Speckle mel 500 Pitch: Speckle semitones Pitch: subtract linear fit Hertz (logarithmic) Pitch: To Sound (sine) Cut voiceless stretches exactly at nearest zero crossings Pitch: To TextGrid... To TextGrid... Mary John bell Tier names bell Point tiers PitchTier & Pitch: Draw Line type for non-periodic intervals Normal Dotted Blank %s_stylized Sound & Pitch: To PointProcess (peaks) Include maxima Include minima Text alignment Use text styles Font size Tier TextGrid & Pitch: Draw 18 Font size (points) Left Centre Right TextGrid & Pitch: Draw erb TextGrid & Pitch: Draw logarithmic TextGrid & Pitch: Draw mel TextGrid & Pitch: Draw semitones Show boundaries TextGrid & Pitch: Draw separately TextGrid & Pitch: Draw separately erb TextGrid & Pitch: Draw separately logarithmic TextGrid & Pitch: Draw separately mel TextGrid & Pitch: Draw separately semitones TextGrid & Pitch: Speckle TextGrid & Pitch: Speckle erb TextGrid & Pitch: Speckle logarithmic TextGrid & Pitch: Speckle mel TextGrid & Pitch: Speckle semitones TextGrid & Pitch: Speckle separately TextGrid & Pitch: Speckle separately erb TextGrid & Pitch: Speckle separately logarithmic TextGrid & Pitch: Speckle separately mel TextGrid & Pitch: Speckle separately semitones Pitch & TextTier: To PitchTier... Pitch & TextTier to PitchTier Unvoiced strategy Zero Error Interpolate PitchTier: Add point... PitchTier: Add point 200 Pitch (Hz) Create empty PitchTier PitchTier: Down to TableOfReal PitchTier: Draw Minimum frequency (Hz) Minimum frequency Cannot edit a PitchTier from batch. PitchTier: Formula... PitchTier: Formula # self = the value of the colth point, in Hertz self * 2 ; one octave up PitchTier: Get mean (curve)... PitchTier: Get mean (curve) PitchTier: Get mean (points)... PitchTier: Get mean (points) PitchTier: Get standard deviation (curve)... PitchTier: Get standard deviation (curve) PitchTier: Get standard deviation (points)... PitchTier: Get standard deviation (points) PitchTier: Get value at time... PitchTier: Get value at time PitchTier: Get value at index... PitchTier: Get value at index PitchTier PitchTier: Interpolate quadratically 4 Number of points per parabola PitchTier: Shift frequencies Frequency shift PitchTier: Multiply frequencies 1.2 Factor PitchTier: Stylize... PitchTier: Stylize 4.0 Frequency resolution PitchTier: To Sound (phonation) Adaptation factor 0.05 Maximum period (s) 0.7 Open phase 0.03 Collision phase 3.0 Power 1 Power 2 Hum Maximum period PitchTier: To Sound (pulse train) Adaptation time PitchTier: To Sound (sine) To include a copy of a Sound in your PitchTier editor: select a PitchTier and a Sound, and click "Edit". Write PitchTier to spreadsheet PointProcess: Add point... PointProcess: Add point Create empty PointProcess... Create an empty PointProcess Finishing time (%.8g) should not be less than starting time (%.8g). Create Poisson process... Create Poisson process poisson Density (/s) Density difference PointProcess: Draw Cannot edit a PointProcess from batch. PointProcess: Fill 0.01 Period (s) Period PointProcess: Get interval... PointProcess: Get interval 1.3 Maximum period factor PointProcess: Get jitter (local)... PointProcess: Get jitter (local) PointProcess: Get jitter (local, absolute)... PointProcess: Get jitter (local, absolute) seconds PointProcess: Get jitter (rap)... PointProcess: Get jitter (rap) PointProcess: Get jitter (ppq5)... PointProcess: Get jitter (ppq5) PointProcess: Get jitter (ddp)... PointProcess: Get jitter (ddp) PointProcess: Get mean period... PointProcess: Get mean period PointProcess: Get stdev period... PointProcess: Get stdev period PointProcess: Get low index... PointProcess: Get low index PointProcess: Get high index... PointProcess: Get high index PointProcess: Get nearest index... PointProcess: Get nearest index PointProcess: Get number of periods... PointProcess: Get number of periods Get time PointProcess intersection PointProcess: Remove point... PointProcess: Remove point Index PointProcess: Remove point near... PointProcess: Remove point near PointProcess: Remove points... PointProcess: Remove points From index To index PointProcess: Remove points between... PointProcess: Remove points between 0.3 PointProcess: To PitchTier... PointProcess: To PitchTier Maximum interval (s) Maximum interval PointProcess: To TextGrid... PointProcess: To TextGrid (vuv)... Mean period (s) Mean period PointProcess: To Sound (phonation)... PointProcess: To Sound (phonation) PointProcess: To Sound (pulse train)... PointProcess: To Sound (pulse train) Adaptation time (s) union PointProcess: Up to IntensityTier... PointProcess: Up to IntensityTier 70.0 PointProcess: Up to PitchTier... PointProcess: Up to PitchTier 190.0 PointProcess: Up to TextTier... PointProcess: Up to TextTier PointProcess: Fill unvoiced parts 0.02000000001 Maximum voiced period (s) Maximum voiced period To include a copy of a Sound in your PointProcess editor: select a PointProcess and a Sound, and click "Edit". PointProcess & Sound: Get shimmer (local)... PointProcess & Sound: Get shimmer (local) PointProcess & Sound: Get shimmer (local, dB)... PointProcess & Sound: Get shimmer (local, dB) PointProcess & Sound: Get shimmer (apq3)... PointProcess & Sound: Get shimmer (apq3) PointProcess & Sound: Get shimmer (apq5)... PointProcess & Sound: Get shimmer (apq) PointProcess & Sound: Get shimmer (apq11)... PointProcess & Sound: Get shimmer (apq11) PointProcess & Sound: Get shimmer (dda)... PointProcess & Sound: Get shimmer (dda) PointProcess & Sound: To AmplitudeTier (period) PointProcess & Sound: To Ltas 5000 Band width (Hz) Band width PointProcess & Sound: To Ltas (harmonics Maximum harmonic Polygon: Draw Polygon: Draw circles Diameter (mm) Diameter Polygons: Draw connection Arrow 0.9 Relative length Polygon Polygon: Paint Colour (0-1 or name) Colour Polygon: Paint circles Polygon: Find shortest path Number of iterations Voice Voice report 75.0 left Pitch range (Hz) right Pitch range (Hz) Silence threshold 0.45 Voicing threshold right Pitch range left Pitch range To Sound manip TextGrid & Sound: Draw... TextGrid & Sound: Extract all intervals Preserve times dummy TextGrid & Sound: Extract non-empty intervals TextGrid & Sound: Extract intervals Label text Extract all intervals whose label... ...the text Spectrogram: Paint... Spectrogram: Paint Maximum (dB/Hz) Autoscaling 6.0 Pre-emphasis (dB/oct) Dynamic compression (0-1) Dynamic compression Pre-emphasis Spectrogram: Formula... Spectrogram: Formula Do for all times and frequencies: `x' is the time in seconds `y' is the frequency in Hertz `self' is the current value in Pa^2/Hz Replace all values with: self * exp (- x / 0.1) Spectrogram: Get power at (time, frequency) Hz) seconds and frequency = Pa2/Hz (at time = Spectrogram Spectrogram movie Spectrogram: To Sound Spectrogram: To Spectrum (slice) Time (seconds) Cannot view a Spectrogram from batch. Spectrum: Cepstral smoothing Bandwidth (Hz) Spectrum: Draw 0 (= auto) Minimum power (dB/Hz) Maximum power (dB/Hz) Maximum power Minimum power Spectrum: Draw (log freq) 10000.0 Cannot edit a Spectrum from batch. Spectrum: Formula... Spectrum: Formula `x' is the frequency in Hertz, `col' is the bin number; `y' = `row' is 1 (real part) or 2 (imaginary part) y := 1; row := 1; x := 0; for col := 1 to ncol do { self [1, col] := `formula' ; x := x + dx } y := 2; row := 2; x := 0; for col := 1 to ncol do { self [2, col] := `formula' ; x := x + dx } Spectrum: Get band density 200.0 Band floor (Hz) Band ceiling (Hz) Pa2 / Hz2 Band ceiling Band floor Spectrum: Get band density difference Low band floor (Hz) Low band ceiling (Hz) High band floor (Hz) 4000 High band ceiling (Hz) High band ceiling High band floor Low band ceiling Low band floor Spectrum: Get band energy Pa2 sec Spectrum: Get band energy difference Spectrum: Get bin from frequency Spectrum: Get central moment... Spectrum: Get central moment Moment 2.0 Hertz to the power 'moment' Spectrum: Get centre of gravity... Spectrum: Get centre of gravity Spectrum: Get frequency from bin Band number Spectrum: Get imaginary value in bin Bin number must not exceed number of bins. Spectrum: Get kurtosis... Spectrum: Get kurtosis Spectrum: Get real value in bin Spectrum: Get skewness... Spectrum: Get skewness Spectrum: Get standard deviation... Spectrum: Get standard deviation Spectrum Spectrum: LPC smoothing 5 Number of peaks Pre-emphasis from (Hz) Pre-emphasis from Spectrum: Filter (pass Hann band)... Spectrum: Filter (pass Hann band) Smoothing (Hz) Smoothing Spectrum: Filter (stop Hann band)... Spectrum: Filter (stop Hann band) Spectrum: To Excitation 0.1 Frequency resolution (Bark) Spectrum: To Formant (peaks) Warning: this simply picks peaks from 0 Hz up! Spectrum: To Long-term average spectrum SpellingChecker Add word to user dictionary New word Edit spelling checker -- Syntax -- Forbidden strings Check matching parentheses Separating characters Allow all parenthesized -- Capitals -- Allow all names Name prefixes Allow all abbreviations -- Capitalization -- Allow caps sentence-initially Allow caps after colon -- Word parts -- Allow all words containing Allow all words starting with Allow all words ending in Is word allowed? Word 1 (allowed) 0 (not allowed) Next not allowed word? Sentence: sentence Starting character Starting character should be 0 or positive. Starting character should not exceed end of sentence. To replace the checker's word list by the contents of a Strings object: 1. select the Strings; 2. convert to a WordList object; 3. select the SpellingChecker and the WordList; 4. choose Replace. Create Strings as file list... Create Strings as file list fileList Path: /people/Miep/*.aifc path \ %s%s*.wav %d Get string Strings Read Strings from raw text file Write Strings to text file Create Table table Read Table from table file Read Table from comma-separated file Read Table from tab-separated file appended Create TableOfReal Draw as numbers From row 0 (= all) To row Format decimal exponential free rational Precision Draw as numbers if... Condition: self <> 0 condition Draw table as squares From column To column Draw horizontal lines Draw left and right lines Draw top and bottom lines Draw vertical lines Extract column ranges Create a new TableOfReal from the following columns: 1 2 ranges To supply rising or falling ranges, use e.g. 2:6 or 5:3. %s_cols Extract columns where Extract all columns with at least one cell where: col mod 3 = 0 ; this example extracts every third column Extract column where label Extract all columns whose label... a Extract columns where row Extract all columns where row... ...is... ...the value %s_%ld_%ld Extract row ranges Create a new TableOfReal from the following rows: %s_rows Extract rows where Extract all rows with at least one cell where: row mod 3 = 0 ; this example extracts every third row Extract rows where column Extract all rows where column... Extract rows where label Extract all rows whose label... TableOfReal: Formula for row from 1 to nrow do for col from 1 to ncol do self [row, col] = ... if col = 5 then self + self [6] else self fi Get column index Column label Get column label Get column mean Column label does not exist. Get column standard deviation Get row index Row label Get row label Get value TableOfReal Insert column Insert row Read TableOfReal from headerless spreadsheet file Remove column Remove row Set column label Old label New label Set row label TableOfReal: Set value... Set value Row number too large. Column number too large. Sort rows by column Secondary column Sort rows by label Secondary sorting keys: Column1 Column2 Write TableOfReal to spreadsheet TextGrid: Count labels... Count labels Tier number Create TextGrid... Create TextGrid Hint: to label or segment an existing Sound, select that Sound and choose "To TextGrid...". All tier names Which of these are point tiers? Finishing time should be greater than starting time TextGrid: Draw TextGrid: Duplicate tier 1 (= at top) Position slice Cannot edit a TextGrid from batch. praat_Fon.c ilongSound != 0 ispellingChecker != 0 ilongSound != 0 && ispellingChecker != 0 TextGrid: Extract part %s_part Tier number (%ld) should not be larger than number of tiers (%ld). Tier should be interval tier. Tier should be point tier (TextTier). Interval number Interval number too large. Point number too large. TextGrid: Extract tier TextGrid: Get interval at time TextGrid: Get number of intervals TextGrid: Get starting point TextGrid: Get end point TextGrid: Get label of interval TextGrid: Get number of points TextGrid: Get tier name TextGrid: Get time of point TextGrid: Get label of point TextGrid TextGrid: Insert boundary TextGrid: Insert interval tier TextGrid: Insert point Text: text TextGrid: Insert point tier TextGrid: Is interval tier? 1 (yes, tier %ld is an interval tier) 0 (no, tier %ld is a point tier) You can draw a TextGrid together with a Pitch after selecting them both. TextGrid: Remove boundary at time TextGrid: Remove tier Sorry, I refuse to remove the last tier. To include a copy of a Sound in your TextGrid editor: select a TextGrid and a Sound, and click "Edit". You can draw a TextGrid together with a Sound after selecting them both. TextGrid: Scale times left New time domain (s) right New time domain (s) left New time domain right New time domain Duration of time domain must be positive. TextGrid: Set interval text Interval TextGrid: Set point text Point TextGrid: Shift times Time shift (s) Time shift Text file TextTier: Add point... TextTier: Add point TextTier: Down to TableOfReal Get points TextTier Read TextTier from Xwaves %ld frames Get frame number from time... Get frame number from time Get time from frame number... Get time from frame number AnyTier: Get high index from time... Get high index AnyTier: Get low index from time... Get low index AnyTier: Get nearest index from time... Get nearest index %ld points AnyTier: Remove point... Remove one point AnyTier: Remove point near... AnyTier: Remove points between... Remove points Transition Transition: Power... WordList Does word occur in list? Praat test Test 1000000 arg1 arg2 arg3 arg4 Object window Intro What's new? Types of objects Editors FAQ (Frequently Asked Questions) Acknowledgments Formulas Scripting Statistics Programming with Praat <?xml version="1.0"?> <!DOCTYPE ttext SYSTEM "ttext.dtd"> "Praat chronological TextGrid text file" Write to headerless spreadsheet file... Draw - Draw as numbers... Draw as squares... -- draw lines -- Draw vertical lines... Draw horizontal lines... Draw left and right lines... Draw top and bottom lines... Query - Get number of rows Get number of columns Get row label... Get column label... Get row index... Get column index... -- get value -- Get value... -- get statistics -- Get column mean (index)... Get column mean (label)... Get column stdev (index)... Get column stdev (label)... Modify - Set value... Sort by label... Sort by column... -- structure -- Remove row (index)... Remove column (index)... Insert row (index)... Insert column (index)... -- set -- Set row label (index)... Set row label (label)... Set column label (index)... Set column label (label)... Synthesize - Append Extract part - Extract row ranges... Extract rows where column... Extract rows where label... Extract rows where... Extract column ranges... Extract columns where row... Extract columns where label... Extract columns where... Extract - Extract row labels as Strings Extract column labels as Strings Convert - To Matrix Time domain Get starting time Get finishing time Get total duration Get duration Time sampling Get number of frames Get time step Get frame length Get frame duration Get time from frame... Get frame from time... Get number of points Get low index from time... Get high index from time... Get nearest index from time... Get time from index... Remove point... Remove point near... Remove points between... Psola Analysis StylPitch MarkTier Praat test... Praat Objects -- new numerics -- New Tables Create Table... Create TableOfReal... Tiers -- new tiers --- Create PitchTier... Create FormantTier... Create IntensityTier... Create AmplitudeTier... -- new textgrid -- -- read raw -- Read Read Matrix from raw text file... Read Matrix from LVS AP file... Read Strings from raw text file... Read TableOfReal from headerless spreadsheet file... Read Table from table file... Read Table from comma-separated file... Read Table from tab-separated file... -- read tier -- Read from special tier file... Read TextTier from Xwaves... Read IntervalTier from Xwaves... Praat Intro ApplicationHelp Help Frequently asked questions -- shell help -- Formulas tutorial Scripting tutorial Programming AmplitudeTier help Edit Edit with Sound? Query - Get shimmer (local)... Get shimmer (local_dB)... Get shimmer (apq3)... Get shimmer (apq5)... Get shimmer (apq11)... Get shimmer (dda)... Modify - Add point... Synthesize To Sound (pulse train)... Convert To IntensityTier... Down to PointProcess Cochleagram help Info Difference... Draw Paint... Modify Analyse To Excitation (slice)... Hack Distributions help Get probability (label)... -- get from two -- Get mean absolute difference... -- add -- Add Generate To Strings... To Strings (exact)... Learn To Transition... To Transition (noise)... DurationTier help & Manipulation: Replace? -- get content -- Get target duration... Excitation help Draw... To Formant... Get loudness Formant help Draw - Speckle... Draw tracks... Scatter plot... Get number of formants... Get minimum number of formants Get maximum number of formants Get value at time... Get bandwidth at time... -- get extreme -- Get minimum... Get time of minimum... Get maximum... Get time of maximum... -- get distribution -- Get quantile... Get quantile of bandwidth... Get mean... Get standard deviation... Sort Formula (frequencies)... Formula (bandwidths)... Track... Down to FormantTier To Matrix... FormantTier help Down Down to TableOfReal... Harmonicity help Get value in frame... Intensity help To IntensityTier (peaks) To IntensityTier (valleys) Down to IntensityTier Down to Matrix IntensityTier help To AmplitudeTier IntervalTier help Collect Into TextGrid Get starting points... Get centre points... Get end points... Down to TableOfReal (any) & Sound: To TextGrid? Ltas help Frequency domain Get lowest frequency Get highest frequency Frequency sampling Get number of bins Get number of bands Get bin width Get band width Get frequency from bin number... Get frequency from band... Get bin number from frequency... Get band from frequency... Get value at frequency... Get value in bin... Get value in band... Get frequency of minimum... Get frequency of maximum... Get slope... Get local peak height... Compute trend line... Subtract trend line... Combine Merge Average Manipulation help Play (PSOLA) Play (LPC) Get resynthesis (PSOLA) Get resynthesis (LPC) Extract original sound Extract pulses Extract pitch tier Extract duration tier Replace pitch tier? Replace duration tier? Write to text file without Sound... Write to binary file without Sound... Matrix help Write to matrix text file... Play movie Draw rows... Draw one contour... Draw contours... Paint image... Paint contours... Paint cells... Paint surface... Get lowest x Get highest x Get lowest y Get highest y -- get structure -- Get row distance Get column distance Get y of row... Get x of column... Get value in cell... Get value at xy... Get sum Eigen Power... Combine two Matrices - Merge (append rows) To ParamCurve Cast - To Cochleagram To Excitation To Harmonicity To Intensity To Ltas To Pitch To PointProcess To Polygon To Sound (slice)... To Spectrogram To TableOfReal To Spectrum To VocalTract PairDistribution help To Stringses... Get fraction correct (maximum likelihood) Get fraction correct (probability matching) Remove zero weights ParamCurve help Pitch help Play - Play pulses Draw - Draw logarithmic... Draw semitones... Draw mel... Draw erb... Speckle logarithmic... Speckle semitones... Speckle mel... Speckle erb... Count voiced frames -- get slope -- Get mean absolute slope... Get slope without octave jumps -- query two -- Count differences Annotate - -- to single tier -- To TextTier To IntervalTier To Sound (pulses) To Sound (hum) To Sound (sine)... Kill octave jumps Smooth... Subtract linear fit... Down to PitchTier Write to PitchTier spreadsheet file... PitchTier help Play sine Get value at index... Get mean (curve)... Get mean (points)... Get standard deviation (curve)... Get standard deviation (points)... -- stylize -- Stylize... Interpolate quadratically... -- modify frequencies -- Shift frequencies... Multiply frequencies... Synthesize - To Sound (phonation)... Convert - PointProcess help Edit - Edit alone Play - Play as pulse train -- script get -- Get low index... Get high index... Get nearest index... Get interval... -- periods -- Get number of periods... Get mean period... Get stdev period... Get jitter (local)... Get jitter (local, absolute)... Get jitter (rap)... Get jitter (ppq5)... Get jitter (ddp)... Remove points... -- voice -- Fill... Voice... Set calculus Union Intersection Difference To PitchTier... To TextGrid (vuv)... To Sound (hum)... Up to TextTier... Up to PitchTier... Up to IntensityTier... Polygon help Draw circles... Paint circles... Draw connection... Randomize Salesperson... Spectrogram help View Get power at... To Spectrum (slice)... To Sound... Spectrum help Draw (log freq)... Get frequency from bin... Get bin from frequency... Get real value in bin... Get imaginary value in bin... -- get energy -- Get band energy... Get band density... Get band energy difference... Get band density difference... -- get moments -- Get centre of gravity... Get skewness... Get kurtosis... Get central moment... Filter (pass Hann band)... Filter (stop Hann band)... To Excitation... To Formant (peaks)... To Ltas... To Ltas (1-to-1) Cepstral smoothing... LPC smoothing... To Sound (fft) Edit... Query Is word allowed... Next not allowed word... Add new word... Analyze Extract WordList Extract user dictionary Strings help Write to raw text file... Equal? Get number of strings Get string... Genericize To Distributions To WordList TableOfReal help TextGrid help Write to chronological text file... & Sound: Edit? & Sound: Draw? & Pitch: Draw? -- query tiers -- Get number of tiers Get tier name... Is interval tier... -- query intervals -- Get number of intervals... Get starting point... Get end point... Get label of interval... Get interval at time... -- query points -- Get number of points... Get time of point... Get label of point... -- query labels -- Count labels... Modify - Nativize Shift times... Shift to zero Scale times... -- modify intervals -- Insert boundary... Remove boundary at time... Set interval text... -- modify points -- Insert point... Set point text... -- modify tiers -- Insert interval tier... Insert point tier... Duplicate tier... Remove tier... Extract tier... Extract part... TextTier help Get points... Transition help Conflate Cast Has word... Up to SpellingChecker Multiply Map To FormantTier Filter Filter (no scale) Draw (phonetogram)... Speckle (phonetogram)... To IntensityTier Multiply... Start to centre... End to centre... To TextGrid Scale times Replace original sound Replace pulses Replace pitch tier Replace duration tier To Manipulation Get fraction correct... To PitchTier Voice report... To PointProcess (cc) To PointProcess (peaks)... -- draw separately -- Draw separately... Draw separately (logarithmic)... Draw separately (semitones)... Draw separately (mel)... Draw separately (erb)... Speckle separately... Speckle separately (logarithmic)... Speckle separately (semitones)... Speckle separately (mel)... Speckle separately (erb)... Transplant time domain To AmplitudeTier (point) To AmplitudeTier (period)... To Ltas (only harmonics)... Extract - Extract all intervals... Extract non-empty intervals... Extract intervals... Extract intervals where... 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Argument %Time (s) the time from which you want to get the point index. Return value This query returns the index of the point with the lowest time greater than or equal to %time.It is @undefined if there are no points. It is the number of points plus 1 (offright) if the specified time is greater than the time of the last point. A @query to ask the selected tier object (@DurationTier, @FormantTier, @IntensityTier, @PitchTier, @TextTier) which point is nearest to, but no later than, the specified time. This query returns the index of the point with the highest time less than or equal to %time.It is @undefined if there are no points. It is 0 (offleft) if the specified time is less than the time of the first point. A @query to ask the selected tier object (@DurationTier, @FormantTier, @IntensityTier, @PitchTier, @TextTier) which point is nearest to the specified time. the time near which you want to get the point index. This query returns the index of the point with the highest time less than or equal to %time.It is @undefined if there are no points. A command to remove one point from every selected time-based tier object (@DurationTier, @FormantTier, @IntensityTier, @PitchTier, @TextTier). %%Point number the index of the point you want to remove. Behaviour If %%point number% is 3, the third point counted from the start of the tier (if it exists) is removed from the tier. the time near which you want to remove a point. The point nearest to %time (if there is any point) is removed from the tier. A command to remove some points from every selected time-based tier object (@DurationTier, @FormantTier, @IntensityTier, @PitchTier, @TextTier). Arguments %%From time% (s), %%To time% (s) the times between which you want to remove all points. Any points between %tmin and %tmax (inclusive) are removed from the tier. One of the @@types of objects@ in P\s{RAAT}. It represents the excitation pattern of the basilar membrane in the inner ear (see @Excitation) as a function of time. A command for changing the data in all selected @Cochleagram objects. See the @Formulas tutorial for examples and explanations. A command in the @@New menu@ to create an empty @DurationTier object. The resulting object will have the specified name and time domain, but contain no duration points. To add some points to it, use @@DurationTier: Add point...@. Scripting example To create a tier 0.9 seconds long, with an deceleration around 0.6 seconds, you do: Create DurationTier... dur 0 0.9 Add point... 0.3 1 Add point... 0.6 2.3 Add point... 0.7 1 The result will look like The target duration will be the area under this curve, which is 0.9 + 1/2 \.c 1.3 \.c 0.4 = 1.16 seconds. A command in the @@New menu@ to create an empty @PointProcess. The newly created object is put in the list of objects. A command in the @@New menu@ to create an empty @IntensityTier object. The resulting object will have the specified name and time domain, but contain no formant points. To add some points to it, use @@IntensityTier: Add point...@. For an example, see @@Source-filter synthesis@. A command in the @@New menu@ to create a @Matrix with the specified sampling attributes, filled with values from a formula (see @@Matrix: Formula...@). A command to create a @PointProcess object that represents a Poisson process. A Poisson process is a stationary point process with a fixed density %\la, which means that there are, on the average, %\la events per second. Settings %%Starting time% (seconds) %t__%min_, the beginning of the time domain. %%Finishing time% (seconds) %t__%max_, the end of the time domain. %Density (Hertz) the average number of points per second. Algorithm First, the number of points %N in the time domain is determined. Its expectation value is %\la = (%t__%max_ \-- %t__%min_) \.c %density but its actual value is taken from the Poisson distribution: %p(%n) = (%%\la^n% / %n!) %e^^\--%\la Then, %N points are computed throughout the time domain, according to a uniform distribution: %p(%t) = 1 / (%t__%max_ \-- %t__%min_) for %t \e= [%t__%min_, %t__%max_] %p(%t) = 0 outside [%t__%min_, %t__%max_] A command in the @@New menu@ to create a @Matrix with the specified number of rows and columns, filled with values from a formula (see @@Matrix: Formula...@). A command to create a @Strings object from a list of file in a given directory. %%Path the directory name, with an optional wildcard for selecting files. The resulting Strings object will contain an alphabetical list of file names, without any preceding directory names. In contrast with what the restrictions in Praat, this object may contain zero strings. Usage First, you could specify a directory name only. On Unix, you would type ##/usr/people/miep/sounds# or ##/usr/people/miep/sounds/#. On Windows, ##C:\bsMiep\bsSounds# or ##C:\bsMiep\bsSounds\bs#. On Macintosh, ##Macintosh HD:Sounds# or ##Macintosh HD:Sounds:#. Any of these return a list of all the files in the specified directory. Secondly, you could specify a wildcard (a single asterisk) for the file names. To get a list of all the files whose names start with "hal" and end in ".aifc", type ##/usr/people/miep/sounds/hal*.aifc#, ##C:\bsMiep\bsSounds\bshal*.aifc#, or ##Macintosh HD:Sounds:hal*.aifc#. Script usage In a script, you can use this command to cycle through the files in a directory. For instance, to read in all the sound files in a specified directory, you could use the following script: directory\$ = "/usr/people/miep/sounds" Create Strings as file list... list 'directory\$ '/*.aifc numberOfFiles = Get number of strings for ifile to numberOfFiles select Strings list fileName\$ = Get string... ifile Read from file... 'directory\$ '/'fileName\$ ' endfor One of the @@types of objects@ in P\s{RAAT}. Inherits most actions from @TableOfReal. Actions @@Distributions: To Strings...@ A command to create a @Strings object from every selected @Distributions object. %%Column number the column (in the #Distributions object) that contains the distribution that you are interested in. Often the #Distributions object will only contain a single distribution, so this argument will often be 1. If the #Distributions object contains nine distributions, specify any number between 1 and 9. %%Number of strings the number of times a string will be drawn from the chosen distribution. This is the number of strings that the resulting @Strings object is going to contain. Every string in the resulting #Strings object will be a row label of the #Distributions object. The number in each row at the specified column will be considered the relative frequency of occurrence of that row. %#Example. Suppose we have the following #Distributions: File type = "ooTextFile" Object class = "Distributions" 2 (number of columns) "English" "French" (column labels) 3 (number of rows) "the" 108 1.5 "a" 58.1 33 "pour" 0.7 15.5 If you set %Column to 1 and %%Number of strings% to 1000, you will get a @Strings object with approximately 647 occurrences of "the", 348 occurrences of "a", and 4 occurrences of "pour". If you had set %Column to 2 ("French"), you would have gotten about 30 times "the", 660 times "a", and 310 times "pour". The actual numbers will vary because the choice of a string will not depend on previous choices. One of the @@types of objects@ in P\s{RAAT}. A DurationTier object contains a number of (%time, %duration) points, where %duration is to be interpreted as a relative duration (e.g. the duration of a manipulated sound as compared to the duration of the original). For instance, if your DurationTier contains two points, one with a duration value of 1.5 at a time of 0.5 seconds and one with a duration value of 0.6 at a time of 1.1 seconds, this is to be interpreted as a relative duration of 1.5 (i.e. a slowing down) for all original times before 0.5 seconds, a relative duration of 0.6 (i.e. a speeding up) for all original times after 1.1 seconds, and a linear interpolation between 0.5 and 1.1 seconds (e.g. a relative duration of 1.2 at 0.7 seconds, and of 0.9 at 0.9 seconds). See @@Intro 8.2. Manipulation of duration@ and @@Create DurationTier...@. A command to add a point to each selected @DurationTier. For an example, see @@Create DurationTier...@. the time at which a point is to be added. %%Relative duration the relative duration value of the requested new point. The tier is modified so that it contains the new point. If a point at the specified time was already present in the tier, nothing happens. A @query to the selected @DurationTier for the target duration of a specified time range. the start and end of the time range. If %fromTime or %toTime is outside the time domain of the Duration object, there will be . the target duration in seconds. One of the @editors in the Praat program, for viewing and editing a @DurationTier object. To create a DurationTierEditor window, select a DurationTier and click Edit. Many @@types of objects@ in P\s{RAAT} can be viewed and edited in their own windows. Editor windows \bu @SoundEditor \bu @LongSoundEditor \bu @TextGridEditor \bu @ManipulationEditor \bu @SpectrumEditor \bu @PitchEditor \bu @PointEditor \bu @PitchTierEditor \bu @IntensityTierEditor \bu @DurationTierEditor \bu #SpectrogramEditor \bu #ArtwordEditor \bu @OTGrammarEditor \bu (any type: @Inspect) How to open an editor for an object To open an editor window for an object in the list, select the object and choose #Edit (if the #Edit button exists, it is usually at the top of the @@Dynamic menu@). The name of the object will appear as the title of the editor window. Objects that cannot be modified (e.g. LongSound) have the command #View instead of #Edit. General behaviour Changes that you make to an object in its editor window will take effect immediately. For instance, you do not have close the editor window before saving the changed object to disk. If you @Remove an object that you are viewing or editing from the @@List of Objects@, the editor window will automatically disappear from the screen. All editors are independent windows: you can minimize and maximize them; if an editor window goes hiding behind another window, you can raise it by choosing the #Edit command again. If you rename an object that you are viewing or editing (with @@Rename...@), the title of the editor window immediately changes to the new name. Ways to control an editor window \bu @@Click \bu @@Shift-click \bu @@Drag \bu @@Shift-drag \bu @@Time selection \bu @@Keyboard shortcuts One of the @@types of objects@ in P\s{RAAT}. It represents the excitation pattern of the basilar membrane in the inner ear. Inside an Excitation object With @Inspect, you will see the following attributes. %xmin = 0 minimum place or frequency (Bark). %xmax = 25.6 Bark maximum place or frequency (Bark). %nx number of places or frequencies. %dx = 25.6 / %nx Place or frequency step (Bark). %x1 = %dx / 2 centre of first place or frequency band (Bark). %ymin = %ymax = %dy = %y__1_ = 1; %ny = 1 dummies. %z [1] intensity (sensation level) in phon. A command for changing the data in all selected @Excitation objects. A @query to ask the selected @Excitation object for its loudness. the loudness in sone units. The loudness is defined as \in%df 2^^(%e(%f) - 40 phon) / 10^ where %f is the frequency in Bark, and %e(%f) the excitation in phon. For our discrete Excitation object, the loudness is computed as \De%f \su 2^^(%e__%i_ - 40) / 10 where \De%f is the distance between the excitation channels (in Bark). A routine for converting frequency into basilar place, the inverse of @Excitation_barkToHertz. Syntax ##double Excitation_hertzToBark (double #%hertz##); Returns 7 \.c ln (%hertz / 650 + \Vr (1 + (%hertz / 650)^2)). A routine for converting basilar place into frequency, the inverse of @Excitation_hertzToBark. ##double Excitation_barkToHertz (double #%bark##); Returns 650 \.c sinh (%bark / 7). See @@Matrix: Formula...@ The way to select a frequency domain in the @SpectrumEditor. This works completely analogously to the @@time selection@ in other editors. A @query to the selected tier object (@PitchTier, @IntensityTier, @DurationTier). the area under the curve. Attributes the selected time domain. Values outside this domain are ignored. If %%To time% is not greater than %%From time%, the entire time domain of the tier is considered. The curve consists of a sequence of line segments. The contribution of the line segment from (%t__1_, %f__1_) to (%t__2_, %f__2_) to the area is 1/2 (%f__1_ + %f__2_) (%t__2_ \-- %t__1_) One of the @@types of objects@ in P\s{RAAT}. An Intensity object represents an intensity contour at linearly spaced time points %t__%i_ = %t__1_ + (%i \-- 1) %dt, with values in dB SPL, i.e. dB relative to 2\.c10^^-5^ Pascal, which is the normative auditory threshold for a 1000-Hz sine wave. A @query to the selected @Intensity object. the maximum value within the specified time domain, expressed in dB. %%Time range% (s) the time range (%t__1_, %t__2_). Values outside this range are ignored. If %t__1_ is not less than %t__2_, the entire time domain of the Intensity is considered. %%Interpolation the interpolation method (None, Parabolic, Cubic, Sinc) of the @@vector peak interpolation@. The standard is Parabolic because of the usual nonlinearity (logarithm) in the computation of intensity; sinc interpolation would be too stiff and may give unexpected results. the mean (in dB) of the intensity values of the frames within a specified time domain. %%Averaging method the units in which the averaging is performed. If the method is #energy, the returned dB value is based on the mean power (in Pa^2/s) between %t__1_ and %t__2_. If the method is #dB, the returned value is the mean of the intensity curve in dB. If the method is #sones, the returned value is in between these two, and based on averaging properties of the human ear. If the averaging method is #dB, the mean intensity between the times %t__1_ and %t__2_ is defined as 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ %x(%t) %dt where %x(%t) is the intensity as a function of time, in dB. If the method is #energy, the result is 10 log__10_ { 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ 10^^%x(%t)/10^ %dt } If the method is #sones, the result is 10 log__2_ { 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ 2^^%x(%t)/10^ %dt } After you do @@Sound: To Intensity...@, the mean intensity of the resulting #Intensity, if the averaging method is #energy, should be close to the mean SPL of the original #Sound, which can be found with #Info. the minimum value within a specified time domain, expressed in dB. the standard deviation (in dB) of the intensity values of the frames within a specified time domain. The standard deviation between the times %t__1_ and %t__2_ is defined as \Vr {1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ %dt (%x(%t) - %\mu)^2} where %x(%t) is the intensity (in dB) as a function of time, and %\mu its mean. For our discrete Intensity object, the standard deviation is approximated by \Vr {1/(%n-1) \su__%i=%m..%m+%n-1_ (%x__%i_ - %\mu)^2} where %n is the number of frames between %t__1_ and %t__2_. Note the "minus 1". the time (in seconds) associated with the maximum intensity within a specified time domain. the time range (%t__1_, %t__2_). Values outside this range are ignored, except for purposes of interpolation. If %t__1_ is not less than %t__2_, the entire time domain of the Intensity is considered. the time (in seconds) associated with the minimum intensity within a specified time domain. the intensity (in dB) at a specified time. If %time is outside the frames of the Intensity, the result is 0. the time at which the value is to be evaluated. the interpolation method, see @@vector value interpolation@. The standard is Cubic because of the usual nonlinearity (logarithm) in the computation of intensity; sinc interpolation would be too stiff and may give unexpected results. %%Frame number the frame whose value is to be looked up. the intensity value (in dB) in the specified frame. If the index is less than 1 or greater than the number of frames, the result is 0; otherwise, it is %z [1] [%%frame number%]. A command to convert each selected @Intensity object to an @IntensityTier. Every sample in the @Intensity object is copied to a point on the @IntensityTier. Postconditions Equal time domains: \bu %result. %xmin == %intensity. %xmin \bu %result. %xmax == %intensity. %xmax Equal number of points: \bu %result. %points. %size == %intensity. %nx For all points %i = 1 ... %intensity. %nx: Explicit times: \bu %result. %points. %item [%i]. %time == %intensity. %x1 + (%i \-- 1) * %intensity. %dx Equal number of points: \bu %result. %points. %item [%i]. %value == %intensity. %z [1] [%i] A command to copy information from an @Intensity, at times specified by a @TextTier, to points on an @IntensityTier. For all the times of the points in the TextTier, an intensity is computed from the information in the Intensity object, by linear interpolation. One of the @@types of objects@ in P\s{RAAT}. An IntensityTier object represents a time-stamped intensity contour, i.e., it contains a series of (%time, %intensity) points. The intensity values are in dB. For examples, see @@Source-filter synthesis@. IntensityTier commands Creation: From scratch: \bu @@Create IntensityTier... \bu @@IntensityTier: Add point... Copy from another object: \bu @@Intensity: To IntensityTier@: trivial copying of linearly spaced points. \bu @@Intensity & TextTier: To IntensityTier...@: copying interpolated values at specified points. \bu @@PointProcess: Up to IntensityTier...@: equal values at specified points. Viewing and editing: Conversion: \bu @@IntensityTier: Down to PointProcess@: copy times. Synthesis (see @@Source-filter synthesis@): \bu @@Sound & IntensityTier: Multiply@ Queries: \bu @@Get low index from time... \bu @@Get high index from time... \bu @@Get nearest index from time... Modification: \bu @@Remove point... \bu @@Remove point near... \bu @@Remove points between... \bu @@IntensityTier: Add point...@ A command to add a point to each selected @IntensityTier. %Intensity (dB) the intensity value of the requested new point. A command to degrade every selected @IntensityTier to a @PointProcess. The times of all the points are trivially copied, and so is the time domain. The intensity information is lost. One of the @editors in the Praat program, for viewing and editing an @IntensityTier object. To create a IntensityTierEditor window, select an IntensityTier and click Edit. A way to accelerate the control of @Editors in P\s{RAAT}. Purpose to choose a menu command with the keyboard. All of these commands can also be chosen from a menu. Command key When mentioning the %%Command key%, this manual refers to the key immediately to the left of the space bar. It is positioned in such a way that the most common keyboard shortcuts (Command-X: Cut, Command-C: Copy, Command-V: Paste, Command-Z: Undo, Command-Q: Quit, Command-W: Close) can be typed easily with one hand. On Macintosh, this key is labelled with an Apple. On SGI, this key is labelled #Alt. Option key When mentioning the %%Option key%, this manual refers to the key immediately to the left of the Command key. In Praat, this key is sometimes used together with the Command key for destructive actions that are the reverse of the actions invoked by using the Command key only. For instance, if Command-T means "add a target at the cursor position", Option-Command-T may mean "remove the selected targets". On Macintosh, this key may be labelled #Option or #Alt. On SGI, this key is labelled #Ctrl. With some commands in the @Query menu of the @SoundEditor and @TextGridEditor, you can write combined information about times, pitch values, formants, and intensities to the @@Info window@ and to a log file. A log file is a text file on disk. It consists of a number of similar lines, whose format you determine with the log settings in the Query menu. Every time you press F12 (or choose ##Log 1# from the Query menu, Praat writes a line to log file 1. If you press Shift-F12, Praat writes a line to log file 2. With the ##log settings# dialog, you determine the following: %%Log 1 to Info window this determines whether your log line will be written to the Info window or not. %%Log 1 to log file this determines whether your log line will be written to the log file or not. %%Log file 1 the name of the log file. On Windows, this has to be a complete path name, such as $$C:\bsWINDOWS\bsDESKTOP\bsPitch Log.txt$. On Unix and MacOS X, it can either be a complete path name, e.g. $$/home/mary/pitch_log$, or a home-relative name such as $$~/Desktop/Pitch log$. %%Log 1 format the format of the line that Praat will write. See below. The same goes for log file 2. The logging facility has been implemented in Praat especially for former users of Kay CSL, who have been used to doing it for years and like to continue doing it in Praat. Otherwise, you may prefer to use the @TextGridEditor to mark time points and run an automatic analysis afterwards. If you do want to use the logging facility, you typically start by deleting any old log file (by choosing ##Delete log file 1# or ##Delete log file 2#), if you want to re-use the file name. Otherwise, you can change the log file name (with ##Log settings...#). After this, you will move the cursor to various time locations and press F12 (or Shift-F12) each time, so that information about the current time will be written to the log file. Example 1: pitch logging Suppose you want to log the time of the cursor and the pitch value at the cursor. You could use the following log format: Time 'time:6' seconds, pitch 'f0:2' Hertz If you now click at 3.456789876 seconds, and the pitch happens to be 355.266 Hertz at that time, the following line will be appended to the log file and/or to the Info window: Time 3.456790 seconds, pitch 355.27 Hertz. The parts ":6" and ":2" denote the number of digits after the decimal point. If you leave them out, the values will be written with a precision of 17 digits. The words 'time' and 'f0' mean exactly the same as the result of the commands ##Get cursor# and ##Get pitch#. Therefore, if instead of setting a cursor line you selected a larger piece of the sound, 'time' will give the centre of the selection and 'f0' will give the mean pitch in the selection. Beware of the following pitfall: if your pitch units are not Hertz, but semitones, then 'f0' will give the result in semitones. A format as in this example will then be misleading. Example 2: formant logging Suppose you want to log the start and finish of the selection, its duration, and the mean values of the first three formants, all separated by tab stops for easy importation into Microsoft\re Excel\tm. You could use the following log format: 't1:4''tab\$ ''t2:4''tab\$ ''f1:0''tab\$ ''f2:0''tab\$ ''f3:0' You see that 't1' and 't2' are the start and finish of the selection, respectively, and that they are written with 4 digits after the decimal point. By using ":0", the three formant values are rounded to whole numbers in Hertz. The word 'tab\$ ' is the tab stop. Loggable values The following values can be logged: 'time': the time of the cursor, or the centre of the selection. 't1': the start of the selection ("B"). 't2': the end of the selection ("E"). 'dur': the duration of the selection. 'f0': the pitch at the cursor time, or the mean pitch in the selection. 'f1', 'f2', 'f3', 'f4', 'f5': the first/second/third/fourth/fifth formant at the cursor time, or the mean first/second/third/fourth/fifth formant in the selection. 'b1', 'b2', 'b3', 'b4', 'b5': the bandwidth of the first/second/third/fourth/fifth formant at the cursor time or at the centre of the selection. 'intensity': the intensity at the cursor time, or the mean intensity in the selection. 'tab\$ ': the tab stop. 'editor\$ ': the title of the editor window (i.e. the name of the visible Sound or TextGrid). More flexibility in logging You may sometimes require information in your log file that cannot be generated directly by the loggable values above. Suppose, for instance, that you want to log the values for F1 and F2-F1 at the points where you click. You could write the following script: f1 = Get first formant f2 = Get second formant f21 = f2 - f1 printline 'f1:0' 'f21:0' fileappend "D:\bsPraat logs\bsFormant log.txt" 'f1:0''tab\$ ''f21:0''newline\$ ' With this script, the information would be appended both to the Info window and to the file "Formant log.txt" on your desktop. You can make this script accessible with Option-F12 (or Command-F12) by saving the script and specifying the name of the script file in the ##Log script 3# (or #4) field in the ##Log settings...# dialog. These scripts may take arguments. Suppose, for instance, that you want to specify a vowel symbol as you press Option-F12. The following script will take care of that: form Save vowel and formants word Vowel a endform printline 'vowel\$ ' 'f1:0' 'f21:0' fileappend "~/Praat logs/Vowels and formants log" 'vowel\$ ''f1:0''tab\$ ''f21:0''newline\$ ' Beware of the following pitfall: because of the nature of scripts, you should not try to do this when you have two editor windows with the same name. I cannot predict which of the two windows will answer the #Get queries... One of the @@types of objects@ in P\s{RAAT}, for changing the pitch and duration contours of a sound. Inside a manipulation object With @Inspect, you will see the following attributes: %%timeStep% the time step (or %%frame length%) used in the pitch analysis. A common value is 0.010 seconds. %%minimumPitch% the minimum pitch frequency considered in the pitch analysis. A common value is 75 Hertz. %%maximumPitch% the maximum pitch frequency considered in the pitch analysis. A common value is 600 Hertz. A Manipulation object also contains the following smaller objects: 1. The original @Sound. 2. A @PointProcess representing glottal pulses. 3. A @PitchTier. 4. A @DurationTier. Analysis When a Manipulation object is created from a sound, the following steps are performed: 1. A pitch analysis is performed on the original sound, with the method of @@Sound: To Pitch...@. This uses the time step, minimum pitch, and maximum pitch parameters. 2. The information of the resulting pitch contour (frequency and voiced/unvoiced decisions) is used to posit glottal pulses where the original sound contains much energy. The method is the same as in @@Sound & Pitch: To PointProcess (cc)@. 3. The pitch contour is converted to a pitch tier with many points (targets), with the method of @@Pitch: To PitchTier@. 4. An empty @DurationTier is created. Resynthesis A Manipulation object can produce Sound input. This Sound can be computed in several ways: \bu @PSOLA: from original sound + pulses + pitch tier + duration tier; \bu #LPC: from LPC (from original sound) + pulses + pitch tier; \bu from the pulses only, as a pulse train or hummed; \bu from the pitch tier only, as a pulse train or hummed. A command to extract a copy of the duration information in each selected @Manipulation object into a new @DurationTier object. A command to copy the original sound in each selected @Manipulation object to a new @Sound object. A command to extract a copy of the pitch information in each selected @Manipulation object into a new @PitchTier object. A command to extract a copy of the vocal-pulse information in each selected @Manipulation object into a new @PointProcess object. A command to play each selected @Manipulation object, resynthesized with the @PSOLA method. A command to extract the sound from each selected @Manipulation object, resynthesized with the @PSOLA method. You can replace the duration tier that you see in your @Manipulation object with a separate @DurationTier object, for instance one that you extracted from another Manipulation or one that you created with @@Create DurationTier...@. To do this, select your Manipulation object together with the @DurationTier object and click ##Replace duration tier#. You can replace the pitch tier that you see in your @Manipulation object with a separate @PitchTier object, for instance one that you extracted from another Manipulation or one that you created with @@Create PitchTier...@. To do this, select your Manipulation object together with the @PitchTier object and click ##Replace pitch tier#. A command to replace the vocal-pulse information in the selected @Manipulation object with the selected @PointProcess object. A command to replace the original sound in the selected @Manipulation object with the selected @Sound object. One of the @Editors in P\s{RAAT}, for viewing and manipulating a @Manipulation object. Objects The editor shows: \bu The original @Sound. \bu The @PointProcess that represents the glottal %pulses. You can edit it for improving the pitch analysis. \bu A pitch contour based on the locations of the pulses, for comparison (drawn as grey dots). Changes shape if you edit the pulses. \bu The @PitchTier that determines the pitch contour of the resynthesized @Sound (drawn as blue circles). At the creation of the @Manipulation object, it is computed from the original pitch contour. You can manipulate it by simplifying it (i.e., removing targets), or by moving parts of it up and down, and back and forth. \bu A @DurationTier for manipulating the relative durations of the voiced parts of the sound. Playing To play (a part of) the %resynthesized sound (by any of the methods shown in the #Synth menu, like @PSOLA and #LPC), @click on any of the 1 to 8 buttons below and above the drawing area or use the Play commands from the View menu. To play the %original sound instead, use ##Shift-click#. Pulses To add: #click at the desired time location, and choose ##Add pulse at cursor# or type ##Command-p#. To remove: make a @@time selection@, and choose ##Remove pulse(s)# or type ##Option-Command-p#. If there is no selection, the pulse nearest to the cursor is removed. Pitch points To add one at a specified %%time and frequency%: #click at the desired time-frequency location, and choose ##Add pitch point at cursor# or type ##Command-t#. To add one at a specified %time only: #click at the desired time, and choose ##Add pitch point at time slice#. ManipulationEditor tries to compute the frequency from the intervals between the pulses, basically by a median-of-three method. make a @@time selection@, and choose ##Remove pitch point(s)# or type ##Option-Command-t#. If there is no selection, the pitch point nearest to the cursor is removed. To move %some: make a @@time selection@ (the points become red) and ##Shift-drag# the points across the window. You cannot drag them across adjacent points, or below 50 Hz, or above the maximum frequency. You can only drag them horizontally if the %%dragging strategy% is ##All# or ##Only horizontal#, and you can drag them vertically if the dragging strategy is not ##Only horizontal#. You can change the dragging strategy with ##Set pitch dragging strategy...# from the #Pitch menu. To move %one: @drag that point across the window. You can only drag it horizontally if the dragging strategy is not ##Only vertical#, and you can drag it vertically if the dragging strategy is not ##Only horizontal#. Duration points Work pretty much the same as pitch points. Stylization Before editing the Pitch points, you may want to reduce their number by choosing any of the #Stylize commands from the #Pitch menu. One of the @@types of objects@ in P\s{RAAT}. A Matrix object represents a function %z (%x, %y) on the domain [%x__%min_, %x__%max_] \xx [%y__%min_, %y__%max_]. The domain has been sampled in the %x and %y directions with constant sampling intervals (%dx and %dy) along each direction. The samples are thus %z [%i__%y_] [%i__%x_], %i__%x_ = 1 ... %n__%x_, %i__%y_ = 1 ... %n__%y_. The samples represent the function values %z (%x__1_ + (%ix - 1) %dx, %y__1_ + (%iy - 1) %dy). Matrix commands \bu @@Create Matrix... \bu @@Create simple Matrix... \bu @@Read from file... \bu @@Read Matrix from raw text file... \bu ##Read Matrix from LVS AP file... Drawing: \bu ##Matrix: Draw rows... \bu ##Matrix: Draw contours... \bu ##Matrix: Paint contours... \bu ##Matrix: Paint cells... \bu ##Matrix: Scatter plot... \bu @@Matrix: Draw as squares... \bu ##Matrix: Draw value distribution... \bu ##Matrix: Paint surface... \bu @@Matrix: Formula... \bu ##Matrix: Scale... Inside a Matrix object %xmin, %xmax \>_ %xmin %x domain. %nx \>_ 1 number of columns. %dx > 0.0 distance between columns. %x1 %x value associated with first column. %ymin, %ymax \>_ %ymin %y domain. %ny \>_ 1 number of rows. %dy > 0.0 distance between rows. %y1 %y value associated with first row. %z [1..%ny] [1..%nx] The sample values. After creation of the #Matrix, %xmin, %xmax, %ymin, %ymax, %nx, %ny, %dx, %dy, %x1, and %y1 do not usually change. The contents of %z do. Normally, you will want %xmin \<_ %x1 and %xmax \>_ %x1 + (%nx - 1) %dx. Example: simple matrix If a simple matrix has %x equal to column number and %y equal to row number, it has the following attributes: %xmin = 1; %xmax = %nx; %dx = 1; %x1 = 1; %ymin = 1; %ymax = %ny; %dy = 1; %y1 = 1; Example: sampled signal If the matrix represents a sampled signal of 1 second duration with a sampling frequency of 10 kHz, it has the following attributes: %xmin = 0.0; %xmax = 1.0; %nx = 10000 ; %dx = 1.0\.c10^^-4^; %x1 = 0.5\.c10^^-4^; %ymin = 1; %ymax = 1; %ny = 1; %dy = 1; %y1 = 1; Example: complex signal If the matrix represents a complex spectrum derived with an @FFT from the sound of example 2, it has the following attributes: %xmin = 0.0; %xmax = 5000.0; %nx = 8193 ; %dx = 5000.0 / 8192; %x1 = 0.0; %ny = 2 (real and imaginary part); %ymin = 1 (first row, real part); %ymax = 2 (second row, imaginary part); %dy = 1; %y1 = 1; (so that %y is equal to row number) A command to draw a @Matrix object into the @@Picture window@. %Xmin, %Xmax the windowing domain in the %x direction. Elements outside will not be drawn. %Autowindowing: if (%Xmin \>_ %Xmax), the entire %x domain [%x__%min_, %x__%max_] of the Matrix is used. %Ymin, %Ymax the windowing domain in the %y direction. Elements outside will not be drawn. %Autowindowing: if (%Ymin \>_ %Ymax), the entire %y domain [%y__%min_, %y__%max_] of the Matrix is used. %Garnish determines whether axes are drawn around the picture. Turn this button off if you prefer to garnish your picture by yourself with the @Margins menu. For every element of the Matrix inside the specified windowing domain, an opaque white or black rectangle is painted (white if the value of the element is positive, black if it is negative), surrounded by a thin black box. The %area of the rectangle is proportional to the value of the element. Trick If you prefer the %sides of the rectangle (instead of the area) to be proportional to the value of the element, you can use the formula "$$self\^ 2$" before drawing (see @@Matrix: Formula...@). A command for changing the data in all selected @Matrix objects. A command to draw the contents of a @Matrix to the @@Picture window@. Every cell of the matrix is drawn as a rectangle filled with a grey value between white (if the content of the cell is small) and black (if the content is large). A command to change the value of one cell in each selected @Matrix object. %%Row number the number of the row of the cell whose value you want to change. the number of the column of the cell whose value you want to change. %%New value the value that you want the specified cell to have. A command to convert every selected @Matrix to a @TableOfReal. This command is available from the #Cast menu. The resulting TableOfReal has the same number of rows and columns as the original Matrix, and the same data in the cells. However, it does not yet have any row or column labels; you can add those with some commands from the TableOfReal #Modify menu. The title of a submenu of the @@dynamic menu@ for many object types. This submenu usually collects all the commands that can change the selected object. One of the @@types of objects@ in P\s{RAAT}. A PairDistribution object represents the relative probabilities with which the specified pairs of strings occur. Class description ##struct-list# pairs a list of relative string-pair probabilities. Each element consists of: #string %string1 the first string. #string %string2 the second string. #real %weight the relative probability associated with the string pair. This value cannot be negative. A command to generate a number of string pairs from the selected @PairDistribution object. This command will create two aligned @Strings objects of equal size. %Number (standard: 1000) the number of the strings in either resulting Strings object. %%Name of first Strings% (standard: "input") the name of the resulting Strings object associated with the first string of each pair. %%Name of second Strings% (standard: "output") the name of the resulting Strings object associated with the second string of each pair. Example Suppose the PairDistribution contains the following: 4 pairs "at+ma" "atma" 100 "at+ma" "apma" 0 "an+pa" "anpa" 20 "an+pa" "ampa" 80 The resulting Strings object "input" may then contain: at+ma, an+pa, an+pa, at+ma, at+ma, an+pa, an+pa, an+pa, an+pa, at+ma, ... The Strings object "output" may then contain: atma, ampa, ampa, atma, atma, ampa, anpa, ampa, ampa, atma, ... An object of class #ParamCurve represents a sequence of time-stamped points (%x (%%t__i_), %y (%%t__i_)) in a two-dimensional space. One of the @Editors in P\s{RAAT}, for viewing and manipulating a @PointProcess object, which is optionally shown together with a @Sound object. \bu The @Sound, if you selected a Sound object together with the PointProcess object before you clicked "Edit". \bu The @PointProcess; vertical blue lines represent the points. To play (a part of) the %resynthesized sound (pulse train): @click on any of the 8 buttons below and above the drawing area, or choose a Play command from the View menu. To play the %original sound instead, use @@Shift-click@. Adding a point @Click at the desired time location, and choose "Add point at cursor" or type ##Command-P#. Removing points To remove one or more points, make a @@time selection@ and choose ##Remove point(s)# from the ##Point# menu. If there is no selection, the point nearest to the cursor is removed. A PointProcess object represents a %%point process%, which is a sequence of %points %t__%i_ in time, defined on a domain [%t__%min_, %t__%max_]. The index %i runs from 1 to the number of points. The points are sorted by time, i.e. %t__%i+1_ > %t__%i_. PointProcess commands Creation from scratch: \bu @@Create empty PointProcess...@ \bu @@Create Poisson process...@ Creation of a pulse train from a pitch contour: \bu @@PitchTier: To PointProcess@: area-1 along entire time domain. \bu @@Pitch: To PointProcess@: same, but excludes voiceless intervals. \bu @@Sound & Pitch: To PointProcess (cc)@: "pitch-synchronous": near locations of high amplitude. \bu @@Sound & Pitch: To PointProcess (peaks)...@: "pitch-synchronous": near locations of high amplitude. \bu @@Sound: To PointProcess (periodic, cc)...@: near locations of high amplitude. \bu @@Sound: To PointProcess (periodic, peaks)...@: near locations of high amplitude. Creation from converting another object: \bu ##Matrix: To PointProcess \bu @@TextTier: Down to PointProcess@ \bu @@PitchTier: Down to PointProcess@ \bu @@IntensityTier: Down to PointProcess@ Hearing: \bu @@PointProcess: Play@: pulse train. \bu @@PointProcess: Hum@: pulse train with formants. \bu @@PointProcess: Draw...@ Editing: \bu ##PointProcess: Edit#: invokes a @PointEditor. \bu ##PointProcess & Sound: Edit#: invokes a @PointEditor. \bu Inside a @ManipulationEditor. \bu @@PointProcess: Get jitter (local)...@: periodic jitter. \bu @@PointProcess: Get jitter (local, absolute)...@: periodic jitter. \bu @@PointProcess: Get jitter (rap)...@: periodic jitter. \bu @@PointProcess: Get jitter (ppq5)...@: periodic jitter. \bu @@PointProcess: Get jitter (ddp)...@: periodic jitter. \bu @@PointProcess: Get low index...@: index of nearest point not after specified time. \bu @@PointProcess: Get high index...@: index of nearest point not before specified time. \bu @@PointProcess: Get nearest index...@: index of point nearest to specified time. \bu @@PointProcess: Get interval...@: duration of interval around specified time. Set calculations: \bu @@PointProcesses: Union@: the union of two point processes. \bu @@PointProcesses: Intersection@: the intersection of two point processes. \bu @@PointProcesses: Difference@: the difference of two point processes. \bu @@PointProcess: Add point...@: at a specified time. \bu @@PointProcess: Remove point...@: at specified index. \bu @@PointProcess: Remove point near...@: near specified time. \bu @@PointProcess: Remove points...@: between specified indices. \bu @@PointProcess: Remove points between...@: between specified times. Analysis: \bu @@PointProcess: To PitchTier...@: pitch values in interval centres. \bu ##PointProcess & Sound: To Manipulation Synthesis: \bu @@PointProcess: To Sound (pulse train)...@ \bu @@PointProcess: To Sound (hum)...@ \bu ##PointProcess: To Matrix \bu @@PointProcess: Up to TextTier... \bu @@PointProcess: Up to PitchTier... \bu @@PointProcess: Up to IntensityTier... A command to add a point to each selected @PointProcess. The point process is modified so that it contains the new point. If a point at the specified time was already present in the point process, nothing happens. A command to compute the difference of two selected @PointProcess objects. The resulting #PointProcess will contain only those points of the first selected original point process that do not occur in the second. The time domain of the resulting point process is equal to the time domain of the first original point process. A command to draw every selected @PointProcess into the @@Picture window@. A @query to the selected @PointProcess object. the index of the nearest point at or after the specified time, 0 if the point process contains no points, or a number higher than the number of points if the specified time is after the last point. %Time (seconds) the time from which a point is looked for. the duration of the interval around a specified time. if the point process contains no points or if the specified time falls before the first point or not before the last point, the value is @undefined. Otherwise, the result is the distance between the nearest points to the left and to the right of the specified time. If the point process happens to contain a point at exactly the specified time, the duration of the interval following this point is returned. the time around which a point is looked for. A @query to the selected @PointProcess object. See @@Voice 2. Jitter@. the periodic jitter, which is defined as the relative mean absolute third-order difference of the point process (= the second-order difference of the interval process): %jitter = \su__%i=2_^^%N-1^ |2%T__%i_ - %T__%i-1_ - %T__%i+1_| / \su__%i=2_^^%N-1^ %T__%i_ where %T__%i_ is the %%i%th interval and %N is the number of intervals. If no sequences of three intervals can be found whose durations are between %%Shortest period% and %%Longest period%, the result is @undefined. %%Shortest period% (seconds) the shortest possible interval that will be considered. For intervals %T__%i_ shorter than this, the (%i-1)st, %%i%th, and (%i+1)st terms in the formula are taken as zero. This argument will normally be very small, say 0.1 ms. %%Longest period% (seconds) the shortest possible interval that will be considered. For intervals %T__%i_ longer than this, the (%i-1)st, %%i%th, and (%i+1)st terms in the formula are taken as zero. For example, if the minimum frequency of periodicity is 50 Hz, set this argument to 20 milliseconds; intervals longer than that will be considered voiceless. The periodic jitter can be used as a measure of voice quality. See @@Voice 2. Jitter@. the index of the nearest point before or at the specified time, or 0 if the point process contains no points or the specified time is before the first point. the index of the point nearest to the specified time, or 0 if the point process contains no points. A command to hear a @PointProcess. A @Sound is created with the algorithm described at @@PointProcess: To Sound (hum)...@. This sound is then played. A command to merge two selected @PointProcess objects into one. The resulting #PointProcess will contain only those points that occur in both original point processes. The time domain of the resulting point process is the intersection of the time domains of the original point processes. A @Sound is created with the algorithm described at @@PointProcess: To Sound (pulse train)...@. A command to remove a point from every selected @PointProcess. %Index the index of the point that is to be removed. Does nothing if %index is less than 1 or greater than the number of points %nt in the point process. Otherwise, one point is removed (e.g., if %index is 3, the third point is removed), and the other points stay the same. the time around which a point is to be removed. Does nothing if there are no points in the point process. Otherwise, the point nearest to %time is removed, and the other points stay the same. A command to remove a range of points from every selected @PointProcess. %%From index% (\>_ 1) the first index of the range of points that are to be removed. %%To index% the last index of the range of points that are to be removed. All points that originally fell in the range [%fromIndex, %toIndex] are removed, and the other points stay the same. %%From time% (seconds) the start of the domain from which all points are to be removed. %%To time% (seconds) the end of the domain from which all points are to be removed. All points that originally fell in the domain [%fromTime, %toTime], including the edges, are removed, and the other points stay the same. A command to convert every selected @PointProcess into a @Sound. A @Sound is created with the algorithm described at @@PointProcess: To Sound (pulse train)...@. This sound is then run through a sequence of second-order filters that represent five formants. A glottal waveform is generated at every point in the point process. Its shape depends on the settings %power1 and %power2 according to the formula %U(%x) = %x^^%power1^ - %x^^%power2^ where %x is a normalized time that runs from 0 to 1 and %U(%x) is the normalized glottal flow in arbitrary units (the real unit is m^3/s). If %power1 = 2.0 and %power2 = 3.0, the glottal flow shape is that proposed by @@Rosenberg (1971)@, upon which for instance the Klatt synthesizer is based (@@Klatt & Klatt (1990)@): Axes... 0 1 -0.1 1 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes no Draw inner box Draw function... 0 1 1000 (x^2-x^3)*6 Text bottom... yes Time (normalized) Text left... yes Glottal flow If %power1 = 3.0 and %power2 = 4.0, the glottal flow shape starts somewhat smoother, reflecting the idea that the glottis opens like a zipper: Axes... 0 1 -0.1 1 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes no Draw inner box Draw function... 0 1 1000 (x^3-x^4)*8 Text bottom... yes Time (normalized) Text left... yes Glottal flow For the generation of speech sounds, we do not take the glottal flow itself, but rather its derivative (this takes into account the influence of raditaion at the lips). The glottal flow derivative is given by %dU(%x)%dx = %power1 %x^^(%power1-1)^ - %power2 %x^^(%power2-1)^ The flow derivative clearly shows the influence of the smoothing mentioned above. The unsmoothed curve, with %power1 = 2.0 and %power2 = 3.0, looks like: Axes... 0 1 -9 3 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes no Draw inner box Draw function... 0 1 1000 (2*x-3*x^2)*6 Text bottom... yes Time (normalized) Text left... yes Glottal flow derivative Unlike the unsmoothed curve, the smoothed curve, with %power1 = 3.0 and %power2 = 4.0, starts out horizontally: Axes... 0 1 -9 3 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes no Draw inner box Draw function... 0 1 1000 (3*x^2-4*x^3)*8 Text bottom... yes Time (normalized) Text left... yes Glottal flow derivative Aother setting is the %%open phase%. If it is 0.70, the glottis will be open during 70 percent of a period. Suppose that the PointProcess has a pulse at time 0, at time 1, at time 2, and so on. The pulses at times 1 and 2 will then be turned into glottal flows starting at times 0.30 and 1.30: Axes... 0 2 -0.1 1 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes yes One mark bottom... 2 yes yes no Draw inner box Draw function... 0 0.3 2 0 Draw function... 0.3 1.3 300 if x<1 then (((x-0.3)/0.7)^3-((x-0.3)/0.7)^4)*8 else 0 fi Draw function... 1.3 2 300 (((x-1.3)/0.7)^3-((x-1.3)/0.7)^4)*8 Text bottom... yes Time (normalized) Text left... yes Glottal flow Axes... 0 2 -9 3 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes yes One mark bottom... 2 yes yes no Draw inner box Draw function... 0 0.3 2 0 Draw function... 0.3 1.3 300 if x<1 then (3*((x-0.3)/0.7)^2-4*((x-0.3)/0.7)^3)*8 else 0 fi Draw function... 1.3 2 300 (3*((x-1.3)/0.7)^2-4*((x-1.3)/0.7)^3)*8 Text bottom... yes Time (normalized) Text left... yes Glottal flow derivative The final setting that influences the shape of the glottal flow is the %%collision phase%. If it is 0.03, for instance, the glottal flow derivative will not go abruptly to 0 at a pulse, but will instead decay by a factor of %e (\~~ 2.7183) every 3 percent of a period. In order to keep the glottal flow curve smooth (and the derivative continuous), the basic shape discussed above has to be shifted slightly to the right and truncated at the time of the pulse, to be replaced there with the exponential decay curve; this also makes sure that the average of the derivative stays zero, as it was above (i.e. the area under the positive part of the curve equals the area above the negative part). This is what the curves look like if %power1 = 3.0, %power2 = 4.0, %openPhase = 0.70 and %collisionPhase = 0.03: Axes... 0 2 -0.1 1 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes yes One mark bottom... 2 yes yes no Draw inner box xo = 0.32646 g1 = 0.269422 Draw function... 0 xo 300 g1 * exp(-x/0.03) Draw function... xo 1 300 (((x-xo)/0.7)^3-((x-xo)/0.7)^4)*8 + g1 * exp(-x/0.03) Draw function... 1 1+xo 300 g1 * exp(-(x-1)/0.03) Draw function... 1+xo 2 300 (((x-1-xo)/0.7)^3-((x-1-xo)/0.7)^4)*8 + g1 * exp(-(x-1)/0.03) Text bottom... yes Time (normalized) Text left... yes Glottal flow Axes... 0 2 -9 3 One mark left... 0 yes yes yes One mark bottom... 0 yes yes no One mark bottom... 1 yes yes yes One mark bottom... 2 yes yes no Draw inner box xo = 0.32646 g1 = -8.980736 * 0.7 Draw function... 0 xo 300 g1 * exp(-x/0.03) Draw function... xo 1 300 (3*((x-xo)/0.7)^2-4*((x-xo)/0.7)^3)*8 + g1 * exp(-x/0.03) Draw function... 1 1+xo 300 g1 * exp(-(x-1)/0.03) Draw function... 1+xo 2 300 (3*((x-1-xo)/0.7)^2-4*((x-1-xo)/0.7)^3)*8 + g1 * exp(-(x-1)/0.03) Text bottom... yes Time (normalized) Text left... yes Glottal flow derivative These curves have moved 2.646 percent of a period to the right. At time 1, the glottal flow curve turns from a convex polynomial into a concave exponential, and the derivative still has its minimum there. %%Sampling frequency the sampling frequency of the resulting Sound object, e.g. 22050 Hertz. %%Adaptation factor the factor by which a pulse height will be multiplied if the pulse time is not within %maximumPeriod from the previous pulse, and by which a pulse height will again be multiplied if the previous pulse time is not within %maximumPeriod from the pre-previous pulse. This factor is against abrupt starts of the pulse train after silences, and is 1.0 if you do want abrupt starts after silences. %%Maximum period the minimal period that will be considered a silence, e.g. 0.05 seconds. Example: if %adaptationFactor is 0.6, and %adaptationTime is 0.02 s, then the heights of the first two pulses after silences of at least 20 ms will be multiplied by 0.36 and 0.6, respectively. A pulse is generated at every point in the point process. This pulse is filtered at the Nyquist frequency of the resulting #Sound by converting it into a sampled #sinc function. the factor by which a pulse height will be multiplied if the pulse time is not within %adaptationTime from the pre-previous pulse, and by which a pulse height will again be multiplied if the pulse time is not within %adaptationTime from the previous pulse. This factor is against abrupt starts of the pulse train after silences, and is 1.0 if you do want abrupt starts after silences. %%Adaptation time the minimal period that will be considered a silence, e.g. 0.05 seconds. %%Interpolation depth the extent of the sinc function to the left and to the right of the peak, e.g. 2000 samples. Example: if %adaptationFactor is 0.6, and %adaptationTime is 0.02 s, then the heights of the first two pulses after silences of at least 20 ms will be multiplied by 0.36 and 0.6, respectively. The resulting #PointProcess will contain all the points of the two original point processes, sorted by time. Points that occur in both original point processes, will occur only once in the resulting point process. The time domain of the resulting point process is the union of the time domains of the original point processes. A command to promote every selected @PointProcess to an @IntensityTier. the intensity that will be associated with every point. The times of all the points are trivially copied, and so is the time domain. The intensity information will be the same for every point. A command to promote every selected @PointProcess to a @PitchTier. %Frequency (Hz) the pitch frequency that will be associated with every point. The times of all the points are trivially copied, and so is the time domain. The pitch information will be the same for every point. A Polygon object represents a sequence of points (%%x__i_, %%y__i_) in a two-dimensional space. A command to read a @Matrix object from a file on disk. File format The file should contain each row of the matrix on a separate line. Within each row, the elements must be separated by spaces or tabs. For instance, the following text file will be read as a Matrix with three rows and four columns: 0.19 3 245 123 18e-6 -3e18 0 0.0 1.5 2.5 3.5 4.5 The resulting Matrix will have the same domain and sampling as Matrices created with ##Create simple Matrix...#. In the above example, this means that the Matrix will have %x__%min_ = 0.5, %x__%max_ = 4.5, %n__%x_ = 4, %dx = 1.0, %x__1_ = 1.0, %y__%min_ = 0.5, %y__%max_ = 3.5, %n__%y_ = 3, %dy = 1.0, %y__1_ = 1.0. A command to read a @Strings object from a simple text file. Each line is read as a separate string. See @Strings for an example. A command to create an @Intensity object from every selected @Sound. %%Minimum pitch% (Hz) specifies the minimum periodicity frequency in your signal. If you set the minimum pitch too high, you will end up with a pitch-synchronous intensity modulation. If you set it too low, your intensity contour may appear smeared, so you should set it as high as allowed by the signal if you want a sharp contour. %%Time step% (s) the time step of the resulting intensity contour. If you set it to zero, the time step is computed as one quarter of the effective window length, i.e. as 0.8 / (%minimum_pitch). %%Subtract mean See @@Intro 6.2. Configuring the intensity contour@. The values in the sound are first squared, then convolved with a Gaussian analysis window (Kaiser-20; sidelobes below -190 dB). The effective duration of this analysis window is 3.2 / (%minimum_pitch), which will guarantee that a periodic signal is analysed as having a pitch-synchronous intensity ripple not greater than our 4-byte floating-point precision (i.e., < 0.00001 dB). A command to create a new Sound from the selected @Sound and @Intensity objects. The resulting Sound equals the original sound, multiplied by a linear interpolation of the intensity. Afterwards, the resulting Sound is scaled so that its maximum absolute amplitude is 0.9. One of the @@types of objects@ in P\s{RAAT}. Represents an ordered list of strings. Creation The difficult way is to create a #Strings object from a generic Praat text file: "ooTextFile" "Strings" 5 ! number of strings "Hello" "Goodbye" "Auf wiedersehen" "Tsch\bsu\" \" ss" "Arrivederci" In this example, we see that a double quote within a string should be written twice; the fourth string will therefore be read as ##Tsch\bsu\" ss#, and will be shown in info messages or in graphical text as ##Tsch\u"ss# (see @@special symbols@). This file can be read simply with the generic @@Read from file...@ command from the Read menu. An easier way is to use the special command @@Read Strings from raw text file...@. The file can then simply look like this: Hello Goodbye Auf wiedersehen Tsch\bsu\" ss Arrivederci In this example, all the strings are in the generic system-independent ASCII format that is used everywhere in Praat (messages, graphical text) for @@special symbols@. You could also have supplied the strings in a native format, which is ISO-Latin1 encoding on Unix and Windows computers, or Mac encoding on Macintosh computers. The file would then have simply looked like: Tsch\u"ss To convert this into the generic system-independent ASCII format, use the #Genericize command. You can also create a #Strings object from a directory listing or from some other objects: \bu @@Create Strings as file list... \bu @@Distributions: To Strings...@ \bu @@OTGrammar: Generate inputs...@ \bu @@OTGrammar & Strings: Inputs to outputs...@ A command to analyse each selected @Strings object into a @Distributions object. The resulting #Distributions will collect the occurrences of every string in the #Strings object, and put the number of occurrences in its first and only column. We start from the following #Strings: 6 (number of strings) "hallo" "dag allemaal" "tot morgen" This will give us the following #Distributions: 1 (number of columns) "" (no column name) "hallo" 3 "dag allemaal" 1 "tot morgen" 2 One of the @@types of objects@ in P\s{RAAT}. See the @Statistics tutorial. A TableOfReal object contains a number of %cells. Each cell belongs to a %row and a %column. For instance, a TableOfReal with 10 rows and 3 columns has 30 cells. Each row and each column may be labeled with a %title. Creating a TableOfReal from data in a text file Suppose you have F1 and F2 data for vowels. You can create a simple text file like the following: "ooTextFile" ! The line by which Praat can recognize your file "TableOfReal" ! The line that tells Praat about the contents 2 "F1" "F2" ! Number of columns, and column labels 3 ! Number of rows "a" 800 1100 ! Row label (vowel), F1 value, F2 value "i" 280 2800 ! Row label (vowel), F1 value, F2 value "u" 260 560 ! Row label (vowel), F1 value, F2 value Praat is rather forgiving about the use of spaces, tabs, and newlines. See @@Write to text file...@ for general information. You will often have your data in a file with a self-describing format, i.e. in which the number of values on a line equals the number of columns of the table: 800 1100 280 2800 260 560 Such a file can be read with @@Read Matrix from raw text file...@. This creates a Matrix object, which can be cast to a TableOfReal object by @@Matrix: To TableOfReal@. The resulting TableOfReal does not have any row or column labels yet. You could add column labels with: Set column label (index)... 1 F1 Set column label (index)... 2 F2 Of course, if the row labels contain crucial information, and the number of rows is large, this is not a feasible method. A command to change the value of one table cell in each selected @TableOfReal object. Get high index from time... ppgb Get low index from time... Get nearest index from time... Remove point... Remove point near... Remove points between... Cochleagram Cochleagram: Formula... Create DurationTier... Create empty PointProcess... Create IntensityTier... Create Matrix... Create Poisson process... Create simple Matrix... Create Strings as file list... Distributions Distributions: To Strings... DurationTier DurationTier: Add point... DurationTier: Get target duration... DurationTierEditor Editors Excitation Excitation: Formula... Excitation: Get loudness Excitation_hertzToBark Excitation_barkToHertz Formula... Frequency selection Get area... Intensity Intensity: Get maximum... Intensity: Get mean... Intensity: Get minimum... Intensity: Get standard deviation... Intensity: Get time of maximum... Intensity: Get time of minimum... Intensity: Get value at time... Intensity: Get value in frame... Intensity: To IntensityTier Intensity & TextTier: To IntensityTier... IntensityTier IntensityTier: Add point... IntensityTier: Down to PointProcess IntensityTierEditor Keyboard shortcuts Log files Manipulation Manipulation: Extract duration tier Manipulation: Extract original sound Manipulation: Extract pitch tier Manipulation: Extract pulses Manipulation: Play (PSOLA) Manipulation: Get resynthesis (PSOLA) Manipulation: Replace duration tier Manipulation: Replace pitch tier Manipulation: Replace pulses Manipulation: Replace original sound ManipulationEditor Matrix Matrix: Draw as squares... Matrix: Formula... Matrix: Paint cells... Matrix: Set value... Matrix: To TableOfReal Modify PairDistribution PairDistribution: To Stringses... ParamCurve PointEditor PointProcess PointProcess: Add point... PointProcesses: Difference PointProcess: Draw... PointProcess: Get high index... PointProcess: Get interval... PointProcess: Get jitter (local)... PointProcess: Get jitter (local, absolute)... PointProcess: Get jitter (rap)... PointProcess: Get jitter (ppq5)... PointProcess: Get jitter (ddp)... PointProcess: Get low index... PointProcess: Get nearest index... PointProcess: Hum PointProcesses: Intersection PointProcess: Play PointProcess: Remove point... PointProcess: Remove point near... PointProcess: Remove points... PointProcess: Remove points between... PointProcess: To Sound (hum)... PointProcess: To Sound (phonation)... PointProcess: To Sound (pulse train)... PointProcesses: Union PointProcess: Up to IntensityTier... PointProcess: Up to PitchTier... Polygon Read Matrix from raw text file... Read Strings from raw text file... Sound: To Intensity... Sound & IntensityTier: Multiply Strings Strings: To Distributions Table TableOfReal TableOfReal: Set value... f af f f 0f f f f f Af lf f ȣf f :f if f f f f f f f f ̥f cf f f Ff tf Шf 'f f >f Ȫf f If f f =f f pf f &f Lf f lf f ȣf f :f f Wf f ,f f f Hf Pf f if qf /f صf f zf f Ϸf ܸf *f sf |f f f f غf f f f f f f f 3f |f f f f f =f ӻf f 7f hf f Ѽf f Hf f 4f 1f if f Ŀf f f f @f f f f @f f kf Hf f if f f f Af f &f f f f f 2f ^f f f f f [f 1f Rf f f f f f 'f of f f ,f f f f f f f Af Yf f %f f %f @f f !f Hf f f f f if f f Qf f @f f f Hf Zf f Jf f if 2f #f f This tutorial describes the sound files that you can read and write with P\s{RAAT}. It assumes you are familiar with the @Intro. You can read this tutorial sequentially with the help of the "< 1" and "1 >" buttons. 1. @@Sound files 1. General structure|General structure@ 1.1. @@Sound files 1.1. Sampling|Sampling@ (sampling frequency) 1.2. @@Sound files 1.2. Quantization|Quantization@ (linear, endian, \mu-law, A-law) 1.3. @@Sound files 1.3. Channels|Channels@ (mono, stereo) 1.4. @@Sound files 1.4. The header|The header@ 1.5. @@Sound files 1.5. Size|Size@ 1.6. @@Sound files 1.6. Compression|Compression@ 2. @@Sound files 2. File types|File types@ 2.1. @@Sound files 2.1. WAV files|WAV files@ 2.2. @@Sound files 2.2. AIFF files|AIFF files@ 2.3. @@Sound files 2.3. AIFC files|AIFC files@ 2.4. @@Sound files 2.4. NeXT/Sun (.au) files|NeXT/Sun (.au) files@ 2.5. @@Sound files 2.5. NIST files|NIST files@ 3. @@Sound files 3. Files that Praat can read|Files that Praat can read@ 4. @@Sound files 4. Files that Praat can write|Files that Praat can write@ This is chapter 1 of the @@Sound files@ tutorial. It describes the general structure of the headers and data parts of sound files. 1.2. @@Sound files 1.2. Quantization|Quantization@ (linear, \mu-law, A-law) When a sound signal from a microphone or on a tape needs to be read into a computer, it is %digitized, which means that it is %sampled and %quantized. Sampling is the discretization of the time domain of the signal: each second of the signal is divided up into 11025, 22050, or 44100 slices (or any other suitable number), and a %%sample value% is associated with each slice. For instance, a continuous 377-Hz sine wave is expressed by %x(%t) = sin (2%\pi 377 %t) If the %%sampling frequency% (or %%sample rate%) is 44100 Hz, this sine wave will be sampled at points spaced \De%t = 1/44100 second apart, and the sample values will be %x__%i_ = sin (2%\pi 377 (%t__0_ + %i \De%t)) where %t__0_ is the time after which sampling begins. \De%t is called the %%sample period%. Quantization is handled in the next section (@@Sound files 1.2. Quantization|\SS1.2@). Apart from sampling (@@Sound files 1.1. Sampling|\SS1.1@), digitization also involves quantization, which is the conversion of a sample value into a number that fits into 8 or 16 bits. For most file types, Praat supports sounds with one channel (mono) and two channels (stereo). The bulk of most sound files is formed by the samples. The sample part is usually preceded by a header, which contains information about: 1. The type of file (WAV, AIFF, AIFC, NeXT/Sun, NIST, Kay,...). 2. The sampling frequency (@@Sound files 1.1. Sampling|\SS1.1@). 3. The encoding (linear, 8 or 16 bit, byte order, \mu-law, A-law, see @@Sound files 1.2. Quantization|\SS1.2@). 4. The number of channels (mono, stereo, see @@Sound files 1.3. Channels|\SS1.3@). 5. The duration (usually the number of samples). The size of a sound file is equal to the size of the header plus the product of the number of samples, the quantization size, and the number of channels. For instance, a stereo sound with a duration of 3 seconds, sampled at 44100 Hz, would, when written into a 16-bit NeXT/Sun file, take up a disk space of 28 + 2 * 3.0 * 44100 * 2 = 529228 bytes whereas the same sound, when averaged to mono, downsampled to 8000 Hz, and written into a \mu-law NeXT/Sun file, take up only a disk space of 28 + 1 * 3.0 * 8000 * 1 = 24028 bytes The first example is typical of CD quality, the second of telephone speech. Praat used to be able to read some compressed sound file formats (shortened NIST, Polyphone), but because of licensing problems (Praat went open source, Shorten did not), you now need to use other (freely available) programs to do the conversion before reading them into Praat. For MP3-encoded audio files, one can e.g. use iTunes\re on the Macintosh. The audio file type most commonly used on Windows computers, also very common on the Internet. AIFF stands for: Audio Interchange File Format. This standard format for sound files was defined by Apple. It is also the format of the sound files on the Iris Indigo, where each sample is quantized into 16 bits. AIFC is short for AIFF(C) or AIFF-C, i.e. the Audio Interchange File Format (@@Sound files 2.2. AIFF files|\SS2.2@) with optional compression. Praat reads and write uncompressed AIFC files, but does not support compressed AIFC files. This is the format of the sound files on the Sun. Reading To read a #Sound from a Sun audio file on disk, use @@Read from file...@.Praat then asks you for a file name. After you click OK, Praat determines the encoding of the file. If the encoding is 16-bit linear, the 16-bit sample values are divided by 32768 so that the amplitude of the resulting Sound is between -1.0 and +1.0. If the encoding is 8-bit %\mu-law, the 16-bit sample value is determined by table look-up first. The resulting Sound will appear in the list of objects; its name will be equal to the file name, without extension. Writing Use @@Write to NeXT/Sun file...@. The samples of the Sound are multiplied by 32768 and quantized between -32768 and 32767; the result is written to the file in 16-bit mono Sun audio format. To avoid clipping, keep the absolute amplitude below 1.000. If the maximum sound pressure level is 91 dB (top = 32767), the quantization threshold is (top = 1/2) -5 dB. An audio file type used by speech researchers. Used, for instance, in the TIMIT database. Praat reads several kinds of NIST files: big-endian, little-endian, \mu-law, A-law, Polyphone. NIST files compressed with #shorten are no longer supported (see @@Sound files 1.6. Compression|\SS1.6@) Praat can read five types of standard sound files in several formats, and a number of proprietary types of sound files as well. Standard sound files The @@Read menu@ contains two commands for opening sound files: \bu With @@Read from file...@, you read the entire file into memory. A @Sound object will appear in the list. This is appropriate if your sound is not too long to fit into memory. The advantage of having a @Sound object is that you can perform analysis on it directly. \bu With @@Open long sound file...@, you open a sound file that is too long to read into memory completely. A @LongSound object will appear in the list. You will typically choose #View to view the contents of this sound and analyse it. Praat will only read so much of the file into memory as is needed to play or display parts of it. Both commands understand the following five standard audio file formats: \bu WAV: \bu linear 16-bit little-endian \bu 8-bit \mu-law \bu 8-bit A-law \bu linear 8-bit unsigned \bu AIFF or AIFC: \bu linear 16-bit big-endian \bu linear 8-bit signed \bu NeXT/Sun (.au): \bu NIST: Praat can write five types of standard sound files in an appropriate linear 16-bit formats, and a number of proprietary types of sound files as well: \bu @@Write to WAV file...@ (16-bit little-endian) \bu @@Write to AIFF file...@ (16-bit big-endian) \bu @@Write to AIFC file...@ (16-bit big-endian) \bu @@Write to NeXT/Sun file...@ (16-bit big-endian) \bu @@Write to NIST file...@ (16-bit little-endian) Ways for storing a @Sound object on disk. File format @@Read from file...@ recognizes AIFF and AIFC files with 8-bit and 16-bit encoding, but not compressed AIFC files. It recognizes any sampling frequency. The two channels of stereo files are averaged. ##Read two Sounds from AIFF file...# reads both channels separately and names them %left and %right. The sample values are divided by 2^^(%numberOfBitsPerSample \-- 1)^, so that the amplitude of the resulting Sound is between \--1.0 and +1.0; the maximum sound pressure level for a sine wave is therefore: 20 \.c ^^10^log (\Vr2 / 2\.c10^^\--5^) = 91 dB. The resulting Sound will appear in the List of Objects; its name will be equal to the file name, without extension. With @@Write to AIFF file...@. The samples of the Sound are multiplied by 32768 and quantized between \--32768 and 32767. To avoid clipping, keep the absolute amplitude below 1.000. If the maximum sound pressure level is 91 dB (top = 32767), the quantization threshold is (top = 1/2) \--5 dB. With this command, you write one or more selected @Sound and/or @LongSound objects to a single 16-bit little-endian WAV file on disk. See the @@Sound files@ tutorial for more information. With this command, you write one or more selected @Sound and/or @LongSound objects to a single 16-bit big-endian AIFF file on disk. See the @@Sound files@ tutorial for more information. With this command, you write one or more selected @Sound and/or @LongSound objects to a single 16-bit big-endian AIFC file on disk. See the @@Sound files@ tutorial for more information. With this command, you write one or more selected @Sound and/or @LongSound objects to a single 16-bit big-endian NeXT/Sun (.au) file on disk. See the @@Sound files@ tutorial for more information. With this command, you write one or more selected @Sound and/or @LongSound objects to a single 16-bit little-endian NIST audio file on disk. See the @@Sound files@ tutorial for more information. With this command, you write two selected @Sound objects to a single 16-bit little-endian stereo WAV file on disk. The top one will become the left channel, the bottom one the right channel. A way for storing a @Sound object on disk. The compressed sound files of the Timit database, and the Groningen speech corpus. With @@Read from file...@. With ##Write to NIST audio file...#. You can concatenate any combination of AIFF, AIFC, WAV, NeXT/Sun, and NIST audio files, and other files that you have read into memory. For instance, if you want to concatenate a 30-minute AIFF file, a 4-minute Kay sound file, and a 60-minute Next/Sun file, by writing them into a 94-minute WAV file, you do the following: 1. Open the AIFF file with @@Open long sound file...@ from the @@Read menu@. A @LongSound object will appear in the list. 2. Read the Kay sound file into memory with @@Read from file...@. A @Sound object will appear in the list. 3. Open the AIFF file with @@Open long sound file...@ from the @@Read menu@. A second @LongSound object will appear in the list. 4. Select the three objects and choose @@Write to WAV file...@ from the @@Write menu@. This only works if all the sounds have the same sampling frequency and the same number of channels (a @Sound object is always mono, of course). Available formats The format of the original sound files may be 16-bit linear (with big-endian or little-endian byte order), 8-bit linear (signed or unsigned), 8-bit \mu-law, or 8-bit A-law. The format of the resulting sound file is always 16-bit linear, with an appropriate default byte order. The following commands are available in the @@Write menu@ of you select any combination of @LongSound and/or @Sound objects: \bu @@Write to WAV file...@ (little-endian) \bu @@Write to AIFF file...@ (big-endian) \bu @@Write to AIFC file...@ (big-endian) \bu @@Write to NeXT/Sun file...@ (big-endian) \bu @@Write to NIST file...@ (little-endian) One of the @@types of objects@ in P\s{RAAT}. See the @@Sound files@ tutorial. A LongSound object gives you the ability to view and label a sound file that resides on disk. You will want to use it for sounds that are too long to read into memory as a @Sound object (typically, a few minutes). How to create a LongSound object You create a LongSound object with @@Open long sound file...@ from the @@Read menu@. What you can do with a LongSound object You can write a LongSound object to a new sound file, perhaps in a different format (AIFF, AIFC, WAV, NeXT/Sun, NIST) with the commands in the Write menu. You can also concatenate several LongSound objects in this way. See @@How to concatenate sound files@. How to view and edit a LongSound object You can view a LongSound object in a @LongSoundEditor by choosing @@LongSound: View@. This also allows you to extract parts of the LongSound as @Sound objects, or write these parts to a sound file. There are currently no ways to actually change the data in the file. How to annotate a LongSound object You can label and segment a LongSound object after the following steps: 1. Select the LongSound object. 2. Choose @@LongSound: To TextGrid...@ and specify your tiers. 3. Select the resulting @TextGrid object together with the LongSound object, and click #Edit. A @TextGridEditor will appear on the screen, with a copy of the LongSound object in it. Limitations The length of the sound file is limited to 2 gigabytes, which is 3 hours of CD-quality stereo, or 12 hours 16-bit mono sampled at 22050 Hz. A command to create a @TextGrid without any labels, copying the time domain from the selected @LongSound. See @@Sound: To TextGrid...@ for the arguments. A command to view the selected @LongSound object in a @LongSoundEditor. One of the @Editors in P\s{RAAT}, for viewing a @LongSound object. This viewer allows you: \bu to view and hear parts of the sound as it is on disk; \bu to copy a selected part as a @Sound object to the list of objects, so that you can perform analyses on it or save it to a smaller sound file; \bu to copy a selected part as a @Sound object to the @Sound clipboard, so that you can paste it into another Sound object that you are viewing in a @SoundEditor. To label and segment the LongSound object, use the @TextGridEditor instead (see @LongSound). The display and playback of the samples is restricted to 60 seconds at a time, for reasons of speed (although you can change this number with ##LongSound prefs# from the main #Preferences menu; the sound file itself can contain several hours of sound. The double-clickable sound file of the Macintosh (8 bits per sample). Cannot be ported to other machines, because the sound is in the @@resource fork@. To read a Sound from a Macintosh sound file on disk, use @@Read from file...@ (Macintosh only). The 8-bit sample values are divided by 128 so that the amplitude of the resulting Sound is between \--1.0 and +1.0. With ##Write to Mac sound file...#. Praat asks you for a file name. After you click OK, 0.5 is added to the samples of the Sound, they are multiplied by 128 and quantized between 0 and 255; the result is written to the file in 8-bit linear Macintosh sound-file format. To avoid clipping, keep the absolute amplitude below 1.000. If the maximum sound pressure level is 91 dB (top = 127), the quantization threshold for a sine wave is (top = 1/2) 43 dB. A command in the @@Read menu@ that creates a @LongSound object. The file will be opened for reading only. The file stays open until you remove the LongSound object. The sound files used by the SESAM and LVS programs. Each sample is normally quantized into 12 bits. To read a #Sound from a Sesam file on disk, use @@Read from file...@. The file name is expected to end in ".sdf" or ".SDF". The 12-bit sample values are divided by 2048 so that the amplitude of the resulting Sound is between -1.0 and +1.0. The resulting #Sound will appear in the List of Objects; its name will be equal to the file name, without extension. If the sound was encoded in 16 bits per sample, you should divide by 16 after reading (with $$Formula... self/16$) With ##Write to Sesam file...#. Praat then asks you for a file name. After you click OK, the samples of the Sound are multiplied by 2048 and quantized between -2048 and 2047; the result is written to the file in 12-bit LVS and Sesam format. To avoid clipping, keep the absolute amplitude below 1.000. If the maximum sound pressure level is 91 dB (top = 2047), the quantization threshold is (top = 1/2) 19 dB. If you prefer 16-bit encoding, you should multiply by 16 before writing (with $$Formula... self*16$) Sound files ppgb Sound files 1. General structure Sound files 1.1. Sampling Sound files 1.2. Quantization Sound files 1.3. Channels Sound files 1.4. The header Sound files 1.5. Size Sound files 1.6. Compression Sound files 2. File types Sound files 2.1. WAV files Sound files 2.2. AIFF files Sound files 2.3. AIFC files Sound files 2.4. NeXT/Sun (.au) files Sound files 2.5. NIST files Sound files 3. Files that Praat can read Sound files 4. Files that Praat can write AIFF and AIFC files Write to WAV file... Write to AIFF file... Write to AIFC file... Write to NeXT/Sun file... Write to NIST file... Write to stereo WAV file... NIST files How to concatenate sound files LongSound LongSound: To TextGrid... LongSound: View LongSoundEditor Macintosh sound files Open long sound file... 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g g h Jg h Ch mh $g 4h g Vh g zh h h g h h h h wh h h $h Uh h >h h h h h h xh h h h h h h h ch i i 4i i i i |i mi 1i i i i i i i 1i Ti xi i i Ii ^i si i i i i i i Ei oi i i i i " i 7 i L i j i t i | i i i i i i i i ! i ] i q i i Ii _i si i i i /i i i i i i i i i #i >i %i _i i i }i Qi i i i i i i i R!i m!i !i i '"i 8"i E"i (#i i #i #i #i $i i %i #i .%i i %i %i %i &i &i n'i 'i 'i 'i (i ^(i {(i (i (i (i (i n)i )i _*i p*i *i *i *i D+i +i +i +i +i +i +i ,i ,i 7,i Y,i },i ,i -i @-i ,i S-i t-i -i -i .i X.i .i .i /i ;/i p/i /i /i Xg 0i 10i ,i H0i o0i 0i 0i 0i 0i 1i D1i V1i g1i 1i 1i ?2i 2i 2i 2i 2i 2i #3i G3i p3i 3i 3i 4i /4i Y4i 4i 4i 4i 4i !5i T5i 5i 5i 5i 5i 6i h g M6i #7i 97i 7i 7i =8i T8i p8i 8i 8i 8i +9i g U9i Jg 9i h :i G:i S:i +9i :i ;i +9i g U9i Jg ;i G:i H<i <i +9i g U9i Jg ;i G:i .=i =i =i =i >i =i z>i >i >i >i >i >i >i >i ?i ?i 6?i P?i @i @i "@i D@i k@i Latest changes in P\s{RAAT}. ##4.4# (December 19, 2005) ##4.3.37# (December 15, 2005) \bu @@Principal component analysis@: now accepts tables with more variables (columns) than cases (rows). \bu TIMIT label files: removed a bug that caused Praat to crash for files whose first part was not labelled. ##4.3.36# (December 11, 2005) \bu Ltas: Average. \bu Optimality Theory: compute crucial rankings (select OTGrammar + PairDistribution). ##4.3.35# (December 8, 2005) \bu @ExperimentMFC: switched off warnings for stereo files. ##4.3.34# (December 8, 2005) \bu Sound window: the arrow scroll step is settable. \bu You can now run multiple listening experiments (@ExperimentMFC) in one "Run". \bu Formant: Get quantile of bandwidth... ##4.3.33# (December 6, 2005) \bu Removed three bugs introduced in 4.3.32 in @ExperimentMFC. ##4.3.32# (December 5, 2005) \bu Many more possibilities in @ExperimentMFC. ##4.3.31# (November 27, 2005) \bu @@Sound: To Ltas (pitch-corrected)...@ ##4.3.30# (November 18, 2005) \bu TableOfReal: Scatter plot: allows reversed axes. ##4.3.29# (November 11, 2005) \bu Windows: many more font sizes. ##4.3.28# (November 7, 2005) \bu Fontless EPS files: corrected character width for Symbol font (depended on SILIPA setting). \bu Windows: more reliable detection of home directory. ##4.3.27# (October 7, 2005) \bu TextGrid & Pitch: draw with text alignment. ##4.3.26# (September 29, 2005) \bu Macintosh: corrected error introduced in 4.3.25. ##4.3.25# (September 28, 2005) \bu Macintosh: allowed recording with sample rates of 12 and 64 kHz. ##4.3.24# (September 26, 2005) \bu Table: Down to TableOfReal...: one column of the Table can be used as the row labels for the TableOfReal, and the strings in the remaining columns of the Table are replaced with whole numbers assigned in alphabetical order. ##4.3.23# (September 24, 2005) \bu Read Table from comma-separated file... \bu Read Table from tab-separated file... \bu Write picture as fontless EPS file: choice between XIPA and SILIPA93. \bu Bold IPA symbols in EPS files (fontless SILIPA93 only). ##4.3.22# (September 8, 2005) \bu Macintosh: variable scroll bar size (finally, 7 years since System 8.5). ##4.3.21# (September 1, 2005) \bu Macintosh: error message if any of the fonts Times, Helvetica, Courier and Symbol are unavailable at start-up. \bu Renamed "Control" menu to "Praat" on all systems (as on the Mac), to reflect the fact that no other programs than Praat have used the Praat shell for five years. \bu Script editor: Undo and Redo buttons (only on the Mac for now). \bu Manual: corrected a bug that sometimes caused Praat to crash when trying to print. ##4.3.20# (August 18, 2005) \bu Log files: include name of editor window. ##4.3.19# (July 20, 2005) \bu Improved buttons in manual. \bu TableOfReal: Read from headerless spreadsheet file: allow row and column labels to be 30,000 rather than 100 characters. ##4.3.18# (July 12, 2005) \bu Glottal source for sound synthesis, corrected and documented. ##4.3.17# (July 7, 2005) \bu Glottal source for sound synthesis. \bu Multi-level Optimality Theory: parallel evaluation and bidirectional learning. ##4.3.16# (June 22, 2005) \bu Pitch drawing: corrected logarithmic scales. ##4.3.15# (June 22, 2005) \bu Graphics: better dotted lines in pitch contours; clipped pitch curves in editor windows. \bu Pitch analysis: more different units (semitones %re 1 Hz). ##4.3.14# (June 14, 2005) \bu Scripting: regular expressions. \bu Removed a bug that caused Praat to crash if a proposed object name was longer than 200 characters. ##4.3.13# (May 19, 2005) \bu Macintosh: an option to switch off screen previews in EPS files. \bu Sources: compatibility of makefiles with MinGW (Minimalist GNU for Windows). ##4.3.12# (May 10, 2005) \bu Some more manual tricks. ##4.3.11# (May 6, 2005) \bu TextGrid editor: show number of intervals. ##4.3.10# (April 25, 2005) \bu Table: Get logistic regression. ##4.3.08# (April 19, 2005) \bu OT learning: store history with "OTGrammar & Strings: Learn from partial outputs...". ##4.3.07# (March 31, 2005) \bu Linux: removed a bug that could cause a sound to stop playing. ##4.3.04# (March 9, 2005) \bu Use SIL Doulos IPA 1993/1996 instead of 1989. ##4.3.03# (March 2, 2005) \bu TextGrid window: green colouring of matching text. \bu Regular expressions can be used in many places. \bu Pitch analysis: switched off formant-pulling. ##4.3.02# (February 16, 2005) \bu TextGrid: Remove boundary at time... \bu Scripting: corrected %nowarn. \bu Linux: guard against blocking audio device. \bu Macintosh: guard against out-of-range audio level meter. ##4.3.01# (February 9, 2005) \bu Replaced PostScript font SILDoulosIPA with XIPA (adapted for Praat by Rafael Laboissi\e`re). \bu Sound: Set part to zero... \bu Pitch: To Sound (sine)... \bu Sound & TextGrid: Clone time domain. ##4.3# (January 26, 2005) ##4.2.35# (January 24, 2005) \bu OT learning: save in spreadsheet format. ##4.2.34# (January 12, 2005) \bu TextGrid editor: better visibility of yellow lines. ##4.2.33# (January 11, 2005) \bu MacOS X: work around bug in StuffIt Expander 9.0.1. ##4.2.32# (January 1, 2005) \bu Scripting: removed small bug that did not allow spaces before "form" statement. ##4.2.31# (December 13, 2004) \bu OT learning: made progress window show rankings on Windows. \bu MacOS 9 scripting: allowed recursive "execute". ##4.2.29# (December 4, 2004) \bu Scripting: allow multiple open forms with Apply buttons, including from commands added to menus. ##4.2.28# (December 3, 2004) \bu OT learning: corrected violations of *Lapse constraint (three unstressed syllables at the edges as well). ##4.2.27# (December 2, 2004) \bu Removed a bug introduced recently that could cause Praat to crash when selecting a small part to the left or right of the pitch curve in the sound window. ##4.2.26# (December 1, 2004) \bu Much updated manual. ##4.2.24# (November 24, 2004) \bu Improved manual about spectra. \bu Single @@Sound: To Spectrum...@. ##4.2.23# (November 17, 2004) \bu Much faster reading of 16-bit sound files. \bu `Apply' button in settings windows for menu commands and in script forms. ##4.2.22# (November 15, 2004) \bu LongSound: save separate channels. \bu Macintosh: much faster reading of WAV files. ##4.2.21# (November 4, 2004) \bu Calibrated long-term average spectrum (Sound: To Ltas...). \bu Removed a bug introduced in 4.2.19 that caused "Sound: To Harmonicity" not to work at all. \bu Scripting: nowarn, noprogress, nocheck. ##4.2.20# (October 24, 2004) \bu Speeded up intensity analysis by a factor of 10 (by making its time resolution 0.01 ms rather than 0.0001 ms at a sampling frequency of 44 kHz). \bu Improved query commands for Intensity and Ltas. \bu Removed 30,000-character limit in Info window. \bu Removed a bug introduced in 4.2.19 that caused Praat to crash in TextGrid: Draw. ##4.2.19# (October 18, 2004) \bu Speeded up pitch analysis and spectrogram analysis by a factor of two. \bu Windows: removed a bug that slowed Praat down after several hours of work or after a very long analysis with the progress window. ##4.2.18# (October 5, 2004) \bu PitchTier: To Sound (sine). \bu Removed a bug that caused too many warnings in ManPages that call scripts. ##4.2.17# (September 14, 2004) \bu Info window: can save. \bu Script editor: line numbers. \bu Unix: picture highlighting as on Mac and Windows. \bu Optimality Theory: monitor rankings when learning. ##4.2.16# (September 5, 2004) \bu One can now drag the inner viewport in the Picture window, excluding the margins. This is nice e.g. for creating square viewports or for drawing a waveform and a spectrogram in close contact. ##4.2.14# (August 20, 2004) \bu Windows: "Write to fontless EPS file..." now correctly references SILDoulosIPA rather than SILDoulosIPA-Regular. ##4.2.13# (August 12, 2004) \bu ExperimentMFC: removed a bug that caused Praat to crash if the carrier-before phrase was longer than the carrier-after phrase. ##4.2.11# (August 11, 2004) \bu Optimality Theory: added WeightByPosition and *MoraicConsonant, to learn coda weights. ##4.2.10# (August 10, 2004) \bu Optimality Theory: Remove harmonically bounded candidates. \bu Linux: removed the same bug as in 4.1.13, but now for scripts. ##4.2.09# (July 28, 2004) \bu Command line scripting: better handling of spaces. \bu Optimality Theory: added *Clash and *Lapse. ##4.2.08# (July 9, 2004) \bu @ExperimentMFC: subjects can now respond with keyboard presses. \bu Shimmer measurements: more accurate and less sensitive to additive noise. ##4.2.07# (June 16, 2004) \bu Sound editor: queries/reports/listings sometimes report on the whole visible part (and then say so). \bu SSCP: Draw sigma ellipse: allow reversed axes. \bu Scripting: corrected readability of voice report. ##4.2.06# (May 14, 2004) \bu Reading and opening 24-bit and 32-bit sound files (saving still goes in 16 bits). \bu Sound: Scale intensity. ##4.2.05# (May 13, 2004) \bu More extensive voice report (pitch statistics; harmonicity). \bu Pitch-corrected LTAS analysis. \bu Much faster Fourier transform (non-FFT version). \bu More drawing methods for Sound and Ltas (curve, bars, poles, speckles). \bu More TableOfReal extraction commands. \bu Removed bugs from the orthographic representation of vowels in the Peterson & Barney table. \bu Removed a bug introduced in 4.2.01 that caused a lack of redrawing in the button editor window. ##4.2.04# (April 21, 2004) \bu Removed a bug introduced in 4.2.01 that caused a lack of redrawing in the PointProcess and LongSound editor windows. \bu Sound: To Spectrum (dft) ##4.2.03# (April 20, 2004) \bu MacOS X and Linux: removed a bug introduced in 4.2.01 by which ##Create Strings from file list...# did not work with a wildcard ("*"). ##4.2.01# (April 7, 2004) \bu Improved frequency precision in spectrogram drawing. \bu Less flashing in sound window. \bu Better warnings against use of the LPC object. Praat 4.2, March 4, 2004 General: \bu July 10, 2003: Open source code (General Public Licence). Phonetics: \bu Faster computation of spectrum, spectrogram, and pitch. \bu More precision in numeric libraries. \bu PitchTier: Interpolate quadratically. \bu TextGrids can be saved chronologically (and Praat can read that file again). \bu Sound editor window @@Time step settings...@: "Automatic", "Fixed", and "View-dependent". \bu Sound window: distinguish basic from advanced spectrogram and pitch settings. \bu Read TableOfReal from headerless spreadsheet file...: cells with strings are considered zero. \bu Sound window: introduced time step as advanced setting. \bu Sound window: reintroduced view range as advanced setting. \bu Ltas: Compute trend line, Subtract trend line. Audio: \bu Sun workstations: support audio servers. Graphics: \bu Better selections in Picture window and editor windows. \bu Picture window: better handling of rectangles and ellipses for reversed axes. \bu Windows: corrected positioning of pictures on clipboard and in metafiles. \bu Windows: EPS files check availability of Times and TimesNewRomanPSMT. \bu Polygon: can now also paint in colour instead of only in grey values. \bu Unlimited number of points for polygons in PostScript (may not work on very old printers). \bu Picture window: line widths on all printers and clipboards are now equal to line widths used on PostScript printers: a line with a line width of "1" will be drawn with a width 3/8 points. This improves the looks of pictures printed on non-PostScript printers, improves the looks of pictures copied to your wordprocessor when printed, and changes the looks of pictures copied to your presentation program. OT learning: \bu Metrics grammar supports 'impoverished overt forms', i.e. without secondary stress even if surface structures do have secondary stress. \bu Support for crucially tied constraints and tied candidates. \bu Support for backtracking in EDCD. \bu Queries for testing grammaticality. Scripting: \bu ManPages: script links can receive arguments. \bu ManPages: variable duration of recording. \bu Support for unlimited size of script files in editor window on Windows XP and MacOS X (the Unix editions already had this). \bu Improved the reception of %sendpraat commands on Windows XP. Praat 4.1, June 5, 2003 \bu MacOS X edition. \bu Removed licensing. \bu More than 99 percent of the source code distributed under the General Public Licence. \bu Windows 2000 and XP: put preferences files in home directory. \bu Spectrum: the sign of the Fourier transform has changed, to comply with common use in technology and physics. Old Spectrum files are converted when read. \bu Spectral moments. \bu Many jitter and shimmer measures, also in the Sound editor window. \bu PitchTier: shift or multiply frequencies (also in ManipulationEditor). \bu TextGrid: shift times, scale times. \bu PSOLA synthesis: reduced buzz in voiceless parts. \bu @@Sound: Change gender... \bu Editors: @@Intro 3.5. Viewing a spectral slice@. \bu Editors: Get spectral power at cursor cross. \bu @@Sound: To PointProcess (periodic, peaks)...@ \bu Ltas: merge. Listening experiments: \bu Goodness judgments. \bu Multiple ResultsMFC: ##To Table#, so that the whole experiment can go into a single statistics file. \bu Stimulus file path can be relative to directory of experiment file. \bu @ExperimentMFC: multiple substimuli for discrimination tests. Statistics: \bu New @Table object for column @statistics: Pearson's %r, Kendall's %\ta-%b, %t-test. \bu Table: scatter plot. \bu Table: column names as variables. \bu @@T-test@. \bu TableOfReal: Extract rows where column... \bu TableOfReal: Get correlation.... \bu @@Correlation: Confidence intervals... \bu @@SSCP: Get diagonality (bartlett)... \bu Tutorial for bidirectional learning. \bu Random choice between equally violating candidates. \bu More constraints in metrics grammar. \bu Learning in editor. \bu Printing: hard-coded image interpolation for EPS files and PostScript printers. \bu New @Formulas tutorial. \bu @Formulas: can use variables without quotes. \bu Formulas for PitchTier, IntensityTier, AmplitudeTier, DurationTier. \bu Refer to any matrices and tables in formulas, e.g. Sound_hello (x) or Table_everything [row, col] or Table_tokens [i, "F1"]. \bu Assignment by modification, as with += -= *= /=. \bu New functions: date\$ (), extractNumber, extractWord\$ , extractLine\$ . See @@Formulas 5. String functions@. \bu @@Scripting 5.7. Including other scripts@. \bu String formulas in the calculator. \bu Stopped support of things that had been undocumented for the last four years: #let, #getnumber, #getstring, #ARGS, #copy, #proc, variables with capitals, and strings in numeric variables; there are messages about how to modify your old scripts. \bu Disallowed ambiguous expressions like -3\^ 2. Praat 4.0, October 15, 2001 Editors: \bu Simplified selection and cursor in editor windows. \bu Spectrogram, pitch contour, formant contour, and intensity available in the Sound, LongSound, and TextGrid editors. \bu TextGrid editor: additions and improvements. \bu @@Log files@. Phonetics library: \bu @ExperimentMFC: multiple-forced-choice listening experiments. \bu @@Sound: To Pitch (ac)...@: pitch contour less dependent on time resolution. This improves the constancy of the contours in the editors when zooming. \bu TextGrid: additions and improvements. \bu Sounds: Concatenate recoverably. Creates a TextGrid whose interval labels are the original names of the sounds. \bu Sound & TextGrid: Extract all intervals. The reverse of the previous command. \bu Filterbank analyses, @MelFilter, @BarkFilter and @FormantFilter, by @@band filtering in the frequency domain@. \bu Cepstrum by David Weenink: @MFCC, @LFCC. @Cepstrum object is a representation of the %%complex cepstrum%. \bu Intensity: To IntensityTier (peaks, valleys). \bu Replaced Analysis and AnalysisEditor with @Manipulation and @ManipulationEditor. Phonology library: \bu PairDistribution: Get percentage correct (maximum likelihood, probability matching). \bu OTGrammar & PairDistribution: Get percentage correct... \bu Improved spectrogram drawing. \bu @@Special symbols@: h\a'c\v^ek. \bu Macintosh: improved screen rendition of rotated text. \bu Macintosh: support for multiple audio input devices (sound cards). Statistics and numerics library: \bu More statistics by David Weenink. \bu Improved random numbers and other numerical stuff. \bu @@Regular expressions@. \bu Formatting in variable substitution, e.g. 'pitch:2' gives two digits after the decimal point. \bu Added ##fixed\$ # to scripting language for formatting of numbers. Documentation: \bu @@Multidimensional scaling@ tutorial. \bu Enabled debugging-at-a-distance. Praat 3.9, October 18, 2000 \bu Shift-click and shift-drag extend or shrink selection in editor windows. \bu Grouped editors can have separate zooming and scrolling (FunctionEditor preferences). \bu Cursor follows playing sound in editors; interruption by Escape key moves the cursor. \bu TextGridEditor: optimized for transcribing large corpora: text field, directly movable boundaries, more visible text in tiers, @SpellingChecker, type while the sound is playing, complete keyboard navigation, control font size, control text alignment, shift-click near boundary adds interval to selection. \bu Stereo display in LongSound and TextGrid editors. \bu LongSoundEditor and TextGridEditor: write selection to audio file. \bu SoundEditor: added command "Extract selection (preserve times)". \bu IntervalTierEditor, DurationTierEditor. \bu Added many query commands in editors. \bu Sound: To Formant...: sample-rate-independent formant analysis. \bu Sound: To Harmonicity (glottal-to-noise excitation ratio). \bu Pitch: support for ERB units, draw all combinations of line/speckle and linear/logarithmic/semitones/mels/erbs, optionally with TextGrid, Subtract linear fit. \bu Spectrum: Draw along logarithmic frequency axis. \bu TextGrid: modification commands, Extract part, Shift to zero, Scale times (with Sound or LongSound). \bu @@Matrix: To TableOfReal@, Draw contour... \bu Concatenate Sound and LongSound objects. \bu File formats: save PitchTier in spreadsheet format, read CGN syntax files (XML version), text files now completely file-server-safe (independent from Windows/Macintosh/Unix line separators). \bu @@Principal component analysis@. \bu @@Discriminant analysis@. \bu @Polynomial: drawing, @@Roots|root@ finding etc. \bu @@TableOfReal: Draw box plots...@. \bu @@Covariance: To TableOfReal (random sampling)...@. \bu @@SSCP: Get sigma ellipse area...@. \bu Query @DTW for 'weighted distance' of time warp. \bu Distributions: To Strings (exact)... \bu Strings: Randomize. \bu OTGrammar: To PairDistribution. \bu Full support for colour inkjet printers on Windows and Macintosh. \bu Full support for high-resolution colour clipboards and metafiles for Windows and Macintosh programs that support them (this include MS Word for Windows, but unfortunately not MS Word for Macintosh). \bu Colour in EPS files. \bu Interpolating grey images, i.e. better zoomed spectrograms. \bu Linux: support for 24-bits screens. \bu Asynchronous sound play. \bu Linux: solved problems with /dev/mixer ("Cannot read MIC gain.") on many computers. \bu Added possibility of zero padding for sound playing, in order to reduce clicks on some Linux and Sun computers. \bu LongSound supports mono and stereo, 8-bit and 16-bit, %\mu-law and A-law, big-endian and little-endian, AIFC, WAV, NeXT/Sun, and NIST files. \bu "Read two Sounds from stereo file..." supports 8-bit and 16-bit, %\mu-law and A-law, big-endian and little-endian, AIFC, WAV, NeXT/Sun, and NIST files. \bu SoundRecorder writes to 16-bit AIFC, WAV, NeXT/Sun, and NIST mono and stereo files. \bu Sound & LongSound: write part or whole to mono or stereo audio file. \bu Read Sound from raw Alaw file. \bu Artword & Speaker (& Sound) movie: real time on all systems. \bu @@Formulas 4. Mathematical functions@: added statistical functions: %\ci^2, Student T, Fisher F, binomial, and their inverse functions. \bu Windows: program #praatcon for use as a Unix-style console application. \bu Windows and Unix: Praat can be run with a command-line interface without quitting on errors. \bu Unix & Windows: can use <stdout> as a file name (supports pipes for binary data). \bu @sendpraat now also for Macintosh. \bu @@Scripting 6.7. Sending a message to another program|sendsocket@. \bu @@Read from file...@ recognizes script files if they begin with "\# !". \bu Script links in @ManPages. Documentation \bu Tutorials on all subjects available through @Intro. Praat 3.8, January 12, 1999 Phonetics library \bu New objects: @LongSound (view and label long sound files), with editor; PairDistribution. \bu @PSOLA manipulation of voiceless intervals, version 2: quality much better now; target duration is exactly as expected from Duration tier or specified lengthening in @@Sound: Lengthen (PSOLA)...@. \bu Audio: Escape key stops audio playing (on Mac also Command-period). \bu @SoundRecorder: allows multiple recordings without close; Play button; Write buttons; buffer size can be set. \bu Reverse a Sound or a selection of a Sound. \bu @@Sound: Get nearest zero crossing...@. \bu Formant: "Scatter plot (reversed axes)...". \bu TextGrid & Pitch: "Speckle separately...". \bu "Extract Sound selection (preserve times)" in TextGridEditor. \bu More query commands for Matrix, TableOfReal, Spectrum, PointProcess. Phonology library \bu 25-page OT learning tutorial. \bu Made the OT learner 14 times as fast. Systems \bu May 23: Windows beta version. \bu April 24: Windows alpha version. Files \bu Read more Kay, Sun (.au), and WAV sound files. \bu "Read Strings from raw text file..." \bu @@Create Strings as file list...@. \bu "Read IntervalTier from Xwaves..." \bu hidden "Read from old Windows Praat picture file..." Graphics \bu Use colours (instead of only greys) in "Paint ellipse..." etc. \bu More true colours (maroon, lime, navy, teal, purple, olive). \bu Direct printing from Macintosh to PostScript printers. \bu Hyperpage printing to PostScript printers and PostScript files. \bu Phonetic symbols: raising sign, lowering sign, script g, corner, ligature, pointing finger. Shell \bu November 4: all dialogs are modeless (which is new for Unix and Mac). \bu September 27: @sendpraat for Windows. Scripting \bu January 7: scriptable editors. \bu October 7: file I/O in scripts. \bu August 23: script language includes all the important functions for string handling. \bu June 24: string variables in scripts. \bu June 22: faster look-up of script variables. \bu June 22: unlimited number of script variables. \bu April 5: suspended chopping of trailing spaces. \bu March 29: enabled formulas as arguments to dialogs (also interactive). Praat 3.7, March 24, 1998 \bu In all FunctionEditors: drag to get a selection. \bu Many new query (#Get) commands for @Sound, @Intensity, @Harmonicity, @Pitch, @Formant, @Ltas, @PitchTier, @IntensityTier, @DurationTier, @FormantTier. \bu Many new modification commands. \bu Many new interpolations. \bu Sound enhancements: @@Sound: Lengthen (PSOLA)...@, @@Sound: Deepen band modulation...@ \bu @@Source-filter synthesis@ tutorial, @@Sound & IntensityTier: Multiply@, @@Sound & FormantTier: Filter@, @@Formant: Formula (frequencies)...@, @@Sound: Pre-emphasize (in-line)...@. Labelling \bu TextGrid queries (#Get times and labels in a script). \bu @@TextGrid: Count labels...@. \bu @@PointProcess: To TextGrid (vuv)...@: get voiced/unvoiced information from a point process. \bu IntervalTier to TableOfReal: labels become row labels. \bu TextTier to TableOfReal. Numerics and statistics library \bu Multidimensional scaling (Kruskal, INDSCAL, etc). \bu @TableOfReal: Set value, Formula, Remove column, Insert column, Draw as squares, To Matrix. \bu OT learning: new strategies: weighted symmetric plasticity (uncancelled or all). Praat shell \bu First Linux version. \bu Eight new functions like e.g. %hertzToBark in @@Formulas 4. Mathematical functions@. \bu @@Praat script@: procedure arguments; object names. \bu 230 more man pages (now 630). \bu Hypertext: increased readability of formulas, navigation with keyboard. Praat 3.6, October 27, 1997 \bu Intuitive position of B and E buttons on left-handed mice. \bu @SoundEditor: copy %windowed selection to list of objects. \bu @SoundEditor: undo Cut, Paste, Zero. \bu @SpectrumEditor: copy band-filtered spectrum or sound to list of objects. \bu @ManipulationEditor: LPC-based pitch manipulation. Objects: \bu Use '-', and '+' in object names. \bu LPC-based resynthesis in @ManipulationEditor. \bu @Sound: direct modification without formulas (addition, multiplication, windowing) \bu @Sound: filtering in spectral domain by formula. \bu Create a simple @Pitch object from a @PitchTier (for %F__0_) and a @Pitch (for V/U). \bu Semitones in @PitchTier tables. \bu @PointProcess: transplant time domain from @Sound. \bu Much more... \bu Computational Optimality Theory. See @@OT learning@. Hypertext \bu You can use @ManPages files for creating your own tutorials. These contains buttons for playing and recording sounds, so you can use this for creating an interactive IPA sound training course. \bu Programmable @@Praat script@ language: variables, expressions, control structures, procedures, complete dialog box, exchange of information with Info window, continuation lines. \bu Use system-independent relative file paths in @@Praat script@. \bu @ScriptEditor: Run selection. \bu Rotation and scaling while printing the @@Picture window@. \bu Apart from bold and italic, now also bold-italic (see @@Text styles@). \bu Rounded rectangles. \bu Conversion of millimetres and world coordinates. \bu Measurement of text widths (screen and PostScript). Unix: \bu Use the @sendpraat program for sending messages to running Praat programs. Mac: \bu Praat looks best with the new and beautiful System 8. Praat 3.5, May 27, 1997 New editors: \bu #TextGridEditor replaces and extends LabelEditor: edit points as well as intervals. \bu #AnalysisEditor replaces and extends PsolaEditor: view pitch, spectrum, formant, and intensity analyses in a single window, and allow pitch and duration resynthesis by #PSOLA and more (would be undone in 3.9.19). \bu #SpectrumEditor allows you to view and edit spectra. Praat shell: \bu ##History mechanism# remembers all the commands that you have chosen, and allows you to put them into a script. \bu #ScriptEditor allows you to edit and run any Praat script, and to put it under a button. \bu All added and removed buttons are remembered across sessions. \bu #ButtonEditor allows you to make buttons visible or invisible. Evaluations: \bu In his 1996 doctoral thesis, Henning Reetz compared five pitch analysis routines; @@Sound: To Pitch (ac)...@ appeared to make the fewest errors. H. Reetz (1996): %%Pitch Perception in Speech: a Time Domain Approach%, Studies in Language and Language Use #26, IFOTT, Amsterdam (ICG Printing, Dordrecht). \bu 140 more man pages (now 330). \bu Tables and pictures in manual. \bu Printing the entire manual. \bu Logo. New classes: \bu Labelling & segmentation: #TextGrid, #IntervalTier, #TextTier. \bu Analysis & manipulation: #Analysis. \bu Statistics: #TableOfReal, #Distributions, #Transition File formats: \bu Read and write rational numbers in text files. \bu Read 8-bit .au sound files. \bu Read and write raw 8-bit two's-complement and offset-binary sound files. \bu 16-bit interactive Sound I/O on Mac. \bu Record sounds at 9.8 kHz on SGI. New commands: \bu Two more pitch-analysis routines. \bu Sound to PointProcess: collect all maxima, minima, zero crossings. \bu PointProcess: set calculus. \bu TextGrid: extract time-point information. \bu Compute pitch or formants at given time points. \bu Put pitch, formants etc. in tables en get statistics. \bu Many more... Macintosh: \bu 16-bit interactive sound I/O. \bu Fast and interpolating spectrogram drawing. \bu Phonetic Mac screen font included in source code (as a fallback to using SIL Doulos IPA). \bu Keyboard shortcuts, text editor, help under question mark, etc. Praat 3.3, October 6, 1996 \bu Documentation: hypertext help browser, including the first 190 man pages. \bu New editors: class #TextTier for labelling times instead of intervals. \bu New actions: #Formant: Viterbi tracker, Statistics menu, Scatter plot. \bu Evaluation: For HNR analysis of speech, the cross-correlation method, which has a sensitivity of 60 dB and a typical time resolution of 12 milliseconds, must be considered better than the autocorrelation method, which has a better sensitivity (80 dB), but a much worse time resolution (30 ms). For pitch analysis, the autocorrelation method still beats the cross-correlation method because of its better resistance against noise and echos, and despite its marginally poorer resolution (15 vs. 12 ms). \bu User preferences are saved across sessions. \bu The phonetic X screen font included in the source code. \bu Xwindows resources included in the source code \bu Graphics: eight colours, small caps, text rotation. \bu File formats: Sun/NexT mu-law files, raw matrix text files, Xwaves mark files. \bu Accelerations: keyboard shortcuts, faster dynamic menu, Shift-OK keeps file selector on screen. \bu Class changes: #StylPitch and #MarkTier are now called #PitchTier and #TextTier, respectively. Old files can still be read. \bu Script warning: all times in dialogs are in seconds now: milliseconds have gone. Praat 3.2, April 29, 1996 \bu Sound I/O for HPUX, Sun Sparc 5, and Sun Sparc LX. \bu Cross-correlation pitch and HNR analysis. \bu Facilities for generating tables from scripts. \bu Editing and playing stylized pitch contours and point processes. \bu PSOLA pitch manipulation. \bu Spectral smoothing techniques: cepstrum and LPC. \bu Time-domain pitch analysis with jitter measurement. \bu Read and write Bell-Labs sound files and Kay CSL audio files. \bu Replaced IpaTimes font by free SILDoulos-IPA font, and embedded phonetic font in PostScript picture. \bu Completed main phonetic characters. Praat 3.1, December 5, 1995 \bu Add and remove buttons dynamically. \bu DataEditor (Inspect button). \bu Initialization scripts. \bu Logarithmic axes. \bu Call remote ADDA server directly. To do \bu TextGrid & Sound: Extract intervals with margins. \bu Spectrum: draw power, re, im, phase. \bu Formant: To Spectrum (slice)... (combines Formant-to-LPC and LPC-to-Spectrum-slice) \bu Read and/or write Matlab files, MBROLA files, Xwaves files, CHAT files. \bu Matrix: draw numbers. \bu Fractions with \bsf{a|b}. \bu Move objects up and down list. \bu Spectrogram cross-correlation. \bu Labels in AIFC file. \bu Improve scrolling and add selection in hyperpages. \bu Segment spectrograph? \bu Phoneme-to-articulation conversion?? Known bugs in all editions \bu (small) No navigation by tabs. \bu (small) Tabs in texts should be considered spaces. Known bugs in the Macintosh version \bu (small) Pause window modal. \bu (small) Cascade buttons grey after suspend+resume during progress window. \bu Movie window cannot be closed. Known bugs in the Windows version \bu Cannot stand infinitesimal zooming in SpectrogramEditor. \bu Clipboards with greys sometimes become black-and-white after use of colour. Known bugs in the Unix versions \bu (small) Motif messaging windows should have no parent and be modeless. Known bugs in the Linux version \bu Sounds shorter than 200 ms do not always play (workaround: add zeroes in prefs). \bu Keyboard shortcuts do not work if NumLock is on. \bu Progress window does not always disappear. Known bugs in the Solaris version \bu (serious for some) File names run out of the window in some Motif versions. Known bugs in the HP version \bu (serious for some) Sound recording should be from audioserver instead of local. For supplying source code: GPL IPA fonts: Fukui Rei (XIPA) & Rafael Laboissi\e`re (adaptation to Praat). IPA fonts: Summer Institute of Linguistics (Doulos1989, until January 2005). Linux audio: Darryl Purnell, Pretoria. GPL Gnu Scientific Library: Gerard Jungman, Brian Gough. Public domain Fourier transforms: Paul Swarztrauber (fftpack), Monty. Public domain LAPACK: Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University. For technical support and advice: Ton Wempe. For their financial support during the development of Praat: Netherlands Organization for Scientific Research (NWO). Talkbank project, Carnegie Mellon / Linguistic Data Consortium. Spoken Dutch Corpus (CGN). Laboratorium Experimentele OtoRhinoLaryngologie, KU Leuven. DFG-Projekt Dialektintonation, Universit\a"t Freiburg. Department of Linguistics and Phonetics, Lund University. Centre for Cognitive Neuroscience, University of Turku. Linguistics Department, University of Joensuu. Laboratoire de Sciences Cognitives et Psycholinguistique, Paris. Department of Linguistics, Northwestern University. Department of Finnish and General Linguistics, University of Tampere. Institute for Language and Speech Processing, Paradissos Amaroussiou. J\o"rg Jescheniak, Universit\a"t Leipzig. The Linguistics Teaching Laboratory, Ohio State University. Linguistics & Cognitive Science, Dartmouth College, Hanover NH. Cornell Phonetics Lab, Ithaca NY. The first menu in the @@Object window@. On MacOS X, this menu is in the main menu bar. One of the fixed buttons in the @@Object window@. Availability You can choose this command after selecting one object of any class. Behaviour The Object window copies the selected object, and all the data it contains, to a new object, which will appear at the bottom of the List of Objects. Example If you select "Sound hallo" and click `Copy...', a dialog will appear, which prompts you for a name; after you click OK, a new object will appear in the list, bearing that name. A menu that occurs in the @@Dynamic menu@ for many objects. This menu contains commands for drawing the object to the @@Picture window@, which will allow you to print the drawing or to copy it to your word processor. A column of buttons in the right-hand part of the @@Object window@, plus the #Write menu in the Object window. If you select one or more @objects in the list, the possible actions that you can perform with the selected objects will appear in the dynamic menu. These actions can include editing, writing, drawing, conversions to other types (including analysis and synthesis), and more. Example of analysis: Record a Sound, select it, and click on ##To Pitch...#. This will create a new Pitch object and put it in the list of objects. You can then edit, write, and draw this Pitch object. Example of synthesis: Create a #Speaker, create and edit an #Artword, and click on ##To Sound...#. A command in the @@Dynamic menu@ of several types of @objects. This command puts an @@Editors|editor@ window on the screen, which shows the contents of the selected object. This window will allow your to view and modify the contents of this object. One of the commands in the Formant menu of the @SoundEditor and the @TextGridEditor. See @@Intro 5. Formant analysis@ One of the commands in the Intensity menu of the @SoundEditor and the @TextGridEditor. See @@Intro 6. Intensity analysis@ One of the commands in the Pitch menu of the @SoundEditor and the @TextGridEditor. See @@Intro 4. Pitch analysis@ One of the commands in the Spectrogram menu of the @SoundEditor and the @TextGridEditor. See @@Intro 3. Spectral analysis@ @@FAQ: How to cite Praat @@FAQ: Formant analysis @@FAQ: Pitch analysis @@FAQ: Spectrograms @@FAQ: Scripts #Problem: I get different formant values if I choose to analyse 3 formants than if I choose to analyse 4 formants. Solution: the "number of formants" in formant analysis determines the number of peaks with which the %entire spectrum is modelled. For an average female voice, you should choose to analyse 5 formants in the region up to 5500 Hz, even if you are interested only in the first three formants. #Problem: I often get only 1 formant in a region where I see clearly 2 formants in the spectrogram. This occurs mainly in back vowels (F1 and F2 close together) for male voices, if the "maximum formant" is set to the standard of 5500 Hz, which is appropriate for female voices. Set the "maximum formant" down to 5000 Hz. No, Praat comes without a guarantee: the formant analysis is based on LPC, and this comes with several assumptions as to what a speech spectrum is like. #Question: what algorithm is used for formant analysis? Answer: see @@Sound: To Formant (burg)...@. #Question: how do I cite Praat in my articles? Answer: nowadays most journals allow you to cite computer programs and web sites. The style approved by the American Psychological Association, and therefore by many journals, is like the following (change the dates and version number as needed): Boersma, Paul & Weenink, David (2005). Praat: doing phonetics by computer (Version 4.4) [Computer program]. Retrieved December 19, 2005, from http://www.praat.org/ If the journal does not allow you to cite a web site, then try: Boersma, Paul (2001). Praat, a system for doing phonetics by computer. %%Glot International% ##5:9/10#, 341-345. #Question: what algorithm is used for pitch analysis? Answer: see @@Sound: To Pitch (ac)...@. The 1993 article is downloadable from http://www.fon.hum.uva.nl/paul/ #Question: why do I get different results for the maximum pitch if...? If you select a Sound and choose @@Sound: To Pitch...@, the time step will usually be 0.01 seconds. The resulting @Pitch object will have values for times that are 0.01 seconds apart. If you then click Info or choose ##Get maximum pitch# from the #Query menu, the result is based on those time points. By contrast, if you choose ##Get maximum pitch# from the #Pitch menu in the SoundEditor window, the result will be based on the visible points, of which there tend to be a hundred in the visible window. These different time spacings will lead to slightly different pitch contours. If you choose ##Move cursor to maximum pitch#, then choose ##Get pitch# from the #%Pitch menu, the result will be different again. This is because ##Get maximum pitch# can do a parabolic interpolation around the maximum, whereas ##Get pitch#, not realizing that the cursor is at a maximum, does a stupid linear interpolation, which tends to lead to lower values. #Question: how do I do something to all the files in a directory? Answer: look at @@Create Strings as file list...@. #Question: why doesn't the editor window react to my commands? Your commands are probably something like: Read from file... hello.wav Edit Zoom... 0.3 0.5 Answer: Praat doesn't know it has to send the #Zoom command to the editor window called ##Sound hello#. There could be several Sound editor windows on your screen. According to @@Scripting 7.1. Scripting an editor from a shell script@, you will have to say this explicitly: editor Sound hello #Problem: a line like "Number = 1" does not work. Solution: names of variables should start with a lower-case letter. #Question: why do names of variables have to start with a lower-case letter? I would like to do things like "F0 = Get mean pitch". Answer: Praat scripts combine button commands with things that only occur in scripts. Button commands always start with a capital letter, e.g. "Play". Script command always start with lower case, e.g. "echo Hello". A minimal pair is "select", which simulates a mouse click in the object list, versus "Select...", which sets the selection in editor windows. Variable names that start with a capital letter would be rather ambiguous in assignments, as in "x = Get", where "Get" would be a variable, versus "x = Get mean", where "Get mean" is a button command. To prevent this, Praat enforces a rigorous lower-case/upper-case distinction. #Question: how do I convert a number into a string? Answer: a\$ = "'a'" #Question: how do I convert a string into a number? Answer: a = 'a\$ ' #Problem: the background is grey instead of white (too little contrast) Solution: reduce the "dynamic range" in the spectrogram settings. The standard value is 50 dB, which is fine for detecting small things like plosive voicing in well recorded speech. For gross features like vowel formants, or for noisy speech, you may want to change the dynamic range to 40 or even 30 dB. One of the menus in all @editors, in the @manual, and in the @@Picture window@. This tutorial describes the use of filtering techniques in P\s{RAAT}. It assumes you are familiar with the @Intro. Frequency-domain filtering Modern computer techniques make possible an especially simple batch filtering method: multiplying the complex spectrum in the frequency domain by any real-valued filter function. This leads to a zero phase shift for each frequency component. The impulse response is symmetric in the time domain, which also means that the filter is %acausal: the filtered signal will show components before they start in the original. \bu @@Spectrum: Filter (pass Hann band)...@ \bu @@Spectrum: Filter (stop Hann band)...@ \bu @@Sound: Filter (pass Hann band)...@ \bu @@Sound: Filter (stop Hann band)...@ \bu @@Sound: Filter (formula)...@ Spectro-temporal: \bu @@band filtering in the frequency domain@ Fast time-domain filtering Some very fast Infinite Impulse Response (IIR) filters can be defined in the time domain. These include recursive all-pole filters and pre-emphasis. These filters are causal but have non-zero phase shifts. There are versions that create new Sound objects: \bu @@Sound: Filter (one formant)...@ \bu @@Sound: Filter (pre-emphasis)...@ \bu @@Sound: Filter (de-emphasis)...@ And there are in-line versions, which modify the existing Sound objects: \bu @@Sound: Filter with one formant (in-line)...@ \bu @@Sound: Pre-emphasize (in-line)...@ \bu @@Sound: De-emphasize (in-line)...@ Convolution A Finite Impulse Response (FIR) filter can be described as a sampled sound. Filtering with such a filter amounts to a %#convolution of the original sound and the filter: \bu @@Sounds: Convolve@ Described elsewhere Described in the @@Source-filter synthesis@ tutorial: \bu @@Sound & Formant: Filter@ \bu @@Sound & FormantTier: Filter@ \bu @@LPC & Sound: Filter...@ \bu @@LPC & Sound: Filter (inverse)@ A menu that occurs in the @@Dynamic menu@ for a @Sound. This menu contains commands for analysing the formant contours of the selected Sound: @@Sound: To Formant (burg)... @@Sound: To Formant (keep all)... @@Sound: To Formant (sl)... @@Sound: To LPC (autocorrelation)... @@Sound: To LPC (covariance)... @@Sound: To LPC (burg)... @@Sound: To LPC (marple)... @@Sound: To MFCC... One of the commands in the @@Query menu@ of the @SoundEditor and the @TextGridEditor. The title of a submenu of the @@Praat menu@. You can choose this command after choosing one object. Purpose To get some information about the selected object. The information will appear in the @@Info window@. A text window into which many query commands write their answers. You can select text from this window and copy it to other places. In a @@Praat script@, you can bypass the Info window by having a query command writing directly into a script variable. Apart from the @Info command, which writes general information about the selected object, the following more specific commands also write into the Info window: You can use this command after selecting one object in the list. The contents of the selected object will become visible in a Data Editor. You can then view and change the data in the object, but beware: changing the data directly in this way may render them inconsistent. Changes that you make to the data with another Editor (e.g., a SoundEditor), or with the commands under #%Modify, are immediately reflected in the top-level Data Editor; any subeditors are destroyed, however, because they may now refer to invalid data. Changes that you make to the data with a Data Editor, are immediately reflected in any open type-specific Editors (e.g., a SoundEditor). This is an introductory tutorial to P\s{RAAT}, a computer program with which you can analyse, synthesize, and manipulate speech, and create high-quality pictures for your articles and thesis. You are advised to work through all of this tutorial. You can read this tutorial sequentially with the help of the "1 >" and "< 1" buttons, or go to the desired information by clicking on the blue links. @@Intro 1. How to get a sound@: @@Intro 1.1. Recording a sound|record@, @@Intro 1.2. Reading a sound from disk|read@, @@Intro 1.3. Creating a sound from a formula|formula@. @@Intro 2. What to do with a sound@: @@Intro 2.1. Writing a sound to disk|write@, @@Intro 2.2. Viewing and editing a sound|view@. @@Intro 3. Spectral analysis spectrograms: @@Intro 3.1. Viewing a spectrogram|view@, @@Intro 3.2. Configuring the spectrogram|configure@, @@Intro 3.3. Querying the spectrogram|query@, @@Intro 3.4. The Spectrogram object|the Spectrogram object@. spectral slices: @@Intro 3.5. Viewing a spectral slice|view@, @@Intro 3.6. Configuring the spectral slice|configure@, @@Intro 3.7. The Spectrum object|the Spectrum object@. @@Intro 4. Pitch analysis pitch contours: @@Intro 4.1. Viewing a pitch contour|view@, @@Intro 4.2. Configuring the pitch contour|configure@, @@Intro 4.3. Querying the pitch contour|query@, @@Intro 4.4. The Pitch object|the Pitch object@. @@Intro 5. Formant analysis formant contours: @@Intro 5.1. Viewing formant contours|view@, @@Intro 5.2. Configuring the formant contours|configure@, @@Intro 5.3. Querying the formant contours|query@, @@Intro 5.4. The Formant object|the Formant object@. @@Intro 6. Intensity analysis intensity contours: @@Intro 6.1. Viewing an intensity contour|view@, @@Intro 6.2. Configuring the intensity contour|configure@, @@Intro 6.3. Querying the intensity contour|query@, @@Intro 6.4. The Intensity object|the Intensity object@. @@Intro 7. Annotation @@Intro 8. Manipulation@: of @@Intro 8.1. Manipulation of pitch|pitch@, @@Intro 8.2. Manipulation of duration|duration@, @@Intro 8.3. Manipulation of intensity|intensity@, @@Intro 8.4. Manipulation of formants|formants@. There are also more specialized tutorials: \bu Voice analysis (jitter, shimmer, noise): @Voice \bu Listening experiments: @@ExperimentMFC@ \bu @@Sound files@ \bu @@Filtering@ \bu @@Source-filter synthesis@ \bu @@Articulatory synthesis@ Learning: \bu @@Feedforward neural networks@ \bu @@OT learning@ \bu @@Principal component analysis@ \bu @@Multidimensional scaling@ \bu @@Discriminant analysis@ \bu @@Printing@ \bu @@Scripting@ The authors The Praat program was created by Paul Boersma and David Weenink of the Institute of Phonetics Sciences of the University of Amsterdam. Home page: ##http://www.praat.org# or ##http://www.fon.hum.uva.nl/praat/#. For questions and suggestions, mail to the Praat discussion list, which is reachable from the Praat home page, or directly to ##paul.boersma\@ uva.nl#. Most of the things most people do with Praat start with a sound. There are at least three ways to get a sound: @@Intro 1.1. Recording a sound @@Intro 1.2. Reading a sound from disk @@Intro 1.3. Creating a sound from a formula To record a speech sound into Praat, you need a computer with a microphone. If you do not have a microphone, try to record from an audio CD instead. To record from the microphone (or the CD), perform the following steps: 1. Choose @@Record mono Sound...@ from the @@New menu@ in the @@Object window@. A @SoundRecorder window will appear on your screen. 2. Choose the appropriate input device, namely the microphone, by the following steps. If there is a small loudspeaker symbol in the Windows Start bar, double click it and you will see the %playing mixer. If there is no loudspeaker symbol, go to ##Control Panels#, then ##Sounds and Audio Devices#, then #Volume, then #Advanced, and you will finally see the playing mixer. Once you see the Windows playing mixer, choose #Properties from the #Option menu, then click #Recording, then #OK. You now see the %recording mixer, where you can select the microphone (if you do not like this complicated operation, try Praat on Macintosh or Linux instead of Windows). 3. Use the #Record and #Stop buttons to record a few seconds of your speech (or a few seconds of music from your playing CD). 4. Use the #Play button to hear what you have recorded. 5. Repeat steps 3 and 4 until you are satisfied with your recording. 6. Click the ##Save to list# button. Your recording will now appear in the Object window, where it will be called "Sound sound". 7. You can now close the SoundRecorder window. 8. When you saved your sound to the Object window, some buttons appeared in that window. These buttons show you what you can do with the sound. Try the #Play and @Edit buttons. For more information on recording, see the @SoundRecorder manual page. Apart from recording a new sound from a microphone, you could read an existing sound file from your disk. With @@Read from file...@ from the Read menu, P\s{RAAT} will be able to read most standard types of sound files, e.g. WAV files. They will appear as @Sound objects in the Object window. For instance, if you open the file ##hello.wav#, an object called "Sound hello" will appear in the list. If you do not have a sound file on your disk, you can download a WAV file (or so) from the Internet, then read that file into Praat with ##Read from file...#. If you have no microphone, no sound files on disk, and no access to the Internet, you could still create a sound from a formula with @@Create Sound...@ from the @@New menu@. As soon as you have a @Sound in the @@List of Objects@, the buttons in the @@Dynamic menu@ (the right-hand part of the @@Object window@) will show you what you can do with it. @@Intro 2.1. Writing a sound to disk @@Intro 2.2. Viewing and editing a sound There are several ways to write a sound to disk. First, the @@File menu@ of the @SoundRecorder window contains commands to save the left channel, the right channel, or both channels of the recorded sound to any of four standard types of sound files (WAV, AIFC, NeXT/Sun, NIST). These four file types are all equally good for P\s{RAAT}: P\s{RAAT} will handle them equally well on every computer. The first three of these types will also be recognized by nearly all other sound-playing programs. Then, once you have a @Sound object in the @@List of Objects@, you can save it in several formats with the commands in the @@Write menu@. Again, the WAV, AIFF, AIFC, NeXT/Sun, and NIST formats are equally fine. For more information, see the @@Sound files@ tutorial. To see the wave form of a @Sound that is in the list of objects, select that Sound and click @Edit. A @SoundEditor window will appear on your screen. You can zoom in and scroll to see the various parts of the sound in detail. You can select a part of the sound by dragging with the mouse. To play a part of the sound, click on any of the rectangles below it. To move a selected part of the sound to another location, use #Cut and #Paste from the #Edit menu. You can open sound windows for more than one sound, and then cut, copy, and paste between the sounds, just as you are used to do with text and pictures in word processing programs. If your sound file is longer than a couple of minutes, or if you want to see and listen to both channels of a stereo sound, you may prefer to open it with @@Open long sound file...@. This puts a @LongSound object into the list. In this way, most of the sound will stay in the file on disk, and at most 60 seconds will be read into memory each time you play or view a part of it. To change these 60 seconds to something else, e.g. 500 seconds, choose ##LongSound prefs...# from the #Preferences submenu. This section describes how you can analyse the spectral content of an existing sound. You will learn how to use %spectrograms and %%spectral slices%. @@Intro 3.1. Viewing a spectrogram @@Intro 3.2. Configuring the spectrogram @@Intro 3.3. Querying the spectrogram @@Intro 3.4. The Spectrogram object @@Intro 3.5. Viewing a spectral slice @@Intro 3.6. Configuring the spectral slice @@Intro 3.7. The Spectrum object To see the spectral content of a sound as a function of time, select a @Sound or @LongSound object and choose @Edit. A @SoundEditor or @LongSoundEditor window will appear on your screen. In the entire bottom half of this window you will see a greyish image, which is called a %spectrogram. If you do not see it, choose @@Show spectrogram@ from the #Spectrogram menu. The spectrogram is a @@spectro-temporal representation@ of the sound. The horizontal direction of the spectrogram represents @time, the vertical direction represents @frequency. The time scale of the spectrogram is the same as that of the waveform, so the spectrogram reacts to your zooming and scrolling. To the left of the spectrogram, you see the frequency scale. The frequency at the bottom of the spectrogram is usually 0 Hz (Hertz, cps, cycles per second), and a common value for the frequency at the top is 5000 Hz. Darker parts of the spectrogram mean higher energy densities, lighter parts mean lower energy densities. If the spectrogram has a dark area around a time of 1.2 seconds and a frequency of 4000 Hz, this means that the sound has lots of energy for those high frequencies at that time. For many examples of spectrograms of speech sounds, see the textbook by @@Ladefoged (2001)@ and the reference work by @@Ladefoged & Maddieson (1996)@. To see what time and frequency a certain part of the spectrogram is associated with, just click on the spectrogram and you will see the vertical time cursor showing the time above the waveform and the horizontal frequency cursor showing the frequency to the left of the spectrogram. This is one of the ways to find the %formant frequencies for vowels, or the main spectral peaks for fricatives. Hey, there are white vertical stripes at the edges! This is normal. Spectral analysis requires an %%analysis window% of a certain duration. For instance, if P\s{RAAT} wants to know the spectrum at 1.342 seconds, it needs to include information about the signal in a 10-milliseconds window around this time point, i.e., P\s{RAAT} will use signal information about all times between 1.337 and 1.347 seconds. At the very edges of the sound, this information is not available: if the sound runs from 0 to 1.8 seconds, no spectrum can be computed between 0 and 0.005 seconds or between 1.795 and 1.800 seconds. Hence the white stripes. If you do not see them immediately when you open the sound, zoom in on the beginning or end of the sound. When you zoom in on the middle of the sound (or anywhere not near the edges), the white stripes vanish. Suddenly you see only the time stretch between 0.45 and 1.35 seconds, for instance. But P\s{RAAT} did not forget what the signal looks like just outside the edges of this time window. To display a spectrogram from 0.45 to 1.35 seconds, P\s{RAAT} will use information from the wave form between 0.445 and 1.355 seconds, and if this is available, you will see no white stripes at the edges of the window. Hey, it changes when I scroll! This is normal as well, especially for long windows. If your visible time window is 20 seconds long, and the window takes up 1000 screen pixels horizontally, then you might think that every one-pixel-wide vertical line should represent the spectrum of 20 milliseconds of sound. But for reasons of computation speed, P\s{RAAT} will only show the spectrum of the part of the sound that lies around the centre of those 20 milliseconds, not the average or sum of all the spectra in those 20 milliseconds. This %undersampling of the underlying spectrogram is different from what happens in the drawing of the wave form, where a vertical black line connects the minimum and maximum amplitude of all the samples that fall inside a screen pixel. We cannot do something similar for spectrograms. And since scrolling goes by fixed time steps (namely, 5 percent of the duration of the visible window), rather than by a whole number of screen pixels, the centres of the pixels will fall in different parts of the spectrogram with each scroll. Hence the apparent changes. If your visible window is shorter than a couple of seconds, the scrolling spectrogram will appear much smoother. The darkness of the spectrogram will also change when you scroll, because the visible part with the most energy is defined as black. When a very energetic part of the signal scrolls out of view, the spectrogram will turn darker. The next section will describe a way to switch this off. With @@Spectrogram settings...@ from the #Spectrogram menu, you can determine how the spectrogram is computed and how it is displayed. These settings will be remembered across Praat sessions. All these settings have standard values ("factory settings"), which appear when you click ##Standards#. %%View range% (Hz) the range of frequencies to display. The standard is 0 Hz at the bottom and 5000 Hz at the top. If this maximum frequency is higher than the Nyquist frequency of the Sound (which is half its sampling frequency), some values in the spectrogram will be zero, and the higher frequencies will be drawn in white. You can see this if you record a Sound at 44100 Hz and set the view range from 0 Hz to 25000 Hz. %%Window length the duration of the analysis window. If this is 0.005 seconds (the standard), Praat uses for each frame the part of the sound that lies between 0.0025 seconds before and 0.0025 seconds after the centre of that frame (for Gaussian windows, Praat actually uses a bit more than that). The window length determines the %bandwidth of the spectral analysis, i.e. the width of the horizontal line in the spectrogram of a pure sine wave (see below). For a Gaussian window, the -3 dB bandwidth is 2*sqrt(6*ln(2))/(\pi*%%Window length%), or 1.2982804 / %%Window length%. To get a `broad-band' spectrogram (bandwidth 260 Hz), keep the standard window length of 5 ms; to get a `narrow-band' spectrogram (bandwidth 43 Hz), set it to 30 ms (0.03 seconds). The other window shapes give slightly different values. %%Dynamic range% (dB) All values that are more than %%Dynamic range% dB below the maximum (perhaps after dynamic compression, see @@Advanced spectrogram settings...@) will be drawn in white. Values in-between have appropriate shades of grey. Thus, if the highest peak in the spectrogram has a height of 30 dB/Hz, and the dynamic range is 50 dB (which is the standard value), then values below -20 dB/Hz will be drawn in white, and values between -20 dB/Hz and 30 dB/Hz will be drawn in various shades of grey. The bandwidth To see how the window length influences the bandwidth, first create a 1000-Hz sine wave with @@Create Sound...@ by typing $$1/2 * sin (2*pi*1000*x)$ as the formula, then click #Edit. The spectrogram will show a horizontal black line. You can now vary the window length in the spectrogram settings and see how the thickness of the lines varies. The line gets thinner if you raise the window length. Apparently, if the analysis window comprises more periods of the wave, the spectrogram can tell us the frequency of the wave with greater precision. To see this more precisely, create a sum of two sine waves, with frequencies of 1000 and 1200 Hz. the formula is $$1/4 * sin (2*pi*1000*x) + 1/4 * sin (2*pi*1200*x)$. In the editor, you will see a single thick band if the analysis window is short (5 ms), and two separate bands if the analysis window is long (30 ms). Apparently, the frequency resolution gets better with longer analysis windows. So why don't we always use long analysis windows? The answer is that their time resolution is poor. To see this, create a sound that consists of two sine waves and two short clicks. The formula is $$0.02*(sin(2*pi*1000*x)+sin(2*pi*1200*x)) + (col=10000)+(col=10200)$. If you view this sound, you can see that the two clicks will overlap in time if the analysis window is long, and that the sine waves overlap in frequency if the analysis window is short. Apparently, there is a trade-off between time resolution and frequency resolution. One cannot know both the time and the frequency with great precision. Advanced settings The Spectrum menu also contains @@Advanced spectrogram settings...@. Optimization %%Number of time steps% the maximum number of points along the time window for which P\s{RAAT} has to compute the spectrum. If your screen is not wider than 1200 pixels, then the standard of 1000 is appropriate, since there is no point in computing more than one spectrum per one-pixel-wide vertical line. If you have a really wide screen, you may see improvement if you raise this number to 1500. %%Number of frequency steps% the maximum number of points along the frequency axis for which P\s{RAAT} has to compute the spectrum. If your screen is not taller than 768 pixels, then the standard of 250 is appropriate, since there is no point in computing more than one spectrum per one-pixel-height horizontal line. If you have a really tall screen, you may see improvement if you raise this number. For purposes of computation speed, Praat may decide to change the time step and the frequency step. This is because the time step never needs to be smaller than 1/(8\Vr\pi) of the window length, and the frequency step never needs to be smaller than (\Vr\pi)/8 of the inverse of the window length. For instance, if the window length is 30 ms, the actual time step will never be less than 30/(8\Vr\pi) = 2.116 ms. And if the window length is 5 ms, the actual frequency step will never be less than (\Vr\pi)/8/0.005 = 44.32 Hz. Spectrogram analysis settings %%Method there is currently only one method available in this window for computing a spectrum from a sound: the Fourier transform. %%Window shape the shape of the analysis window. To compute the spectrum at, say, 3.850 seconds, samples that lie close to 3.850 seconds are given more weight than samples further away. The relative extent to which each sample contributes to the spectrum is given by the window shape. You can choose from: Gaussian, Square (none, rectangular), Hamming (raised sine-squared), Bartlett (triangular), Welch (parabolic), and Hanning (sine-squared). The Gaussian window is superior, as it gives no %sidelobes in your spectrogram (see below); it analyzes a factor of 2 slower than the other window shapes, because the analysis is actually performed on twice as many samples per frame. Sidelobes; anybody wants to win a cake? The Gaussian window is the only shape that we can consider seriously as a candidate for the analysis window. To see this, create a 1000-Hz sine wave with @@Create Sound...@ by typing $$1/2 * sin (2*pi*1000*x)$ as the formula, then click #Edit. If the window shape is Gaussian, the spectrogram will show a horizontal black line. If the window shape is anything else, the spectrogram will show many horizontal grey lines (%sidelobes), which do not represent anything that is available in the signal. They are artifacts of the window shapes. We include these other window shapes only for pedagogical purposes and because the Hanning and Hamming windows have traditionally been used in other programs before computers were as fast as they are now (a spectrogram is computed twice as fast with these other windows). Several other programs still use these inferior window shapes, and you are likely to run into people who claim that the Gaussian window has disadvantages. We promise such people a large cake if they can come up with sounds that look better with Hanning or Hamming windows than with a Gaussian window. An example of the reverse is easy to find; we have just seen one. Spectrogram blackness settings %%Autoscaling% %%Maximum% (dB/Hz) all parts of the spectrogram that have a power above %maximum (after preemphasis) will be drawn in black. The standard maximum is 100 dB/Hz, but if %autoscaling is on (which is the standard), P\s{RAAT} will use the maximum of the visible part of the spectrogram instead; this ensures that the window will always look well, but it also means that the blackness of a certain part of the spectrogram will change as you scroll. %%Preemphasis% (dB/octave) determines the steepness of a high-pass filter, i.e., how much the power of higher frequencies will be raised before drawing, as compared to lower frequencies. Since the spectral slope of human vowels is approximately -6 dB per octave, the standard value for this setting is +6 dB per octave, so that the spectrum is flattened and the higher formants look as strong as the lower ones. When you raise the preemphasis, frequency bands above 1000 Hz will become darker, those below 1000 Hz will become lighter. %%Dynamic compression determines how much stronger weak spectra should be made before drawing. Normally, this parameter is between 0 and 1. If it is 0 (the standard value), there is no dynamic compression. If it is 1, all spectra will be drawn equally strong, i.e., all of them will contain frequencies that are drawn in black. If this parameter is 0.4 and the global maximum is at 80 dB, then a spectrum with a maximum at 20 dB (which will normally be drawn all white if the dynamic range is 50 dB), will be raised by 0.4 * (80 - 20) = 24 dB, so that its maximum will be seen at 44 dB (thus making this frame visible). If you click anywhere inside the spectrogram, a cursor cross will appear, and you will see the time and frequency in red at the top and to the left of the window. To see the time in the Info window, choose ##Get cursor# from the #Query menu or press the F6 key. To see the frequency in the Info window, choose ##Get frequency# from the #Spectrum menu. To query the power of the spectrogram at the cursor cross, choose ##Get spectral power at cursor cross# from the #Spectrum menu or press the F9 key. The Info window will show you the power density, expressed in Pascal^2/Hz. To print a spectrogram, or to put it in an EPS file or on the clipboard for inclusion in your word processor, you first have to create a @Spectrogram object in the @@List of Objects@. You do this either by choosing ##Extract visible spectrogram# from the Spectrum menu in the SoundEditor or TextGridEditor window, or by selecting a Sound object in the list and choosing @@Sound: To Spectrogram...@ from the #Spectrum menu. In either case, a new Spectrogram object will appear in the list. To draw this Spectrogram object to the @@Picture window@, select it and choose the @@Spectrogram: Paint...@ command. From the Picture window, you can print it, save it to an EPS file, or copy it to the clipboard. With ##View spectral slice# from the #Spectrum menu in the @SoundEditor and the @TextGridEditor, you can see the frequency spectrum at the time cursor or the average frequency spectrum in the time selection. Spectral slice at the cursor If you click anywhere in the wave form of the SoundEditor or TextGridEditor windows, a cursor will appear at that time. If you then choose ##View spectral slice#, P\s{RAAT} will create a @Spectrum object named %slice in the Objects window and show it in a @SpectrumEditor window. In this way, you can inspect the frequency contents of the signal around the cursor position. Spectral slice from a selection If you drag the mouse through the wave form of the SoundEditor or TextGridEditor windows, a @@time selection@ will appear. If you then choose ##View spectral slice#, P\s{RAAT} will again create a @Spectrum object named %slice in the Objects window and show it in a @SpectrumEditor window. In this way, you can inspect the frequency contents of the signal in the selection. What P\s{RAAT} does precisely, depends on your Spectrogram settings. Suppose that the %%window length% setting is 0.005 seconds (5 milliseconds). If the %%window shape% is not Gaussian, P\s{RAAT} will extract the part of the sound that runs from 2.5 milliseconds before the cursor to 2.5 ms after the cursor. P\s{RAAT} then multiplies this 5 ms long signal by the window shape, then computes a spectrum with the method of @@Sound: To Spectrum...@, which is put into the Objects window and opened in an editor window. If the window shape is Gaussian, P\s{RAAT} will extract a part of the sound that runs from 5 milliseconds before the cursor to 5 ms after the cursor. The spectrum will then be based on a `physical' window length of 10 ms, although the `effective' window length is still 5 ms (see @@Intro 3.2. Configuring the spectrogram@ for details). What P\s{RAAT} does precisely, again depends on the %%window shape% of your Spectrogram settings. Suppose that your selection is 50 ms long. P\s{RAAT} will extract the entire selection, then multiply this 50 ms long signal by the window shape, then compute a spectrum, put it into the Objects window and open it an editor window. This procedure is equivalent to choosing ##Extract windowed selection...# (with a %%relative duration% of 1.0), followed by ##To Spectrum...# (with %fast switched on), followed by #Edit. If the window is Gaussian, P\s{RAAT} will still only use the selection, without doubling its duration. This means that the spectrum that you see in this case will mainly be based on the centre half of the selection, and the signal near the edges will be largely ignored. To compute a Fourier frequency spectrum of an entire sound, select a @Sound object and choose @@Sound: To Spectrum...|To Spectrum...@ from the #Spectrum menu. A new @Spectrum object will appear in the @@List of Objects@. To view or modify it (or listen to its parts), click @Edit. To print it, choose one of the #Draw commands to draw the Spectrum object to the @@Picture window@ first. This section describes how you can analyse the pitch contour of an existing sound. @@Intro 4.1. Viewing a pitch contour @@Intro 4.2. Configuring the pitch contour @@Intro 4.3. Querying the pitch contour @@Intro 4.4. The Pitch object To see the pitch contour of an existing sound as a function of time, select a @Sound or @LongSound object and choose @Edit. A @SoundEditor window will appear on your screen. The bottom half of this window will contain a pitch contour, drawn as a blue line or as a sequence of blue dots. If you do not see the pitch contour, choose @@Show pitch@ from the #Pitch menu. To the right of the window, you may see three pitch values, written with blue digits: at the bottom, you see the floor of the viewable pitch range, perhaps 75 Hz; at the top, you see the ceiling of the pitch range, perhaps 600 Hz; and somewhere in between, you see the pitch value at the cursor, or the average pitch in the selection. With @@Pitch settings...@ from the #Pitch menu, you can determine how the pitch contour is displayed and how it is computed. These settings will be remembered across Praat sessions. All these settings have standard values ("factory settings"), which appear when you click #Standards. The %%pitch range% setting This is the most important setting for pitch analysis. The standard range is from 75 to 500 Hertz, which means that the pitch analysis method will only find values between 75 and 500 Hz. The range that you set here will be shown to the right of the analysis window. For a male voice, you may want to set the floor to 75 Hz, and the ceiling to 300 Hz; for a female voice, set the range to 100-500 Hz instead. For creaky voice you will want to set it much lower than 75 Hz. Here is why you have to supply these settings. If the pitch floor is 75 Hz, the pitch analysis method requires a 40-millisecond analysis window, i.e., in order to measure the F0 at a time of, say, 0.850 seconds, P\s{RAAT} needs to consider a part of the sound that runs from 0.830 to 0.870 seconds. These 40 milliseconds correspond to 3 maximum pitch periods (3/75 = 0.040). If you set the pitch floor down to 25 Hz, the analysis window will grow to 120 milliseconds (which is again 3 maximum pitch periods), i.e., all times between 0.790 and 0.910 seconds will be considered. This makes it less easy to see fast F0 changes. So setting the floor of the pitch range is a technical requirement for the pitch analysis. If you set it too low, you will miss very fast F0 changes, and if you set it too high, you will miss very low F0 values. For children's voices you can often use 200 Hz, although 75 Hz will still give you the same time resolution as you get for the males. The %units setting This setting determines the units of the vertical pitch scale. Most people like to see the pitch range in Hertz, but there are several other possibilities. The Pitch menu also contains @@Advanced pitch settings...@. A command in the #View menu of the @SoundEditor and @TextGridEditor to determine the time interval between consecutive measurements of pitch, formants, and intensity. Automatic time steps It is recommended that you set the %%Time step strategy% to #Automatic. In this way, Praat computes just enough pitch, formant, and intensity values to draw reliable pitch, formant, and intensity contours. In general, Praat will compute 4 values within an analysis window ("four times oversampling"). As described in @@Sound: To Pitch...@, Praat's standard time step for pitch analysis is 0.75 divided by the pitch floor, e.g., if the pitch floor is 75 Hz, the time step will be 0.01 seconds. In this way, there will be 4 pitch measurements within an analysis window, which is 3 / (75 Hz) = 40 milliseconds long. As described in @@Sound: To Formant (burg)...@, Praat's standard time step for formant measurements is the %%Window length% divided by 4, e.g. if the window length is 0.025 seconds, the time step will be 6.25 milliseconds. As described in @@Sound: To Intensity...@, Praat's standard time step for intensity measurements is 0.8 divided by the pitch floor, e.g. if the pitch floor is 75 Hz, the time step will be 10.6666667 milliseconds. In this way, there will be 4 intensity measurements within an intensity analysis window, which is 3.2 / (75 Hz) = 42.6666667 milliseconds long. Fixed time step You can override the automatic time step by setting the %%Time step strategy% to #Fixed. The %%Fixed time step% setting then determines the time step that Praat will use: if you set it to 0.001 seconds, Praat will compute pitch, formant, and intensity values for every millisecond. Beware that this can slow down the editor window appreciably, because this step is much smaller than usual values of the automatic time step (see above). Enlarging the time step to e.g. 0.1 seconds will speed up the editor window but may render the pitch, formant, and intensity curves less exact (they become %undersampled), which will influence your measurements and the locations of the pulses. If there are fewer than 2.0 pitch measurement points per analysis window, Praat will draw the pitch curve as separate little blue disks rather than as a continuous blue curve, in order to warn you of the undersampling. E.g. if the pitch floor is 75 Hz, Praat will draw the pitch curve as disks if the time step is greater than 0.02 seconds. View-dependent time step Another way to override the standard time step is by setting the %%Time step strategy% to ##View-dependent#. The %%Number of time steps per view% setting then determines the time step that Praat will use: if you set it to 100, Praat will always compute 100 pitch, formant, and intensity values within the view window. More precisely: if you zoom the view window to 3 seconds, Praat will show you 100 pitch, formant, and intensity points at distances of 0.03 seconds (or fewer than 100, if you are near the left or right edge of the signal). As with the %%Fixed time step% setting, Praat will draw the pitch as separate disks in case of undersampling. You may want to use this setting if you want the pitch curve to be drawn equally fast independently of the degree of zooming. A command in the #Pitch menu of the @SoundEditor or @TextGridEditor windows. Before changing the advanced pitch settings, make sure you understand @@Intro 4.2. Configuring the pitch contour@. View range different from analysis range Normally, the range of pitch values that can be seen in the editor window is equal to the range of pitch values that the analysis algorithm can determine. If you set the analysis range from 75 to 500 Hz, this will be the range you see in the editor window as well. If the pitch values in the curve happen to be between 350 and 400 Hz, you may want to zoom in to the 350-400 Hz pitch region. You will usually do this by changing the pitch range in the @@Pitch settings...@ dialog. However, the analysis range will also change in that case, so that the curve itself may change. If you do not want that, you can change the %%View range% settings from "0.0 (= auto)" \-- "0.0 (=auto)" to something else, perhaps "350" \-- "400". Pitch analysis settings For information about these, see @@Sound: To Pitch (ac)...@. The standard settings are best in most cases. For some pathological voices, you will want to set the voicing threshold to much less than the standard of 0.45, in order to get pitch values even in irregular parts of the signal. With @@Get pitch@ from the #Pitch menu in the @SoundEditor or @TextGridEditor, you get information about the pitch at the cursor or in the selection. If a cursor is visible in the window, ##Get pitch# writes to the @@Info window@ the linearly interpolated pitch at that time; if a time selection is visible inside the window, ##Get pitch# writes to the @@Info window@ the mean (average) pitch in the visible part of that selection; otherwise, ##Get pitch# writes the average pitch in the visible part of the sound. The pitch contour that is visible in the @SoundEditor or @TextGridEditor window, can be copied as a separate @Pitch object to the @@List of Objects@. To do this, choose @@Extract visible pitch contour@ from the #Pitch menu. Another way to get a separate Pitch object is to select a @Sound object in the list choose @@Sound: To Pitch...@ (preferred) or any of the other methods from the @@Periodicity menu@. To view and modify the contents of a Pitch object, select it and choose @Edit. This creates a @PitchEditor window on your screen. To save a pitch contour to disk, select the @Pitch object in the list and choose one of the commands in the @@Write menu@. Later on, you can read the saved file again with @@Read from file...@ from the @@Read menu@. To draw a @Pitch object to the @@Picture window@, select it and choose any of the commands in the @@Draw menu@. From the Picture window, you can print it, save it to an EPS file, or copy it to the clipboard for inclusion in your word processor. This section describes how you can analyse the formant contours of an existing sound. @@Intro 5.1. Viewing formant contours @@Intro 5.2. Configuring the formant contours @@Intro 5.3. Querying the formant contours @@Intro 5.4. The Formant object To see the formant contours of a sound as functions of time, select a @Sound or @LongSound object and choose @Edit. A @SoundEditor window will appear on your screen. The analysis part of this window will contain formant contours, drawn as red speckles. If you do not see the formant contours, choose @@Show formant@ from the #Formant menu. The formant analysis parameters, with you can set with the #Formant menu, are important. For a female voice, you may want to set the maximum frequency to 5500 Hz; for a male voice, set it to 5000 Hz instead. For more information about analysis parameters, see @@Sound: To Formant (burg)...@. With @@Get first formant@ from the Formant menu in the @SoundEditor or @TextGridEditor, you get information about the first formant at the cursor or in the selection. If there is a cursor, ##Get first formant# writes to the @@Info window@ the linearly interpolated first formant at that time. If there is a true selection, ##Get first formant# writes to the @@Info window@ the mean first formant in the visble part of that selection. The same goes for @@Get second formant@ and so on. The formant contours that are visible in the @SoundEditor or @TextGridEditor window, can be copied as a separate @Formant object to the @@List of Objects@. To do this, choose @@Extract visible formant contour@ from the Formant menu. Another way to get a separate Formant object is to select a @Sound object in the list choose @@Sound: To Formant (burg)...@ (preferred) or any of the other methods from the @@Formants & LPC menu@. Saving formant contours to disk To save formant contours to disk, select the @Formant object in the list and choose one of the commands in the @@Write menu@. Drawing formant contours To draw a @Formant object to the @@Picture window@, select it and choose any of the commands in the @@Draw menu@. From the Picture window, you can print it, save it to an EPS file, or copy it to the clipboard for inclusion in your word processor. This section describes how you can analyse the intensity contour of an existing sound. @@Intro 6.1. Viewing an intensity contour @@Intro 6.2. Configuring the intensity contour @@Intro 6.3. Querying the intensity contour @@Intro 6.4. The Intensity object To see the intensity contour of a sound as a function of time, select a @Sound or @LongSound object and choose @Edit. A @SoundEditor window will appear on your screen. The analysis part of this window will contain an intensity contour, drawn as a yellow or green line (choose ##Show intensity# from the #Intensity menu if it is not visible). This also works in the @TextGridEditor. With ##Intensity settings...# from the #Intensity menu, you can control how the intensity contour is computed and how it is shown. The view range By changing these two numbers you can set the vertical scale. The standard setting is from 50 to 100 dB, but if you are interested in the power of the background noise you may want to set it to the range from 0 to 100 dB. The averaging method Averaging is what occurs if you make a @@time selection@ (rather than setting the cursor at a single time). The green number in dB to the left or right side of the intensity contour will show the average intensity in the selection. The same value is what you get when choosing ##Get intensity# from the #Intensity menu. You can choose any of the three averaging methods available for @@Intensity: Get mean...@, or choose for the #median value in the selection. Pitch floor The intensity curve is %smoothed, since you usually do not want the intensity curve to go up and down with the intensity variations within a pitch period. To avoid such pitch-synchronous variations, the intensity at every time point is a weighted average over many neighbouring time points. The weighting is performed by a Gaussian (`double Kaiser') window that has a duration that is determined by the ##Minimum pitch# setting (see @@Intro 4.2. Configuring the pitch contour@). To see more detail than usual, raise the minimum pitch; to get more smoothing than usual, lower it. For more information, see @@Sound: To Intensity...@. Subtract mean pressure or not? Many microphones, microphone preamplifiers, or other components in the recording system can add a constant level to the air pressure (a %%DC offset%). You can see this at quiet locations in the wave form, where the average pressure is not zero but the background noise hovers about some non-zero value. You will usually not want to take this constant pressure seriously, i.e. the intensity curve should normally not take into account the energy provided by this constant pressure level. If you switch on the ##Subtract mean pressure# switch (whose standard setting is also on), the intensity value at a time point is computed by first subtracting the mean pressure around this point, and then applying the Gaussian window. To ask for the intensity at the cursor, or the average intensity in the visible part of the selection, choose ##Get intensity# from the #Intensity menu or press the F11 key. You get the same value in dB that is visible to the left or right side of the intensity curve, but with more digits. To print an intensity contour, or to put it in an EPS file or on the clipboard for inclusion in your word processor, you first have to create an @Intensity object in the @@List of Objects@. You do this either by choosing ##Extract visible intensity contour# from the #Intensity menu in the SoundEditor or TextGridEditor window, or by selecting a Sound object in the list and choosing @@Sound: To Intensity...@. In either case, a new Intensity object will appear in the list. To draw the Intensity object to the @@Picture window@, select it and choose ##Draw...#. From the Picture window, you can print it, save it to an EPS file, or copy it to the clipboard. You can annotate existing @Sound objects and sound files (@LongSound objects). The labelling data will reside in a @TextGrid object. This object is separate from the sound, which means that you will often see two objects in the list: a Sound or LongSound, and a TextGrid. Creating a TextGrid You create a new empty TextGrid from the Sound or LongSound with @@Sound: To TextGrid...@ or @@LongSound: To TextGrid...@ from the #Annotate menu. In this way, the time domain of the @TextGrid will automatically equal that of the sound (if you choose @@Create TextGrid...@ from the @@New menu@ instead, you will have to supply the time domain by yourself). When you create a TextGrid, you specify the names of the %tiers. For instance, if you want to segment the sound into words and into phonemes, you may want to create two tiers and call them "words" and "phonemes" (you can easily add, remove, and rename tiers later). Since both of these tiers are %%interval tiers% (you label the intervals between the word and phoneme boundaries, not the boundaries themselves), you specify "phonemes words" for %%Tier names%, and you leave the %%Point tiers% empty. View and edit You can edit a TextGrid object all by itself, but you will normally want to see the sound in the editor window as well. To achieve this, you select both the Sound (or LongSound) and the TextGrid, and click @Edit. A @TextGridEditor will appear on your screen. Like the Sound editor, the TextGrid editor will show you a spectrogram, a pitch contour, a formant contour, and an intensity contour. This editor will allow you to add, remove, and edit labels, boundaries, and tiers. Under Help in the TextGridEditor, you will find the @TextGridEditor manual page. You are strongly advised to read it, because it will show you how you can quickly zoom (drag the mouse), play (click a rectangle), or edit a label (just type). Save You will normally write the TextGrid to disk with @@Write to text file...@ or @@Write to short text file...@. It is true that @@Write to binary file...@ will also work, but the others give you a file you can read with any text editor. However you saved it, you can read the TextGrid into Praat later with @@Read from file...@. @@Intro 8.1. Manipulation of pitch @@Intro 8.2. Manipulation of duration @@Intro 8.3. Manipulation of intensity To modify the pitch contour of an existing @Sound object, you select this @Sound and click ##To Manipulation#. A @Manipulation object will then appear in the list. You can then click @Edit to raise a @ManipulationEditor, which will show the pitch contour (@PitchTier) as a series of thick dots. To reduce the number of dots, choose ##Stylize pitch (2 st)# from the #Pitch menu; it will then be easy to drag the dots about the time-pitch area. If you click any of the rectangles (or choose any of the #Play commands from the #View menu), you will hear the modified sound. By shift-clicking, you will hear the original sound. To get the modified sound as a separate object, choose ##Publish resynthesis# from the @@File menu@. If you modify the duration curve as well (see @@Intro 8.2. Manipulation of duration@), the modified sound will be based on the modified pitch and duration. Cloning a pitch contour To use the pitch contour of one Manipulation object as the pitch contour of another Manipulation object, you first choose ##Extract pitch tier# for the first Manipulation object, then select the resulting PitchTier object together with the other Manipulation object (e.g. by a click on the PitchTier and a Command-click on the Manipulation), and choose ##Replace pitch tier#. Precise manipulation of pitch If you know exactly what pitch contour you want, you can create an empty PitchTier with @@Create PitchTier...@ from the New menu, then add points with @@PitchTier: Add point...@. For instance, suppose you want to have a pitch that falls from 350 to 150 Hz in one second. You create the PitchTier, then add a point at 0 seconds and a frequency of 350 Hz, and a point at 1 second with a frequency of 150 Hz. You can put this PitchTier into a Manipulation object in the way described above. You can use P\s{RAAT} to modify the relative durations in an existing sound. First, you select a @Sound object and click "To Manipulation". A @Manipulation object will then appear in the list. You can then click @Edit to raise a @ManipulationEditor, which will show an empty @DurationTier. You can add targets to this tier by choosing "Add duration point at cursor" from the "Dur" menu. The targets will show up as green dots, which you can easily drag about the duration area. If you click any of the rectangles (or choose any of the @Play commands from the @View menu), you will hear the modified sound. By shift-clicking, you will hear the original sound. If you modify the pitch curve as well (see @@Intro 8.1. Manipulation of pitch@), the modified sound will be based on the modified duration and pitch. Precise manipulation of duration If you know exactly the times and relative durations, it is advisable to write a script (see @Scripting). Suppose, for instance, that you have a 355-ms piece of sound, and you want to shorten the first 85 ms to 70 ms, and the remaining 270 ms to 200 ms. In your first 85 ms, your relative duration should be 70/85, and during the last 270 ms, it should be 200/270. The DurationTier does linear interpolation, so it can only be approximate these precise times, but fortunately to any precision you like: Create DurationTier... shorten 0 0.085+0.270 Add point... 0.000 70/85 Add point... 0.084999 70/85 Add point... 0.085001 200/270 Add point... 0.0355 200/270 To put this DurationTier back into a Manipulation object, you select the two objects together (e.g. a click on the DurationTier and a Command-click on the Manipulation), and choose ##Replace duration tier#. You can modify the intensity contour of an existing sound. While the pitch and duration of a sound can be modified with the @ManipulationEditor (see @@Intro 8.1. Manipulation of pitch@ and @@Intro 8.2. Manipulation of duration@), the modification of the intensity curve is done in a different way. You can create an @IntensityTier with the command @@Create IntensityTier...@ from the @@New menu@. With @Edit, you can add points to this tier. You can then multiply this tier with a sound, by selecting the @Sound and the IntensityTier together and clicking @@Sound & IntensityTier: Multiply|Multiply@. The points in the IntensityTier thus represent %relative intensities in dB. The manipulation of formant contours cannot be as straightforward as the manipulation of pitch, duration, or intensity contours. See the @@Source-filter synthesis@ tutorial for an explanation of how formants can be modified in Praat. See @@Intro 7. Annotation@. A list in the left-hand part of the @@Object window@. If you select one or more @objects in this list, the possible actions that you can perform with the selected objects will appear in the @@Dynamic menu@. How to select objects To select one object (and deselect all the others), click on the object. To extend the selection, drag the mouse (Unix, Windows) or use Shift-click (all systems). To change the selection of one object (without changing the others), use Control-click (Unix, Windows) or Command-click (Macintosh). This page is about how you see the Praat shell and work with it in an interactive session. The Praat shell on Macintosh^\re Most of the %look is Macintosh: rounded buttons, a menu bar at the top. Some of the look is Motif^\tm: a menu bar in every window. Most of the %feel is Macintosh: only one window active simultaneously. The Praat shell on Windows^\re 95 and NT Most of the look and feel is Windows, though all windows are separate overlapping windows, instead of children of a large application window. The Praat shell on the X Window system From every computer with OSF/Motif, you can run the Praat shell on every X server in the world. If your program is %praat, you just type: praat -motif With this command, you will always get the same old Motif look and feel. Many systems, however, have their own favoured look and feel. For this reason, the Praat shell recognizes several client computers: if you just type praat (or double-click on the %praat icon), the Praat shell assumes that the X server matches the client computer. The following client computers are recognized: SGI, Sun, HP. On other computers (Linux, IBM RS6000), typing $praat will give the same look and feel as typing $$praat -motif$. The Praat shell on SGI On a Silicon Graphics^\re Iris^\tm computer, typing or double-clicking the %praat icon, will give you either of the following look-and-feel styles: \bu the native SGI "Indigo Magic" style, with lighting buttons and user-controllable color schemes, if available; \bu the plain Motif style, if color schemes are not available (to find this out, the Praat shell checks the existence of the color-scheme browser %%/usr/sbin/schemebr% on the client side). You can force the Praat shell to use the SGI style with praat -sgi or the Motif style with The Praat shell on Sun On a Sun computer, typing will give you the look and feel of Sun4, Solaris, or the Common Desktop Environment (CDE). These styles use non-standard fonts for their menus, buttons, and texts. Whether CDE is available, is determined by checking the existence of %%/usr/dt/bin/dtaction%. You can force any of these styles with $$praat -solaris$, $$praat -sun4$, or $$praat -cde$. The Praat shell on HP On a Hewlett-Packard computer, typing will give you the look and feel of the HP version of the Common Desktop Environment. If you do not have that, try $$praat -motif$. Running the Praat shell across a network Like most X programs, you can run the Praat program across a network, with the executable running on the %client computer, and yourself sitting at a computer that acts as an %%X server%. For this to work, you will have to take care of two things: \bu Tell the client computer to use the server %display. If you use %telnet (but not %rlogin), this will be done automatically for you, because %telnet propagates the DISPLAY environment variable. Otherwise, if you are sitting at %%indigo3.uni-franeker.nl%, you type the following line to your remote login shell: setenv DISPLAY indigo3.uni-franeker.nl:0 \bu Your X server should grant the client computer access to its display. This may sometimes be automatic (e.g., if the server allows the whole world to connect to it). Otherwise, if the client is %%distant1.uni-harderwijk.nl%, you type the following line to your local shell: xhost +distant1.uni-harderwijk.nl Finally, you type $$praat -motif$ to your remote login shell, and the two windows will appear on your screen. If you run the Praat shell from an SGI client across a network on an X server (a PC or Sun, for example), the normal $praat command will probably work and give you the native SGI look and feel. This works because the SGI style only uses fonts that are available everywhere. If your X server is a Sun with Solaris, you can probably use the Motif, and Solaris or CDE styles. Likewise, if you run %praat from a different machine on a HP X server, you may try $$praat -hp$. If you run %praat from a Sun client on an X server, you will probably use $$praat -motif$. Resource files? Many X Windows applications work with %%client-side% resource files, which describe the fonts etc. that they need. However, as the fonts are server-dependent, changing to a different X server will often require you to change the resource file %%on the client side%, unless you only use fonts that are available on all systems (like Helvetica and Times). However, your application may not adhere to any native look-and-feel strategy then. Incorporating all resource files into the application, as done in the Praat shell, solves this problem. Locally, you just type $praat, and across a network you use one of the explicit look-and-feel options. In the Praat shell, the user-controllability of window sizes and fonts, which is sometimes expressed by editing resource files, is implemented by a hidden mechanism, which remembers across sessions the changes made by the user while the application is running. The ##New menu# is one of the menus in the @@Object window@. You use this menu to create new objects from scratch. It contains the following commands: \bu @@Record mono Sound...@ \bu @@Record stereo Sound...@ \bu @@Create Sound...@ (from a formula) \bu @@Create Sound from tone complex... \bu @@Create Sound from gamma-tone... \bu @@Create Sound from Shepard tone... \bu @@Create Matrix...@ (from a formula) \bu @@Create simple Matrix...@ (from a formula) \bu @@Create empty PointProcess...@ \bu @@Create Poisson process...@ \bu @@Create PitchTier...@ \bu @@Create DurationTier...@ \bu @@Create IntensityTier...@ \bu @@Create FormantTier...@ \bu @@Create Strings as file list...@ \bu @@Create TextGrid...@ \bu @@OT learning@ tutorial \bu @@Create tongue-root grammar...@ To create new objects from files on disk, use the @@Read menu@ instead. Objects can also often be create from other objects, with commands that start with ##To#. One of the two main windows in the P\s{RAAT} program. Subdivision To the left: the @@List of Objects@. To the right: the @@Dynamic menu@. Fixed buttons The following buttons appear below the List of Objects: \bu @@Rename... \bu @@Info \bu @@Copy... \bu @@Remove \bu @@Inspect Menus The Object window contains several fixed menus: the #Praat, #New, #Read, and #Help menus. It also contains the #Write menu, whose contents vary with the kinds of selected objects, and must, therefore, be considered part of the dynamic menu. The Praat menu \bu (@@Run script...@) \bu @@New Praat script@: creates an empty @@ScriptEditor@ \bu @@Open Praat script...@: creates a @@ScriptEditor@ with a script from disk \bu The ##Goodies submenu#: for doing things (like using the Calculator) that do not create new objects and do not depend on the kinds of selected objects. \bu The ##Preferences submenu#: for program-wide preferences, like audio input and output settings. \bu ##Buttons...#: raises a @@ButtonEditor@ \bu (@@Add menu command...@) \bu (@@Add action command...@) \bu @@Quit Other menus \bu The @@New menu@: for creating objects from scratch. \bu The @@Read menu@: for reading objects from file into memory. \bu The @@Write menu@: for writing objects from memory to file. \bu The ##Help menu#: for viewing the manual. This menu contains commands for analysing the pitch contour of the selected Sound: @@Sound: To Pitch... @@Sound: To Pitch (ac)... @@Sound: To Pitch (cc)... @@Sound: To Harmonicity (cc)... @@Sound: To Harmonicity (ac)... A command in the Pitch menu of the @SoundEditor and @TextGridEditor windows. See @@Intro 4.2. Configuring the pitch contour@. A command that is available if you select a @Sound, @Pitch, or @PointProcess object. It gives you an acoustic representation of the selected object, if your loudspeakers are on and you did not "mute" your computer sound system. A Play button is also available in the @SoundRecorder window and in the @View menu of the @SoundEditor or @TextGridEditor. In the editors, you will usually play a sound by clicking on any of the rectangles around the data. Query commands give you information about objects. Most query commands start with the word #%Get or sometimes the word #%Count. You will find these commands in two places: under the #Query menu that usually appears if you select an @@Objects|object@ in the list, and in the #Query menus of the @editors. If you click a query command, the answer will be written to the @@Info window@. In a script, you can still use query commands to write the information to the Info window but you can also use any query command to put the information into a variable. (see @@Scripting 6.4. Query commands@). In such a case, the value will not be written into the Info window. Query commands in the Praat program The Praat program contains the following query commands: One of the menus in most @editors. One of the commands in the @@Praat menu@. To leave the program. All @objects not written to a file will be lost. However, file-based objects (like large lexica) will be saved correctly. Usage To save your data to a disk file before quitting, choose a command from the @@Write menu@. One of the commands in the @@Read menu@. To read one or more @objects from a file on disk. Many kinds of files are recognized: 1. Text files that are structured as described under @@Write to text file...@; these can contain an object of any class, or a collection of objects. 2. Files that were produced by @@Write to binary file...@ (any class). 3. Files in a LISP text format (only for classes that can be written to a LISP file). 4. Files that were made recognizable by the libraries built on Praat. For instance, the phonetics library adds recognizers for many kinds of sound files. If the file contains more than one object, these objects will appear in the list, and their names will be the same as the names that they had when they were saved with ##Write to text file...# or ##Write to binary file...#. Examples \bu If the file contains only one Pitch object and is called "hallo.pit", an object with the name "Pitch hallo" will appear in the list of objects. You may have more objects with the same name. \bu If the file contains one object of class Pitch, named "hallo", and one object of class Polygon, named "kromme", there will appear two objects in the list, called "Pitch hallo" and "Polygon kromme". One of the menus in the @@Object window@. With the Read menu, you read one or more @objects from a file on disk into memory. The resulting object(s) will appear in the @@List of Objects@. The Read menu contains the command @@Read from file...@, which recognizes most file types, and perhaps several other commands for reading unrecognizable file types (e.g., raw sound data), or for interpreting known file types in a different way (e.g., reading two sounds from a stereo sound file, which is normally read as mono): You can choose this command after selecting one or more @objects in the list. The selected objects will permanently disappear from the list, and the computer memory that they occupied will be freed. To save your data before removing, choose a command from the @@Write menu@. You can give the selected object a new name. If you type special symbols or spaces, the Object window will replace them with underscores. One of the two %forks of a Macintosh file (the other is the %%data fork%). If a Macintosh file is moved to another system directly, the resource fork is lost. To backup your Macintosh files, use compression, for instance with #DropStuff\tm. See @@Intro 5. Formant analysis@. See @@Intro 6. Intensity analysis@. See @@Intro 4. Pitch analysis@. One of the commands in the Pulses menu of the @SoundEditor and the @TextGridEditor. See @Voice. See @@Intro 3. Spectral analysis@. This tutorial describes how you can do acoustic synthesis with P\s{RAAT}. It assumes that you are familiar with the @Intro. 1. The source-filter theory of speech production The source-filter theory (@@Fant (1960)|Fant 1960@) hypothesizes that an acoustic speech signal can be seen as a %source signal (the glottal source, or noise generated at a constriction in the vocal tract), %filtered with the resonances in the cavities of the vocal tract downstream from the glottis or the constriction. The %%Klatt synthesizer% (@@Klatt & Klatt (1990)|Klatt & Klatt 1990@), for instance, is based on this idea. In the Praat program, you can create a %source signal from scratch of from an existing speech signal, and you can create a %filter from scrtach or extract it from an existing speech signal. You can manipulate (change, adapt) both the source and the filter before doing the actual synthesis, which combines the two. @@Source-filter synthesis 1. Creating a source from pitch targets @@Source-filter synthesis 2. Filtering a source @@Source-filter synthesis 3. The ba-da continuum @@Source-filter synthesis 4. Using existing sounds Creating a glottal source signal for speech synthesis involves creating a @PointProcess, which is a series of time points that should represent the exact moments of glottal closure. You may want to start with creating a well-defined pitch contour. Suppose you want to create a sound with a duration of half a second with a pitch that falls from 300 to 200 Hz during that time. You first create an empty @PitchTier by choosing @@Create PitchTier...@ from the #New menu (I call this PitchTier "empty" because it does not contain any pitch information yet); you may want to name the PitchTier "source" and have it start at 0 seconds and end at 0.5 seconds. Once the PitchTier exists and is selected, you can choose @@PitchTier: Add point...@ from the #Modify menu repeatedly to add pitch points (pitch targets) at certain times. You would add a pitch point of 300 Hz at time 0.0 and a pitch point of 200 Hz at time 1.0. This whole mouse-clicking procedure can be abbreviated as follows (if you want to automate this procedure in a script, it would look exactly like this): Create PitchTier... source 0 0.5 Add point... 0 300 Add point... 0.5 200 If you #Draw or #Edit this PitchTier, you can see that the pitch curve falls linearly from 300 to 200 Hz during its time domain. You can hear the falling pitch by choosing ##Play pulses#, #Hum, or ##Play sine#. From this PitchTier, you can create a @PointProcess with @@PitchTier: To PointProcess@. The resulting PointProcess now represents a series of glottal pulses. To make some parts of this point process voiceless, you can use @@PointProcess: Remove points between...@. It is advisable to make the very beginning and end of this point process voiceless, so that the filtered sound will not start or end abruptly. For instance: Remove points between... 0 0.02 Remove points between... 0.24 0.31 Remove points between... 0.48 0.5 In this example, the first and last 20 ms are devoiced, and a stretch of 70 ms in the middle is made voiceless as well, perhaps because you want to simulate a voiceless plosive there. Now that we have a glottal point process (a glottal pulse train), the only thing left is to turn it into a sound by choosing @@PointProcess: To Sound (phonation)...@. If you use the standard settings of this command, the result will be a @Sound with reasonable glottal flow derivatives centred around each of the original pulses in the point process. You can check this by selecting the Sound and choosing #Edit. You will also see that the amplitude of the first two glottal wave shapes of every voiced stretch is (realistically) somewhat smaller than the amplitudes of the following wave shapes. What you have now is what we call a %%glottal source signal%. It does two things: it contains information on the glottal flow, and it already takes into account one aspect of the %filter, namely the radiation at the lips. This combination is standard procedure in acoustic synthesis. The glottal source signal sounds as a voice without a vocal tract. The following section describes how you add vocal-tract resonances, i.e. the %filter. Once you have a glottal source signal, you are ready to create a filter that represents the resonances of the vocal tract, as a function of time. In other words, you create a @FormantTier object. For a vowel spoken by an average (i.e. adult female) human voice, tradition assumes five formants in the range between 0 and 5500 Hertz. This number comes from a computation of the formants of a straight tube, which has resonances at wavelengths of four tube lengths, four thirds of a tube length, four fifths, and so on. For a straight tube 16 centimetres long, the shortest wavelength is 64 cm, which, with a sound velocity of 352 m/s, means a resonance frequency of 352/0.64 = 550 Hertz. The other resonances will be at 1650, 2750, 3850, and 4950 Hertz. You can create a @FormantTier object with @@Create FormantTier...@, and add some points to it with @@FormantTier: Add point...@: Create FormantTier... filter 0 0.5 Add point... 0.00 100 50 500 100 2750 200 3850 300 4950 400 6050 500 7150 600 8250 700 9350 800 Add point... 0.05 700 50 1100 100 2750 200 3850 300 4950 400 6050 500 7150 600 8250 700 9350 800 This example creates a spectral specification whose %F__1_ rises from 100 to 700 Hertz during the first 50 milliseconds (as for any obstruent), and whose %F__2_ rises from 500 to 1100 Hertz. This may be a [ba]-like formant transition. To get the final acoustic result (the sound), you select the glottal source signal together with the FormantTier and choose @@Sound & FormantTier: Filter@. The resulting sound will have a fairly straight intensity contour. You can change this with the #Formula command (@@Sound: Formula...@), or by multiplying the source signal or the acoustic result with an @Intensity or @IntensityTier object. As an example, we are going to create a male [ba]-[da] continuum in six steps. The acoustic difference between [ba] and [da] is the initial %F__2_, which is 500 Hz for [ba], and 2500 Hz for [da]. We use the same @PitchTier throughout, to model a falling intonation contour: Create PitchTier... f0 0.00 0.50 Add point... 0.00 150 Add point... 0.50 100 The first and last 50 milliseconds are voiceless: To PointProcess Remove points between... 0.00 0.05 Remove points between... 0.45 0.50 Generate the glottal source signal: To Sound (phonation)... 44100 0.6 0.05 0.7 0.03 3.0 4.0 During the labial or coronal closure, the sound is almost silent, so we use an @IntensityTier that models this: Create IntensityTier... intens 0.00 0.50 Add point... 0.05 60 Add point... 0.10 80 Generate the source signal: #plus Sound f0 Multiply Rename... source The ten sounds are generated in a loop: #for i #from 1 #to 10 f2_locus = 500 + (2500/9) * (i - 1) ; variable names start with lower case! Create FormantTier... filter 0.00 0.50 Add point... 0.05 100 50 'f2_locus' 100 ... 3000 300 4000 400 5000 500 6000 600 7000 700 8000 800 9000 900 Add point... 0.10 700 50 1100 100 #plus Sound source Filter (no scale) Rename... bada'i' #select FormantTier filter Remove #endfor Clean up: #select Sound source #plus IntensityTier intens #plus PointProcess f0 #plus PitchTier f0 Remove In this example, filtering was done without automatic scaling, so that the resulting signals have equal intensities in the areas where they have equal formants. You will probably want to multiply all these signals with the same value in order to bring their amplitudes in a suitable range between -1 and +1 Pascal. 1. How to extract the %filter from an existing speech sound You can separate source and filter with the help of the technique of %%linear prediction% (see @@Sound: LPC analysis@). This technique tries to approximate a given frequency spectrum with a small number of peaks, for which it finds the mid frequencies and the bandwidths. If we do this for an overlapping sequence of windowed parts of a sound signal (i.e. a %%short-term analysis%), we get a quasi-stationary approximation of the signal's spectral characteristics as a function of time, i.e. a smoothed version of the @Spectrogram. For a speech signal, the peaks are identified with the resonances (%formants) of the vocal tract. Since the spectrum of a vowel spoken by an average human being falls off with approximately 6 dB per octave, %%pre-emphasis% is applied to the signal before the linear-prediction analysis, so that the algorithm will not try to match only the lower parts of the spectrum. For an adult female human voice, tradition assumes five formants in the range between 0 and 5500 Hertz, say at 550, 1650, 2750, 3850, and 4950 Hertz. For the linear prediction in Praat, you will have to implement this 5500-Hz band-limiting by resampling the original speech signal to 11 kHz. For a male voice, you would use 10 kHz; for a young child, 20 kHz. To perform the resampling, you use @@Sound: Resample...@: you select a @Sound object, and click ##Resample...#. In the rest of this tutorial, I will use the syntax that you would use in a script, though you will usually do these things by clicking on objects and buttons. Thus: #select Sound hallo Resample... 11000 50 You can then perform a linear-prediction analysis on the resampled sound with @@Sound: To LPC (burg)...@: #select Sound hallo_11000 To LPC (burg)... 10 0.025 0.005 50 This says that your analysis is done with 10 linear-prediction parameters (which will yield at most five formant-bandwidth pairs), with an analysis window effectively 25 milliseconds long, with time steps of 5 milliseconds (so that the windows will appreciably overlap), and with a pre-emphasis frequency of 50 Hz (which is the point above which the sound will be amplified by 6 dB/octave prior to the analysis proper). As a result, an object called "LPC hallo" will appear in the list of objects. This @LPC object is a time function with 10 %%linear-prediction coefficients% in each %%time frame%. These coefficients are rather opaque even to the expert (try to view them with @Inspect), but they are the raw material from which formant and bandwidth values can be computed. To see the smoothed @Spectrogram associated with the LPC object, choose @@LPC: To Spectrogram...@: #select LPC hallo_11000 To Spectrogram... 20 0 50 Paint... 0 0 0 0 50 0 0 yes Note that when drawing this Spectrogram, you will want to set the pre-emphasis to zero (the fifth 0 in the last line), because pre-emphasis has already been applied in the analysis. You can get and draw the formant-bandwidth pairs from the LPC object, with @@LPC: To Formant@ and @@Formant: Speckle...@: To Formant Speckle... 0 0 5500 30 yes Note that in converting the @LPC into a @Formant object, you may have lost some information about spectral peaks at very low frequencies (below 50 Hz) or at very high frequencies (near the @@Nyquist frequency@ of 5500 Hz. Such peaks usually try to fit an overall spectral slope (if the 6 dB/octave model is inappropriate), and are not seen as related with resonances in the vocal tract, so they are ignored in a formant analysis. For resynthesis purposes, they might still be important. Instead of using the intermediate LPC object, you could have done a formant analysis directly on the original Sound, with @@Sound: To Formant (burg)...@: To Formant (burg)... 0.005 5 5500 0.025 50 A @Formant object has a fixed sampling (time step, frame length), and for every %%formant frame%, it contains a number of formant-bandwidth pairs. From a Formant object, you can create a @FormantTier with @@Formant: Down to FormantTier@. A FormantTier object contains a number of time-stamped %%formant points%, each with a number of formant-bandwidth pairs. Any of these three classes (@LPC, @Formant, and @FormantTier) can represent the %filter in source-filter synthesis. 2. How to extract the %source from an existing speech sound If you are only interested in the %filter characteristics, you can get by with @Formant objects. To get at the %source signal, however, you need the raw @LPC object: you select it together with the resampled @Sound, and apply %%inverse filtering%: #plus LPC hallo_11000 Filter (inverse) A new Sound named "hallo_11000" will appear in the list of objects (you could rename it to "source"). This is the estimated source signal. Since the LPC analysis was designed to yield a spectrally flat filter (through the use of pre-emphasis), this source signal represents everything in the speech signal that cannot be attributed to the resonating cavities. Thus, the "source signal" will consist of the glottal volume-velocity source (with an expected spectral slope of -12 dB/octave for vowels) and the radiation characteristics at the lips, which cause a 6 dB/octave spectral rise, so that the resulting spectrum of the "source signal" is actually the %derivative of the glottal flow, with an expected spectral slope of -6 dB/octave. Note that with inverse filtering you cannot measure the actual spectral slope of the source signal. Even if the actual slope is very different from -6 dB/octave, formant extraction will try to match the pre-emphasized spectrum. Thus, by choosing a pre-emhasis of -6 dB/octave, you %impose a slope of -6 dB/octave on the source signal. 3. How to do the synthesis You can create a new Sound from a source Sound and a filter, in at least four ways. If your filter is an @LPC object, you select it and the source, and choose @@LPC & Sound: Filter...@: #plus LPC filter Filter... no If you had computed the source and filter from an LPC analysis, this procedure should give you back the original Sound, except that windowing has caused 25 milliseconds at the beginning and end of the signal to be set to zero. If your filter is a @Formant object, you select it and the source, and choose @@Sound & Formant: Filter@: #plus Formant filter Filter If you had computed the source and filter from an LPC analysis, this procedure will not generally give you back the original Sound, because some linear-prediction coefficients will have been ignored in the conversion to formant-bandwidth pairs. If your filter is a @FormantTier object, you select it and the source, and choose @@Sound & FormantTier: Filter@: #plus FormantTier filter Finally, you could just know the %%impulse response% of your filter (in a @Sound object). You then select both Sound objects, and choose @@Sounds: Convolve@: #plus Sound filter Convolve 4. How to manipulate the filter You can hardly change the values in an @LPC object in a meaningful way: you would have to manually change its rather opaque data with the help of @Inspect. A @Formant object can be changed in a friendlier way, with @@Formant: Formula (frequencies)...@ and @@Formant: Formula (bandwidths)...@. For instance, to multiply all formant frequencies by 0.9, you do #select Formant filter Formula (frequencies)... self * 0.9 To add 200 Hertz to all values of %F__2_, you do Formula (frequencies)... if row = 2 then self + 200 else self fi A @FormantTier object can be changed by adding or removing points: @@FormantTier: Add point...@ @@Remove point...@ @@Remove point near...@ @@Remove points between...@ 5. How to manipulate the source signal You can manipulate the source signal in the same way you that would manipulate any sound, for instance with the @ManipulationEditor. A command in the Spectrogram menu of the @SoundEditor and @TextGridEditor windows. See @@Intro 3.2. Configuring the spectrogram@. P\s{RAAT} contains the following types of objects and @Editors. For an introduction and tutorials, see @Intro. General purpose: \bu @Matrix: a sampled real-valued function of two variables \bu @Polygon \bu @PointProcess: a point process (@PointEditor) \bu @Sound: a sampled continuous process (@SoundEditor, @SoundRecorder, @@Sound files@) \bu @LongSound: a file-based version of a sound (@LongSoundEditor) \bu @Strings \bu @Distributions, @PairDistribution \bu @Table, @TableOfReal \bu @Permutation \bu @ParamCurve Periodicity analysis: \bu Tutorials: \bu @@Intro 4. Pitch analysis \bu @@Intro 6. Intensity analysis \bu @Voice (jitter, shimmer, noise) \bu @Pitch: articulatory fundamental frequency, acoustic periodicity, or perceptual pitch (@PitchEditor) \bu @Harmonicity: degree of periodicity \bu @Intensity, @IntensityTier: intensity contour Spectral analysis: \bu @@Intro 3. Spectral analysis \bu @@Intro 5. Formant analysis \bu @Spectrum: complex-valued equally spaced frequency spectrum (@SpectrumEditor) \bu @Ltas: long-term average spectrum \bu Spectro-temporal: @Spectrogram, @BarkFilter, @MelFilter, @FormantFilter \bu @Formant: acoustic formant contours \bu @LPC: coefficients of Linear Predictive Coding, as a function of time \bu @Cepstrum, @CC, @LFCC, @MFCC (cepstral coefficients) \bu @Excitation: excitation pattern of basilar membrane \bu @Excitations: an ensemble of #Excitation objects \bu @Cochleagram: excitation pattern as a function of time Labelling and segmentation (see @@Intro 7. Annotation@): \bu @TextGrid (@TextGridEditor), @IntervalTier, @TextTier \bu @ExperimentMFC Manipulation of sound: \bu @@Intro 8.1. Manipulation of pitch \bu @@Intro 8.2. Manipulation of duration \bu @@Intro 8.3. Manipulation of intensity \bu @@Filtering \bu @@Source-filter synthesis \bu @PitchTier (@PitchTierEditor) \bu @Manipulation (@ManipulationEditor): @PSOLA \bu @DurationTier \bu @FormantTier Articulatory synthesis (see the @@Articulatory synthesis@ tutorial): \bu @Speaker: speaker characteristics of a woman, a man, or a child \bu #Articulation: snapshot of articulatory specifications (muscle activities) \bu @Artword: articulatory target specifications as functions of time \bu (@VocalTract: area function) Neural net package: \bu @FFNet: feed-forward neural net \bu @Pattern \bu @Categories: for classification (#CategoriesEditor) Numerical and statistical analysis: \bu @Eigen: eigenvectors and eigenvalues \bu @Polynomial, @Roots, @ChebyshevSeries, @LegendreSeries, @ISpline, @MSpline \bu @Covariance: covariance matrix \bu @Confusion: confusion matrix \bu @@Discriminant analysis@: @Discriminant \bu @@Principal component analysis@: @PCA \bu @Correlation, @ClassificationTable, @SSCP \bu @DTW: dynamic time warping @@Multidimensional scaling@: \bu @Configuration (@Salience) \bu @@Kruskal analysis@: @Dissimilarity (@Weight), @Similarity \bu @@INDSCAL analysis@: @Distance, @ScalarProduct \bu @@Correspondence analysis@: @ContingencyTable Optimality-theoretic learning (see the @@OT learning@ tutorial) \bu @OTGrammar (@OTGrammarEditor) Bureaucracy \bu @WordList, @SpellingChecker One of the menus in several @editors and in the @manual. With the Write menu, you write one or more selected @objects from memory to a file on disk. The data can be read in again with one of the commands in the @@Read menu@ (most often simply with @@Read from file...@). Usage: save your work You will often choose a command from this menu just before clicking the @Remove button or choosing the @Quit command. Fixed commands If no object is selected, the Write menu is empty. If any object is selected, it will at least contain the following commands: \bu @@Write to console \bu @@Write to text file... \bu ##Write to short text file... \bu @@Write to binary file... Dynamic commands Depending on the class of the selected object, the following commands may be available in the Write menu: One of the commands in the @@Write menu@. You can choose this command after selecting one or more @objects. The Object window will ask you for a file name. After you click OK, the objects will be written to a binary file on disk. The file can be read again with @@Read from file...@. File format These files are in a device-independent binary format, and can be written and read on any machine. You can choose this command after selecting one object. The data that it contains, is written to the Console window, in the same format as with the @@Write to text file...@ command, except for the first line, which reads something like: Write to console: class Sound, "name hallo" The Object window will ask you for a file name. After you click OK, the objects will be written to a text file on disk. The format is much shorter than the one described at @@Write to text file...@. Most of the comments are gone, and there is normally one piece of data per line. The file can be read again with the all-purpose @@Read from file...@. The format is the same as used by @@Write to console@, except for the first two lines: \bu if you selected a single object, e.g., of class Pitch, the file will start with the lines: File type = "ooTextFile" Class = "Pitch" \bu if you selected more than one object, e.g., `Pitch hallo' and `Polygon kromme', the file will look like: Class = "Collection" size = 2 item []: item [1]: class = "Pitch" name = "hallo" (pitch data...) item [2]: class = "Polygon" name = "kromme" (polygon data...) The file can be read again with @@Read from file...@, which, by the way, does not need the verbosity of the above example. The following minimal format will also be read correctly: "ooTextFile" "Collection" 2 "Pitch" "hallo" (pitch data...) "Polygon" "kromme" (polygon data...) Thus, all text that is not a free-standing number and is not enclosed in double quotes or < >, is considered a comment, as is all text following an exclamation mark (`!') on the same line. What's new? ppgb Acknowledgments Praat menu Copy... Draw menu Dynamic menu Extract visible formant contour Extract visible intensity contour Extract visible pitch contour Extract visible spectrogram FAQ (Frequently Asked Questions) FAQ: Formant analysis FAQ: How to cite Praat FAQ: Pitch analysis FAQ: Scripts FAQ: Spectrograms File menu Filtering Formants & LPC menu Get first formant Get pitch Get second formant Goodies Info Info window Inspect Intro Intro 1. How to get a sound Intro 1.1. Recording a sound Intro 1.2. Reading a sound from disk Intro 1.3. Creating a sound from a formula Intro 2. What to do with a sound Intro 2.1. Writing a sound to disk Intro 2.2. Viewing and editing a sound Intro 3. Spectral analysis Intro 3.1. Viewing a spectrogram Intro 3.2. Configuring the spectrogram Advanced spectrogram settings... Intro 3.3. Querying the spectrogram Intro 3.4. The Spectrogram object Intro 3.5. Viewing a spectral slice Intro 3.6. Configuring the spectral slice Intro 3.7. The Spectrum object Intro 4. Pitch analysis Intro 4.1. Viewing a pitch contour Intro 4.2. Configuring the pitch contour Time step settings... Advanced pitch settings... Intro 4.3. Querying the pitch contour Intro 4.4. The Pitch object Intro 5. Formant analysis Intro 5.1. Viewing formant contours Intro 5.2. Configuring the formant contours Intro 5.3. Querying the formant contours Intro 5.4. The Formant object Intro 6. Intensity analysis Intro 6.1. Viewing an intensity contour Intro 6.2. Configuring the intensity contour Intro 6.3. Querying the intensity contour Intro 6.4. The Intensity object Intro 7. Annotation Intro 8. Manipulation Intro 8.1. Manipulation of pitch Intro 8.2. Manipulation of duration Intro 8.3. Manipulation of intensity Intro 8.4. Manipulation of formants List of Objects Look and feel New menu Object window Periodicity menu Pitch settings... Play Query Query menu Quit Read from file... Read menu Rename... Resource fork Segmentation Show formant Show intensity Show pitch Show pulses Show spectrogram Source-filter synthesis Source-filter synthesis 1. Creating a source from pitch targets Source-filter synthesis 2. Filtering a source Source-filter synthesis 3. The ba-da continuum Source-filter synthesis 4. Using existing sounds Spectrogram settings... Types of objects View Write menu Write to binary file... Write to console Write to short text file... Write to text file... Numerics library @Qi @Qi ji HPi MQi xi NPi SQi i UPi `Qi `i [Pi $ jQi ri jPi ( xQi \i sPi , Qi oi Pi 0 Qi lfi Pi 4 Qi lj Pi 8 Qi lj Pi < Qi lj Pi @ Pi H Qi xi Pi P Pi X Pi ` Qi pi Pi d Qi ai Qi h Qi p Qi x Qi Qi $Qi Qi Qi ^ IFK @Qi ji Ni {Gz? ? ?-DT! @ ? @ @~jt?Mb?-q=?ffffff? @{Gzt?333333? @ I@{Gz??Gz?sound pulses pitch dummyIntensity duration dummySpectrogram dummyFormantTier dummy1 dummy2 dummy3 dummy10 dummyPitchAnalysis dummy11 dummy12 dummyIntensityAnalysis dummyFormantAnalysis dummy4 dummy5 dummy6 dummy7 dummy8 dummy9 Trying to read "%s". Manipulation Sound PointProcess PitchTier IntensityTier DurationTier Image FormantTier Data Pitch Intensity Formant lpc LPC (Sound_to_Manipulation:) Not performed. (Sound_Pitch_to_Manipulation:) Not performed. (Sound_PointProcess_to_Manipulation:) Not performed. Cannot synthesize PSOLA without a sound. No duration points. Cannot synthesize PSOLA without original sound. Cannot synthesize PSOLA without pulses analysis. Cannot synthesize PSOLA without pitch manipulation. (Manipulation_to_Sound:) Not performed. Cannot synthesize pitch manipulation without pitch manipulation. Cannot synthesize this without pulses analysis. Cannot synthesize this without pitch manipulation. Cannot synthesize this without LPC or original sound. Manipulation_to_Sound: not performed. Cannot synthesize pitch manipulation without pulses. (Manipulation_AnyTier_to_Manipulation:) Not performed. Vi Vi j Ui ReK Vi lj 4Ui time points: size points [%ld]: Trying to read "%s". AnyPoint AnyTier points SortedSetOfDouble 0hK LWi i ` 4Vi ? A @ ? A A B B 4B HB \B pB B B B BCochleagram Time (s) Place (Bark) Cochleagram_difference: unequal time sampling or number of frequencies. Cochleagram_difference: window too short. mK Xi i Wi Number of distributions = %ld Number of values = %ld Distributions No column %ld. No candidates. Column total not positive. No string in row %ld. (Distributions_peek:) Not performed. ?(Distributions_to_Strings:) Not performed. No column %ld. No candidates. Non-integer value %.17g in row %ld. Found a negative value %g in row %ld. Column total not positive. No string in row %ld. (Distributions_to_Strings_exact:) Not performed. ?Environment (%ld) out of range (1-%ld). Sizes of underlying and surface distributions do not match. Number of states (%ld) in adjacency matrix does not match number of distributions (%ld) (Distributions_to_Transition:) Not performed. Number of data (%ld) in mapping matrix does not match number of data (%ld) in distributions (Distributions_Transition_map:) Not performed. (Transition_to_Distributions_conflate:) Not performed. yK \i 0i \i ?DurationTier Relative duration P@ ? @DDDDDD? >@ h㈵> 4@ V@ @ @ @ @ ? B A @|K f^i 0i ` h]i Loudness %.2f sones. Maximum at %.2f Bark, %ld Hertz, %.1f phon. Excitation Excitation.c my nx == thy nx Frequency (Bark) Excitation (phon) ? ? @ ? @ai ai ai ai Obi Wbi ^i gbi tbi 8 tbi ̨i bi 0 |bi 4 bi l_i bi ? @@ ? $@ꌠ9Y>)F+eG?K tbi i 8 ai frequency Trying to read "%s". bandwidth intensity nFormants maxnFormants (empty) formant []: %s formant [%ld]: frame []: %s frame [%ld]: formant Formant_Formant my nFormants Formant frame Formant_Frame my nx Time domain: from %.15g to %.15g seconds. Number of frames: %ld Frame duration: %.15g seconds First frame around: %.15g seconds. Time (s) Formant frequency (Hz) (Formant_formula_bandwidths:) No formants available. (Formant_formula_frequencies:) No formants available. %%F_%d (Hz) Formant.c place <= my my frame [iframe]. nFormants (Formant_tracker:) Number of tracks (%d) should not exceed minimum number of formants (%ld) Nhi Nhi j hgi mgi gi [hi Dhi h [hi ohi ohi ji {hi hi \j ei K Nhi lj ei K ohi ji lfi ? ?-DT!@-DT! !? Gz?time numberOfFormants (empty) formant []: %s formant [%d] bandwidth []: %s bandwidth [%d] points: size points [%ld]: Trying to read "%s". formant Number of "%s" (%d) greater than %d. Trying to read element %ld of "%s". bandwidth FormantPoint my numberOfFormants FormantTier points SortedSetOfDouble FormantTier.c n >= 2 ileft >= 1 && iright <= n Time (s) Frequency (Hz) value != NUMundefined (Formant_PointProcess_to_FormantTier:) Not performed. Time F%d B%d bandwidth != NUMundefined vki vki j 8ki =ki mK vki lj ji $@ ? @ ?-DT!@p= ף迤p= ף?q= ףp?HzG? (@uAj? = ףp=4@E<#xmin xmax Trying to read "%s". Wrong xmin %.8g and xmax %.8g. Function Function.c unit >= my getMinimumUnit (me, ilevel) && unit <= my getMaximumUnit (me, ilevel) H zG?{Gz??? ? ?K Wni 0i ` li Harmonicity info: Starting time: %.16g seconds End time: %.16g seconds Number of frames: %ld (%ld sounding) Time step: %.16g seconds First frame at: %.16g seconds Periodicity-to-noise ratios of sounding frames: Median %.1f dB 10 %% = %.1f dB 90 %% = %.1f dB 16 %% = %.1f dB 84 %% = %.1f dB Minimum %.1f dB, maximum %.1f dB Average %.1f dB , standard deviation %.1f dB %s Harmonicity pi ` pi ̨i pi 0 pi 8 pi @ pi H pi P pi X pi pi K pi i ` oi ymin ymax ny dy y1 z Trying to read "%s". Image my ny my nx ? $@ @+eG? ? ?\K yri 0i ` pi Time domain: Starting time: %s seconds Finishing time: %s seconds Total duration: %s seconds Time sampling: Number of frames: %ld Time step: %s seconds First frame centred at: %s seconds Intensity Time (s) Intensity (dB) K psi 0i ri 4@ $@?IntensityTier Intensity (dB) No intensity points. Time (s) Lvi Lvi ji Xvi K Lvi ji 0ti 1K ]vi j ti ꌠ9Y>)Fꌠ9Y>) ?_K bvi hj ui Autosegment name Tier Label < wi wi wi wi wi wi wi xi #xi <xi Xxi qxi xi xi xi xi xi xi ?{Gz? @{Gz?R Q? ? @ ? @ @RK 6zi i x wi LongSound.bufferLength none mono stereo three quadro linear 8 bit signed linear 8 bit unsigned linear 16 bit big-endian linear 16 bit little-endian linear 24 bit big-endian linear 24 bit little-endian linear 32 bit big-endian linear 32 bit little-endian mu-law A-law shorten polyphone unknown Duration: %.17g seconds File name: %s File type: %s Channels: %s Encoding: %s Sample rate: %.17g Hz Size: %ld samples Start of sample data: %ld bytes from the start of the file. File not recognized (LongSound only supports AIFF, AIFC, WAV, NeXT/Sun, and NIST files). LongSound does not support sound files compressed with "shorten". LongSound LongSound not created. Less than 1 sample in window. Cannot seek in file %s. Sound not extracted from LongSound. Less than 1 sample selected. PpgB Sound file not written. left right This audio file is not a stereo file. It does not have a %s channel. LongSound.c n <= my nmax imax - imin + 1 <= my nmax Sound too long (%ld seconds). Cannot play. Cannot resample and play this sound. (LongSound_concatenate:) No Sound or LongSound objects to concatenate. (LongSound_concatenate:) Sampling frequencies do not match. (LongSound_concatenate:) Cannot mix stereo and mono. $@? @+eG? ? ? $|= ? K m~i 0i ` |i Frequency domain: Lowest frequency: %s Hz Highest frequency: %s Hz Total frequency domain: %s Hz Frequency sampling: Number of frequency bands: %s Width of each band: %s Hz First band centred at: %s Hz Total SPL: %s dB Ltas Frequency (Hz) Sound pressure level (dB/Hz) Cannot merge zero Ltas objects. Frequency domains do not match. Bandwidths do not match. Frequency bands do not match. (Ltas_computeTrendLine:) Number of bins too low (%ld). Should be at least 2. (Ltas_subtractTrendLine:) Number of bins too low (%ld). Should be at least 2. Bandwidth must be greater than %f. Cannot compute an Ltas if there are no periods in the point process. Sound & PointProcess: To Ltas: pulse %ld out of %ld Cannot create an Ltas without energy in any bins. i ` i ̨i ܂i 0 i 8 i @ i H i P i X i i ? ? ? "@ ?@9? L i i ` i ymin ymax ny dy y1 z Matrix my ny my nx (Matrix::readAscii:) xmin should <= xmax and ymin <= ymax. (Matrix::readAscii:) nx should >= 1 and ny >= 1. (Matrix::readAscii:) dx should > 0 and dy > 0. xmin = %.8g xmax = %.8g ymin = %.8g ymax = %.8g Number of columns = %ld Number of rows = %ld dx = %.8g (-> sampling frequency %.8g) dy = %.8g (-> sampling frequency %.8g) x1 = %.8g y1 = %.8g Minimum value = %.8g Maximum value = %.8g rb Sampling frequency %.10g. ... Loading %d frames of %d words ... File empty %f The number of elements (%ld) is not a multiple of the number of columns (%ld) (Matrix_readFromRawTextFile:) File %s not read. (Matrix_eigen:) Matrix not square. (Matrix_eigen:) Not implemented. Write to the authors. (Matrix_power:) Matrix not square. w "ooTextFile" "Matrix" %.17g %.17g %ld %.17g %.17g %.17g %.17g %ld %.17g %.17g %.17g %s ? @ (Matrix_to_Pitch:) Not performed. (Pitch_formula:) Not performed. ?PointProcess_to_Matrix: no times in PointProcess. ? @Matrix_to_Polygon: matrix must have exactly 2 rows or columns. i i j Љi ؉i i %i %i j 6i <i hj i +L i lj i +L %i lj (i string1 string2 weight pairs: size pairs [%ld]: Trying to read "%s". PairProbability PairDistribution pairs Ordered No candidates. Number of generated string pairs should be positive. Sum of weights not positive. No string in probability pair %ld. (PairDistribution_to_Stringses:) Not performed. (PairDistribution_peekPair:) Not performed. Total is zero. (PairDistribution_getFractionCorrect:) Not computed. %s \-> %s %s \-> (PairDistribution_Distributions_getFractionCorrect:) Not computed. u <7~u <7 ? 9L vi ji i domain: start: %.8g end: %.8g x: minimum: %.8g maximum: %.8g sampling: nx = %ld, dx = %.8g (rate %.8g), x1 = %.8g y: minimum: %.8g maximum: %.8g sampling: ny = %ld, dy = %.8g (rate %.8g), y1 = %.8g ParamCurve Domains do not overlap. ParamCurve not created. 4i >i Gi Qi Αi ؑi i i i @ i ̨i i 0 i 8 i < i 8i i (@9B.? Y@ i@ {@V瞯< 4&k C? $@? @?{Gz? ?zG?? ? @{Gz?+eG? -?bL i i @ xi frequency strength intensity nCandidates (empty) candidate []: %s candidate [%ld]: ceiling maxnCandidates frame []: %s frame [%ld]: Trying to read "%s". candidate Pitch_Candidate my nCandidates Pitch frame Pitch_Frame my nx Hertz Hz Hertz (logarithmic) %%Hz% mel logHertz logHz st__1_ semitones %%re% 1 Hz semitones re 1 Hz st__100_ semitones %%re% 100 Hz semitones re 100 Hz st__200_ semitones %%re% 200 Hz semitones re 200 Hz st__a_ semitones %%re% 440 Hz semitones re 440 Hz erb ERB dB unknown Time domain: s Starting time: Finishing time: Total duration: Time sampling: voiced) ( Number of frames: seconds Time step: First frame at: Hertz Ceiling at: Estimated quantiles: Mel = Hz = 10% = ERB semitones above 100 Hz = 16% = 50% = 84% = 90% = Estimated spreading: 84%-median = semitones = median-16% = 90%-10% = Minimum Maximum Range Average: Standard deviation: Mel/s = Hz/s = Mean absolute slope: ERB/s semitones/s = semitones/s Mean absolute slope without octave jumps: Pitch not created. Time (s) Pitch (%s) Pitch_difference: these Pitches are not aligned. Frame %ld time %f: unvoiced to voiced. Frame %ld time %f: voiced to unvoiced. Frame %ld time %f: downward frequency jump from %.5g Hz to %.5g Hz. Frame %ld time %f: upward frequency jump from %.5g Hz to %.5g Hz. Difference between two Pitches: Unvoiced to voiced: %ld frames. Voiced to unvoiced: %ld frames. Downward frequency jump: %ld frames. Upward frequency jump: %ld frames. Pitch.c precision >= 0.0 && precision < 1.0 wL 8i 0i `i (@9B.? $@PitchTier Frequency (Hz) w "ooTextFile" "PitchTier" %.17g %.17g %ld %.17g %.17g Resulting frequency has to be greater than 0 Hz. Resulting frequency has to be greater than 0 mel. Resulting frequency has to be greater than 0 ERB. (PitchTier_shiftFrequency:) Not completed. PitchTier.c factor > 0.0 ? ? @ ?(PitchTier_to_PointProcess:) Not performed. (Pitch_to_PointProcess:) Not performed. (PointProcess_to_PitchTier:) Not performed. No pitch points. F0 Time No pitch points. (Pitch_AnyTier_to_PitchTier:) Not performed. No periodicity at time %.8g. ꌠ9Y>)ꌠ9Y>)F ?Fundamental frequency (Hz) Intensity (dB) q= ףp? @ ? ? (Pitch_to_PitchTier: ) Not performed. Time (s) Frequency (Hz) No pitch points. ? @ ? ? @ {Gz? ?? ?ffffff?333333?Pitch_to_PointProcess.c NUMdefined (tmin) NUMdefined (tmax) Sound & Pitch to PointProcess Sound_Pitch_to_PointProcess_cc: tleft %s, tright %s, f0middle %s NUMdefined (f0middle) D D E TE E E HB B HC C C C ?ffffff? @ ?Pitch_to_Sound: not performed. Pitch_play: not played. Pitch_hum: not played. i ( i ji Ȟi ˞i i ?{Gz?-C 6?u <7~ ? ?{Gzt?ߨL i ji ( i nt t Trying to read "%s". PointProcess my nt Number of periods: seconds Mean period: Stdev period: Jitter (local): Jitter (local, absolute): Jitter (rap): Jitter (ppq5): Jitter (ddp): Time domain: from %.15g to %.15g seconds. Number of times: %ld First time: %.15g seconds. Last time: %.15g seconds. Periods between 0.1 ms and 20 ms (pitch between 50 and 10000 Hz), with a maximum "period factor" of 1.3: All periods: PointProcess.c my nt != 1 right == left + 1 Cannot add a point at an undefined time. Time (s) ? ? @-DT! @ư> 4@??ffffff? @ D D E TE E E HB B HC C C C D D E TE E E HB B HC C C C`i `i j hi wi yi i yi mL `i lj i ? ?Polygon numberOfPoints x my numberOfPoints y Number of points: %ld Perimeter: %.8g x [%ld] y [%ld] (Polygon::readAscii:) Cannot read 'number of points' < 1. Polygon not created. Polygon_salesperson: found %ld times the same shortest path. Polygon.c me [i [i j i %i ei ei ji ni ui \j i L [i lj i L ei ji 0i ?u <7u <7~UUUUUU? ? ? @time value points: size points [%ld]: Trying to read "%s". RealPoint RealTier points SortedSetOfDouble RealTier.c n >= 2 ileft >= 1 && iright <= n imin < n imax > 1 Time (s) i 0 i ji i i i ( L i ji 0 i ? ? ? @ Km~ Kmnx dx x1 Trying to read "%s". Sampled Sampled.c windowDuration > 0.0 timeStep > 0.0 %s shorter than window length. *numberOfFrames >= 1 startOfDefinedStretch >= ixmin - 1 NUMdefined (previousValue) 4i Ai Mi Xi bi ji ri |i i i i i i y@ -q= $@ ? ?|= @ffffff?ư>-DT!@Gz?q= ףp?HzG? ( H ; [ h R rE<=4@ 4@ I@?% M i 0i ` xi Sound_WINDOW Rectangular Triangular Parabolic Hanning Hamming Gaussian1 Gaussian2 Gaussian3 Gaussian4 Gaussian5 Kaiser1 Kaiser2 Time domain: Starting time: %s seconds Finishing time: %s seconds Total duration: %s seconds Time sampling: Number of samples: %ld Sampling period: %s seconds Sampling frequency: %s Hz First sample centred at: %s seconds Pascal Amplitude: Minimum: Maximum: Mean: Root-mean-square: Pascal^2 sec Total energy: Joule/m^2) (energy in air: Mean power (intensity) in air: %.8g Watt/m^2 = %.4g dB Mean power (intensity) in air: %.8g Watt/m^2 Standard deviation: %.8g Pascal Sound Cannot resample to 0 samples. Sounds_append: sampling frequencies do not match. Sounds_convolve: sampling frequencies do not match. Time (s) (Sound_createFromToneComplex:) Frequency step must not be zero. (Sound_createFromToneComplex:) Zero sine waves. Extracted Sound would contain no samples. (Sound_extractPart:) Not performed. Sound too short. (Sounds_crossCorrelation:) Sampling frequencies do not match. (Sounds_crossCorrelation:) Window too small. ? @-DT! @ ?-DT!@q= ףp?HzG? ( HSquare (rectangular) Hamming (raised sine-squared) Bartlett (triangular) Welch (parabolic) Hanning (sine-squared) Gaussian (unknown) two window lengths one window length (Sound_to_Spectrogram:) Your sound is too short: it should be at least as long as %s. Sound to Spectrogram... Sound_and_Spectrogram.c startSample >= 1 endSample <= my nx Sound to Spectrogram: analysis of frame %ld out of %ld ? ? ? $@A Fourier-transformable Spectrum must have a first frequency of 0 Hz, not %.8g Hz. @@ @ @@ @ @@ @ p@ ? ? ? @(Sound_record:) Audio hardware does not support sampling frequency %.8g. (Sound_record:) Duration too short. Sound_audio.c my nx == numberOfSamples (Sound_record:) Error %d while opening. (Sound_record:) Error %d while preparing header. (Sound_record:) Error %d while listening. (Sound_record:) Error %d while starting. (Sound_record:) Error %d while unpreparing header. (Sound_record:) Error %d while closing. Sound not recorded. ? ? ? 4@ $@ @ ?ư> @ -DT! @ *@Gz?Band: %.0f ... %.0f Hz $@ חA @? ? cA @ @@ ? E GNot an audio file. (Sound_readFromSoundFile:) Reading stereo file as mono. No data in audio file. (Sound_readFromSoundFile:) Cannot unshorten. Write to paul.boersma@uva.nl for more information. (Sound_readFromSoundFile:) File %s not read. Can only read AIFF/C, WAV, NeXT/Sun, and NIST files. (Sound_read2FromSoundFile:) Cannot unshorten two channels. (Sound_read2FromSoundFile:) File %s not read. rb (Sound_readFromSesamFile:) File "%s" is not a correct SESAM or LVS file. Error reading file "%s". SIG Not a Bell-Labs sound file. Second line missing or too long. Wrong header-length info. Header too short. samples No samples found. frequency Error reading file. (Sound_readFromBellLabsFile:) File "%s" not read. (Sound_readFrom...File:) Cannot read file "%s". FORMDS16 (Sound_readFromKayFile:) File "%s" is not a KAY DS-16 file. HEDR (Sound_readFromKayFile:) File "%s" does not contain HEDR chunk. (Sound_readFromKayFile:) File "%s" is not a correct Kay file. (Sound_readFromKayFile:) File "%s" does not contain readable SD chunk. SDA_ SD_B (Sound_readFromRawAlawFile:) File %s not read. PpgB wb Sound_writeToSesamFile: writing %ld samples at %g Hz Error writing file "%s". ?9@ ? -DT!@ @@333333q_?a2U0*C?K7MbP? I@ @@ mާd@@ A @ r@ j@ @ es-8R?Start sample too small: %ld instead of 1. End sample too small: %ld instead of %ld. Sound_to_Cochleagram.c n >= 1 isamp %ld ? -DT! @ ?h㈵>-DT! @ @ ( H-q= I@ @ ? @ @ @ @ 0 0@ $@ D @@ B@ X P@Sound_to_Formant.c frame -> nFormants == 0 && frame -> formant == NULL iformant == frame -> nFormants There is no zero between %.8g and %.8g. The function values are %.8g and %.8g, respectively. Degree %d not completed. (Sound_to_Formant:) Window too short. Formant analysis Sound contains infinities. (Sound_to_Formant:) Analysis results of frame %ld will be wrong. Formant analysis: frame %ld (Sound_to_Formant:) Not performed. ? V瞯<? $@ @-DT!@ ? @ eA{Gz? Q? ?MP4?MP4Computing Hilbert envelopes... Computing Hilbert envelope %ld... @ ? ? E<=4@?|=KH9 $@Sound_to_Intensity.c minimumPitch > 0.0 Sound should be at least 6.4 / minimumPitch long. Intensity analysis not performed. @ @ ? ? ( H-DT! @??+eG?333333?ffffff?Q ?ffffff?{Gz?? Q? @Sound_to_Pitch.c maxnCandidates >= 2 method >= AC_HANNING && method <= FCC_ACCURATE Sound to Pitch... For this Sound, the parameter 'minimum pitch' may not be less than %.8g Hz. Analysis window too short. Sound to Pitch: analysis of frame %ld out of %ld startSample >= 1 endSample <= my nx Sound to Pitch: path finder ? (Sound_to_PointProcess:) Not performed. pM !i i ` i 9? @@9B.?KH9|=(O8,_@ ?#_ y? seconds Starting time: seconds) seconds (duration: Finishing time: Number of time slices (frames): Time step (frame distance): First time slice (frame centre) at: Hertz Minimum frequency: Maximum frequency: Number of frequency bands (bins): Frequency step (bin width): First frequency band around (bin centre at): Spectrogram Time (s) Frequency (Hz) @|= $@ ? @ N@ 4@Y n ?-DT! @ @ @M Oi i ` i Frequency domain: Lowest frequency: %s Hz Highest frequency: %s Hz Total bandwidth: %s Hz Frequency sampling: Number of frequency bins: %s Bin width: %s Hz First bin centred at: %s Hz Total energy: %s Pa2 sec Spectrum Frequency (Hz) Sound pressure level (dB/Hz) (Matrix_to_Spectrum:) Matrix must have exactly 2 rows. (Spectrum_cepstralSmoothing:) Not performed. ? ?Negative values in spectrogram. (Spectrogram_to_Spectrum:) Not performed. 9@ ?tV? ? ? ?K? $@ @ ? ? @ ?fi 4 fi j i 1i Ji _i ui i i i i i i $ i ( i , vi j i 0 i j tn tM fi lj 4 i forbiddenStrings checkMatchingParentheses separatingCharacters allowAllParenthesized allowAllNames namePrefixes allowAllAbbreviations allowCapsSentenceInitially allowCapsAfterColon allowAllWordsContaining allowAllWordsStartingWith allowAllWordsEndingIn wordList userDictionary: size userDictionary [%ld]: Trying to read "%s". SpellingChecker WordList userDictionary SortedSetOfString .,;:()" This spelling checker does not contain a user dictionary. i i j 4i i i M i lj i numberOfStrings (empty) strings []: %s strings [%ld] Trying to read "%s". strings Trying to read element %ld of "%s". Strings my numberOfStrings %ld strings Total length %ld Maximum length %ld * \ %s%s%s Cannot find first file. (Strings_readFromRawTextFile:) File %s not read. w %s xi xi j i i i i i i i i i M xi lj i ?ư> ? ?ffffff9@ R@ 333333? @ffffff?TableOfReal numberOfRows numberOfColumns rowLabels my numberOfRows columnLabels my numberOfColumns data (empty) columnLabels []: %s row [%ld]: %s Number of rows = %ld Number of columns = %ld (TableOfReal_init:) Cannot create cell-less table. Cannot remove the only row. No row %ld. (TableOfReal_removeRow:) Not performed. Cannot create row %ld. (TableOfReal_insertRow:) Not performed. Cannot remove the only column. No column %ld. (TableOfReal_removeColumn:) Not performed. Cannot create column %ld. (TableOfReal_insertColumn:) Not performed. TableOfReal.c me != thee my numberOfRows == thy numberOfRows my numberOfColumns == thy numberOfColumns No such column: %ld. No row matches this criterion. No such row: %ld. No column matches this criterion. No such %s: 0 (minimum is 1). No such %s: %ld (maximum is %ld). Cannot start range with colon. Cannot end range with colon. End of range should be a positive whole number. Start of range should be a positive whole number. row column No rows match this condition. No columns match this condition. undefined 0 %ld/%ld %.7g %%%d.%d%c Numbers not drawn. Numbers of columns do not match. (TablesOfReal_append:) Not performed. Cannot add zero tables. nrow == his numberOfRows (TablesOfReal_appendMany:) Not performed. w rowLabel ? %s rb No columns. %s The number of elements (%ld) is not a multiple of the number of columns plus 1 (%ld). (TableOfReal_readFromHeaderlessSpreadsheetFile:) File %s not read. i i TUi i #i #i ji i 0i 0i ji 9i @i \j i Ri Ri ji _i @i \j \i ii ii ji i ri hj -N i 4Ui i t.N #i ji \i i/N 0i ji i X0N Ri ji i b3N ii ji i Y@ ? ? ?? @ :@ @ [@ @ 4@ @p@ I@ @ D@333333? $@ h@ @j@ @ 5@ @ffffff@ ? @ 0@ @@333333@ @ P@333333@ (@ `@333333#@ 8@ ?Ci Hi Li Qi Ui Zi ^i ci ^i ci gi li pi ui yi ~i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i #i *i .i 5i 9i @i Di Ki Oi Vi Zi `i di ji ni ti xi ~i xi ~i i i i i i i i i i i mark text points: size points [%ld]: intervals: size intervals [%ld]: tiers Trying to read "%s". TextPoint TextInterval TextTier points SortedSetOfDouble IntervalTier intervals TextGrid Ordered s %ld interval tier%s %ld point tier%s %ld interval%s %ld point%s No '#' line. %lf%ld%s Line too short: "%s". (TextTier_readFromXwaves:) Not read. Cannot merge zero TextGrid objects. %g %g %g Time (s) Tier number %ld out of range 1..%ld. Tier %ld is not an interval tier. untitled No non-empty intervals were found. %s_%s_%ld No label that %s the text "%s" was found. Pitch (%s) Start End Duration Time (IntervalTier_readFromXwaves:) Not read. vuv U V Cannot add a boundary on tier %d, because that tier does not exist. Cannot add a boundary on tier %d, because that tier is not an interval tier. Cannot add a boundary at %f seconds, because there is already a boundary there. Cannot add a boundary at %f seconds, because this is outside the time domain of the intervals. Cannot remove a boundary from tier %d, because that tier does not exist. Cannot remove a boundary from tier %d, because that tier is not an interval tier. Cannot remove a boundary at %f seconds, because there is no boundary there. Cannot remove a boundary at %f seconds, because this is outside the time domain of the intervals. Cannot remove a boundary at %f seconds, because this is at the left edge of the tier. %s%s Cannot modify tier %d, because that tier does not exist. Cannot modify tier %d, because that tier is not an interval tier. Cannot modify interval %ld on tier %d, because that interval does not exist. Cannot add a point on tier %d, because that tier does not exist. Cannot add a point on tier %d, because that tier is not a point tier. Cannot add a point at %f seconds, because there is already a point there. Cannot modify tier %d, because that tier is not a point tier. Cannot modify point %ld on tier %d, because that point does not exist. auml \a" euml \e" iuml \i" ouml \o" Auml \A" Euml \E" Iuml \I" Ouml \O" Uuml \U" aacute \a' eacute \e' iacute \i' oacute \o' Aacute \A' Eacute \E' Iacute \I' Oacute \O' Uacute \U' agrave \a` egrave \e` igrave \i` ograve \o` Agrave \A` Egrave \E` Igrave \I` Ograve \O` Ugrave \U` acirc \a^ ecirc \e^ icirc \i^ ocirc \o^ Acirc \A^ Ecirc \E^ Icirc \I^ Ocirc \O^ Ucirc \U^ Empty SGML code. Unfinished SGML code. Unknown SGML code &%s;. r Praat chronological TextGrid text file Not a chronological TextGrid text file. Unknown tier class "%s". Early end of file Wrong tier number %ld. (TextGrid_readFromChronologicalTextFile:) File %s not read. w "Praat chronological TextGrid text file" %s %s ! Time domain. %ld ! Number of tiers. %s %s %ld %s %s %ld %s <?xml version="1.0"?> No CGN syntax file. <!DOCTYPE ttext SYSTEM "ttext.dtd"> <tau ref=" %40s%40s%40s%40s%40s%40s%200s Too few strings in tau line. Duration not greater than zero. s=" Missing speaker name. Zero duration for sentence. Overlap on tier not allowed. Negative times not allowed. %ld <tw ref=" Too few strings in tw line. tb=" Missing tb. te=" Missing te. Zero duration for phrase. w=" Missing word. Phrase outside sentence. i i j i i $i i $i $i oN i lj i ?ư> ? ?ffffff9@ R@ffffff??numberOfStates Trying to read "%s". stateLabels Trying to read element %ld of "%s". data Transition my numberOfStates (empty) stateLabels []: %s "%s" state [%ld]: %.17g Number of stetes = %ld (Transition_init:) Cannot create empty matrix. 0 %ld/%ld %.7g %%%d.%d%c Matrix should be square. (Matrix_to_Transition:) Not performed. ? ? @ JN i i ` 0i Vector bars poles speckles N \j 0i ` i ? ? {Gzt?-C 6?gj " ???X@ff@33? ?L?L?L? ?33?ff@9@E@ff@ @ @@ @ @33@ffA A AffA A @@ @33@ @ @@ ij ! 33@?p??@@@@33AA33A!A33#A A Aff@ @@̬@̜@33@y@ `@ffF@,@@ @ @Y@ @ff@ A A kj # @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ?333?33s?ff? @ @@ @ A mj % ff&@33@?ff?ff@G@)\_@ff&@ff@ff??33? ?Q?(?ff&@9@ @ff&@fff@@@@@ AffAA (A<AiA hAffNAff&A @Y@Y@ @ oj ( @ @ @@ @AffAffAffA @@y@33@??ff?̌?33? @ @ff? @ @33@333@l@ @ff@@ff.AffNAffRA PA HAff Ay@ff? ף>>?qj % @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ?333?33s?ff? @ @@ff? ף>>? tj & @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ?333?33s?ff? @ @@ @ff? ף>>? wj ' @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ?333?33s?ff? @ @@ @ @ff? ף>>? zj & L@L@L@L@ (A (A PA PA (A (A (A (A (A A @ @ @ @ @ff&@?ff? ? ?ff?? @ @ff&@L@ @ A A A @ @ @ @ j ' `@L@9@ff&@@@@̜@ @H@ @ ? ?zT??? ??Y? ??33@33#@ E@Hj@̄@@ @@@ @AOAffNAff6A33@ @ff>=8 j $ 333@,@@ff&@ff@Q@@33@@q=@ @33@G@{~@ffv@l@Y@33C@q=:@ffF@33c@y@33@ @33s@33S@33#@ff? ?ff>=8L? @ @ A j & @,@ @@33S@ @{A A A@ff@̬@ @333@33?̬?fff? ?>\B>)\=8={.>> ?fff?33? @33S@ @ A 4Aff.A@@ `@l@ @ j ( @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @j ' ???X@ff@33? ?L?L?L? ?33?ff@9@E@ff@ @ @@ @ @33@ffA A AffA A @@ @33@ @ @@33@ @ff>=8 j " ???X@ff@33? ?L?L?L? ?33?ff@9@E@ff@ @ @@ @ @33@ffA A A A @ @ff>8L? @ @@ j " ???X@ff@33? ?L?L?L? ?33?ff@9@E@ff@>8> @ @33@ffA A AffA A @@ @33@ @ @@ j ' @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ?333?33s?ff? @ @@ @33@ @ff>=8 j # @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A@ @ @333@33?ff?fff?ff&? ? ? ? ?>=8L? @ A j # @@9@ 0@ %@,@33@@ffAAff"A(Aff.Aff2A4A333A,A A @ @>8>ff?fff?ff&? ? ? ?333?33s?ff? @ @@ @ A j ( @ @ @@ @AffAffAffA @@y@33@??ff?̌?33? @ @ff? @ @33@333@l@ @ff@@ff.AffNAffRA PA HAff A33@ @ff>=8j ( @ @ @@ @AffAffAffA @@y@33@??ff?̌?33? @ @ff? @ @33@333@l@ @ff@@ff.A A @@>8L? @ff? ף>>?j ( @ @ @@ @AffAffAffA @@y@33@??ff?̌?33??>8> @33@333@l@ @ff@@ff.AffNAffRA PA HAff Ay@ff? ף>>? Vocal tract length: %.7g metres Number of sections: %ld Section length: %.7g metres VocalTract a e i o u y1 y2 y3 jery p t k x pa ta ka pi ti ki pu tu ku VocalTract_createFromFant60: unknown phone %.100s -DT!@;> :.>h> Q&y@ ?-DT! @ @= ףp=?Gz2WA ? ? v@ @ @ @ H.?{Gz?j j j =N j lj j string Trying to read "%s". WordList %ld words %ld characters (WordList::readBinary:) Wrong length %ld. (WordList::readBinary:) Early end of file. (WordList::readBinary:) Length in header (%ld) does not match string (%ld). (Strings_to_WordList:) String "%s" not generic. Please genericize first. (Strings_to_WordList:) String "%s" not sorted. Please sort first. WordList.c q - thy string == thy length j j j j j j j j j A ?(ascio/getInteger:) Early end of file detected. (ascio/getInteger:) Early end of file detected in comment. (ascio/getInteger:) Found a string while searching for an integer. (ascio/getInteger:) Found an enumerated value while searching for an integer. (ascio/getInteger:) Found strange text while searching for an integer. (ascio/getUnsigned:) Early end of file detected. (ascio/getUnsigned:) Early end of file detected in comment. (ascio/getUnsigned:) Found a string while searching for an unsigned integer. (ascio/getUnsigned:) Found an enumerated value while searching for an unsigned integer. (ascio/getUnsigned:) Found a negative value while searching for an unsigned integer. (ascio/getUnsigned:) Found strange text while searching for an unsigned integer. %lu (ascio/getReal:) Early end of file detected. (ascio/getReal:) Early end of file detected in comment. (ascio/getReal:) Found a string while searching for a real number. (ascio/getReal:) Found an enumerated value while searching for a real number. (ascio/getReal:) Found strange text while searching for a real number. (ascio/getEnum:) Early end of file detected. (ascio/getEnum:) Early end of file detected in comment. (ascio/getEnum:) Found an integer while searching for an enumerated value. (ascio/getEnum:) Found a string while searching for an enumerated value. (ascio/getEnum:) No matching '>'. (ascio/getEnum:) Found strange text while searching for an enumerated value. (ascio/getString:) Early end of file detected. (ascio/getString:) Early end of file detected in comment. (ascio/getString:) Found a number while searching for a string. (ascio/getString:) Found an enumerated value while searching for a string. (ascio/getString:) No memory to extend string buffer by %ld bytes. (ascio/getString:) Character '%c' following quote. End of string or undoubled quote? ascio_Boolean false true ascio_Question no yes ascio_Existence absent exists = %d %d = %ld %ld = %u %u = %lu = %s %s = --undefined-- --undefined-- = %.20g %.20g = %.8g + %.8g i %.8g %.8g = %.17g + %.17g i %.17g %.17g = <%s> <%s> = <true> <true> = <false> <false> ? <yes> <yes> ? <no> <no> ? <exists> <exists> ? <absent> <absent> = " " " (bingete1:) %d is not a value of enumerated type "%s". (bingete2:) %d is not a value of enumerated type "%s". (bingets1:) Out of memory. Cannot create string of length %d. (bingets2:) Out of memory. Cannot create string of length %d. (bingets4:) Out of memory. Cannot create string of length %ld. abcio.c my ptr + nbytes <= my max (cacgete1:) %d is not a value of enumerated type "%s". (cacgete2:) %d is not a value of enumerated type "%s". (cacgets1:) Out of memory. Cannot create a string of length %d. (cacgets2:) Out of memory. Cannot create a string of length %d. (cacgets4:) Out of memory. Cannot create a string of length %ld. ?333333?N j 0Rj j REMOVED HIDDEN hidden SHOWN ADDED START-UP shown #unhidable @@m%ld|%s@ %s: @@p%ld|%s@ %s --------- , %%%%after "%s"%% , script "%s" @@a%ld|%s@ %s (%d) & %s : @@e%ld|%s@ : %s : --------- Objects Picture N Buttons %s Command not executed. Editors Actions A-M Actions N-Z ButtonEditor ButtonEditor help Help j j j lj j N j lj j N j j hj fN j j j N j j j TN j j \j N j j j %ld items Collection::copy: cannot copy item of class %s. Collection::equal: cannot compare items of class %s. size (empty) item []: %s %s %ld item [%ld]: (Collection::writeAscii:) Objects of class %s cannot be written. class name %ld Collection::readAscii: cannot read size. Object Object %ld: class %s %s%n Collection::readAscii: cannot read header of object %ld. Collection::readAscii: read item number %ld while expecting %ld. Collection::readAscii: wrong header at object %ld. Collection::readAscii: cannot read item of class %s. (Collection::readAscii:) Cannot read item of class %s. (Collection::writeBinary:) Objects of class %s cannot be written. %s%s Collection::readBinary: cannot read item of class %s. ? (Collection::readBinary:) Cannot read item of class %s. item Data my size Collection Collection_insert: out of memory. Collection.c data pos >= 1 && pos <= my size (Collection_join:) Objects are of different class (%s and %s). (Collection_join:) Not performed. Ordered right == left + 1 Sorted SortedSet SortedSetOfInt SortedSetOfShort SortedSetOfLong SortedSetOfFloat SortedSetOfDouble SortedSetOfString Cyclic::compare: subclass responsibility. Cyclic ? ? @ N j n lj Data (Data_copy:) Class %s cannot be copied. (Data_copy:) Object of class %s not copied. (Data_writeAscii:) I/O error. (Data_writeToConsole:) Class %s cannot be written. <none> Write to console: class %s, name "%s". (Data_writeToTextFile:) Objects of class %s cannot be written to a text file. w %s %ld File type = "ooTextFile" Object class = "%s" (Data_writeToTextFile:) Cannot write file "%.200s". (Data_writeToShortTextFile:) Objects of class %s cannot be written to a text file. File type = "ooTextFile short" "%s" (Data_writeToShortTextFile:) Cannot write file "%.200s". I/O error. (Data_writeToBinaryFile:) Objects of class %s cannot be written to a generic binary file. wb ooBinaryFile (Data_writeToBinaryFile:) Cannot write file "%.200s". (Data_writeLisp:) I/O error. (Data_writeLispToConsole:) Class %s cannot be written as LISP. Write as LISP sequence to console: class %s, name "%s". (Data_writeToLispFile:) Class %s cannot be written as LISP. %sLispFile (Data_writeToLispFile:) Error while writing file "%.200s". Disk probably full. (Data_readAscii:) %s not read. (Data_readAscii:) Early end of file. %s not read. (Data_readAscii:) I/O error. %s not read. r ooTextFile TextFile (Data_readBinary:) %s not read. (Data_readBinary:) Early end of file. %s not read. (Data_readBinary:) I/O error. %s not read. rb BinaryFile (Data_readFromBinaryFile:) File "%.200s" is not a Data binary file. (Data_readLisp:) %s not read. (Data_readLisp:) I/O error. %s not read. LispFile (Data_readFromLispFile:) File "%.200s" is not a Data LISP file. Data.c numFileTypeRecognizers < 100 (Data_readFromFile:) File %.200s not recognized. my - 1 -> size # ; ! ! < < < O %j 'j "j O s&j "j $#j O &j "j t#j O &j "j #j O &j $#j $j 1 O &'j $j d$j my %s my %s - 1 Changing field "%s" would damage the array "%s". %f + %f i %lf + %lf i <true> <false> <yes> <no> Edit field "%s" or click "Cancel". DataEditor.c ifield != 0 Not yet implemented. %s. %s [%ld..%ld] %s. %s [%ld..%ld] [%ld..%ld] %s. %s Change Cancel list verticalScrollBar label Open text Inspect DataEditor help Help DataSubEditor %d %ld %.8g %.17g %.8g + %.8g i %.17g + %.17g i <%s> (unknown) Class part "%s": %s %s [ ] %s [ ] [ ] _ StructEditor %s [%s] %s [%ld] [%ld] %s [%ld]: --------------------------- VectorEditor %s [%ld] [%ld] MatrixEditor ClassEditor (ClassEditor_init:) Class "%s" cannot be inspected. DataEditor (DataEditor_create:) Class "%s" cannot be inspected. ! O 'j n $ h'j t O (j n 'j %O (j n 'j EditorCommand EditorMenu %s (Editor_addCommand:) No menu "%s". Cannot insert command. (Editor_getMenuCommand:) No menu "%s" with item "%s". Command not available in %s. Undo Redo Undo? File Edit Cannot undo Editor WM_DELETE_WINDOW editor Help -- search -- Search manual... New editor script Open editor script... -- script -- Close Undo %s (_enum_search:) "%s" is not a value of enumerated type "%s". X*O *j n H )j ?ffffff@ R@ ? Q? ףp= ?? @ ?ffffff9@ffffff9Graphics Graphics_setWsViewport: coordinates too large: %d..%d x %d..%d goes outside %d..%d x %d..%d. h@ R@ ? (@ *@ ? 9O n6j )j *j %%%%BeginProlog %%%%BeginResource: procset (ppgb GraphicsPostscript procs) 1.0 0 /N { newpath } bind def /M { newpath moveto } bind def /L { rlineto } bind def /F { 10 { 1 exch rlineto } repeat } bind def /FONT { exch findfont exch scalefont setfont } bind def /C { 0 360 arc stroke } bind def /FC { 0 360 arc fill } bind def /PraatEncoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesinglright /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one /two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z /bracketleft/backslash/bracketright/asciicircum/underscore/quotesinglleft /a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute/agrave/acircumflex /adieresis/atilde/aring/ccedilla/eacute/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex /idieresis/ntilde/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls/registered/copyright/trademark /acute/dieresis/notequal/AE/Oslash/infinity/plusminus/lessequal/greaterequal/yen/mu /partialdiff/summation/product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft/guillemotright /ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe/endash/emdash/quotedblleft/quotedblright /quoteleft/quoteright/divide/lozenge/ydieresis/Ydieresis/fraction/currency /guilsinglleft/guilsinglright/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase /perthousand/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis /Igrave/Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi /circumflex/tilde/macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron ] def /PraatEncode { /font exch def /base exch def /basedict base findfont def /new basedict maxlength dict def basedict { exch dup dup /FID ne exch /Encoding ne and { exch new 3 1 roll put } { pop pop } ifelse } forall new /FontName font put new /Encoding PraatEncoding put font new definefont pop } def %%%%EndResource %%%%EndProlog %%%%BeginSetup %d %d { dup mul exch dup mul add 1.0 exch sub } setscreen /languagelevel where {pop languagelevel 1 ne {true setstrokeadjust} if} if true setstrokeadjust %%%%EndSetup %%%%Page: %d %d %%%%BeginPageSetup %g setlinewidth 2 setlinejoin %d 0 translate 90 rotate %.6g dup scale %%%%EndPageSetup showpage showpage %% redefined by encapsulating program %%%%Trailer %%%%Pages: %d %%%%EOF GraphicsPostscript w %%!PS-Adobe-3.0 %%%%Creator: Praat Shell 4.2 %%%%Title: %s %%%%CreationDate: %s %%%%PageOrder: Special %%%%Pages: (atend) %%%%EndComments %%!PS-Adobe-3.0 EPSF-3.0 %%%%BoundingBox: %d %d %d %d %%%%Creator: Praat Shell 3.8 %%%%Title: NO SCREEN PREVIEW, BUT WILL PRINT CORRECTLY [AO 7j )j h 7j ? *@ (@ ? GraphicsScreen GraphicsScreen.c my dc != NULL Graphics_altitude.c numberOfPoints <= MAXALTPATH Graphics_altitude: not enough memory. k ATV }/ p p ` p @ ?? @ ? o@%f setgray %.6g %.6g %.6g setrgbcolor %.6g setgray ? ?{Gz?u <7~u <7 Graphics_grey.c numberOfPoints <= MAXGREYPATH numberOfEdgeContours < MAXGREYEDGECONTOURS * numberOfBorders numberOfClosedContours < MAXGREYCLOSEDCONTOURS * numberOfBorders numberOfEdgePoints <= MAXGREYEDGEPOINTS * numberOfBorders iContour > 0 iPoint < MAXGREYPATH iPoint <= MAXGREYPATH Graphics_grey: not enough memory. o@ ? ? HCC @3o@ffffff9@ Q?Graphics_image.c iy >= iy1 && iy <= iy2 gsave N %d %d M %d %d L %d %d L %d %d L closepath clip %d %d translate %d %d scale /picstr %ld string def %ld %ld 8 [%ld 0 0 %ld 0 0] { currentfile picstr readhexstring pop } image /lorow %ld string def /hirow %ld string def /scanline %ld string def %ld %ld 8 [%ld 0 0 %ld 0 0] /irow 0 def { irow 0 eq { currentfile lorow readhexstring pop pop lorow hirow copy pop } if irow %ld mod %ld eq { hirow lorow copy pop irow %ld ne { currentfile hirow readhexstring pop pop } if } if /rowphase irow %ld add %ld mod %ld div def 0 1 %ld { /icol exch def /locol icol %ld sub %ld idiv def /hicol icol %ld ge { %ld } { icol %ld add %ld idiv } ifelse def /colphase icol %ld add %ld mod %ld div def /plow lorow locol get def /phigh lorow hicol get def /qlow hirow locol get def /qhigh hirow hicol get def /value plow phigh plow sub colphase mul add 1 rowphase sub mul qlow qhigh qlow sub colphase mul add rowphase mul add def scanline icol value 0 le { 0 } { value 255 ge { 255 } { value } ifelse } ifelse cvi put } for /irow irow 1 add def scanline } image /row %ld string def { currentfile row readhexstring pop pop /plow row locol get def /phigh row hicol get def /value plow phigh plow sub colphase mul add def scanline icol value 0 le { 0 } { value 255 ge { 255 } { value } ifelse } ifelse cvi put } for scanline } image /p lorow icol get def /q hirow icol get def /value p 1 rowphase sub mul q rowphase mul add def scanline icol value 0 le { 0 } { value 255 ge { 255 } { value } ifelse } ifelse cvi put } for /irow irow 1 add def scanline } image %.2x grestore h@ ? ? ? @9RFߑ? V V@ f@ p@ffffff9@ $@ R@ d@-DT! @cܥL@[%d %d] 0 setdash %g setlinewidth [] 0 setdash N %d %d moveto %d %d %d %d %d %d %d %d %d %d F %d %d L currentpoint stroke moveto stroke N %d %d M closepath fill N %d %d M %d %d lineto %d %d lineto %d %d lineto closepath stroke N %d %d M %d %d lineto %d %d lineto %d %d lineto closepath fill N %d %d %d C gsave %f %f translate %f %f scale N 0 0 1 0 360 arc %f %f scale stroke grestore N %d %d %d %f %f arc stroke N %d %d %d FC gsave %d %d translate %d %d scale N 0 0 1 FC grestore N %d %d M %d %d L gsave %d %d translate %f rotate N 0 0 M -%d 0 %d -60 60 arc closepath fill grestore Cannot get cursor position. _Graphics_growRecorder: out of memory. This message will not show up on future occasions. Graphics_play: unknown opcode (%d). %f %f Graphics_record.c my irecord == old_irecord + added_irecord Graphics_readRecordings: error reading record %ld out of %ld. Graphics_readRecordings: error reading record %ld out of %ld. Opcode %d, args %ld. jrecord != my irecord: %ld, %ld 333333? ? Gz?? R@{Gz? @@ q q?h/r? B C-DT! @ f@ V@ p@llV?llF? @ ?llv?q q qq? @? ? (@II? @??>>? ? ? ? ? ? ? ? ? SILDoulos IPA93 Arial Times New Roman Courier New New Century Schoolbook Book Antiqua Symbol Wingdings Courier-Bold Courier-Oblique Courier-BoldOblique Courier CourierNewPS-BoldMT CourierNewPS-ItalicMT CourierNewPS-BoldItalicMT CourierNewPSMT CourierNew-Bold CourierNew-Italic CourierNew-BoldItalic CourierNew Times-Bold Times-Italic Times-BoldItalic Times-Roman TimesNewRomanPS-BoldMT TimesNewRomanPS-ItalicMT TimesNewRomanPS-BoldItalicMT TimesNewRomanPSMT TimesNewRoman-Bold TimesNewRoman-Italic TimesNewRoman-BoldItalic TimesNewRoman NewCenturySchlbk-Bold NewCenturySchlbk-Italic NewCenturySchlbk-BoldItalic NewCenturySchlbk-Roman Palatino-Bold Palatino-Italic Palatino-BoldItalic Palatino-Roman BookAntiquaPS-BoldMT BookAntiquaPS-ItalicMT BookAntiquaPS-BoldItalicMT BookAntiquaPSMT BookAntiqua-Bold BookAntiqua-Italic BookAntiqua-BoldItalic BookAntiqua %s SILDoulosIPA93Bold SILDoulosIPA93Regular TeX-xipa10-Praat-Regular ZapfDingbats Helvetica-Bold Helvetica-Oblique Helvetica-BoldOblique Helvetica Arial-BoldMT Arial-ItalicMT Arial-BoldItalicMT ArialMT Arial-Bold Arial-Italic Arial-BoldItalic %s-Praat /%s /%s-Praat PraatEncode /%s /Font resourcestatus { pop pop /%s /%s-Praat PraatEncode } { /%s /%s-Praat PraatEncode } ifelse /%s %d FONT /%s %d selectfont 0 0 1 setrgbcolor %d %d M gsave currentpoint translate %.6g rotate 0 0 M [1 0 0.25 1 0 0] concat 0 0 M ( \%c %c \%d%d%d ) show grestore 0 0 0 setrgbcolor Graphics_text.c iline == lines ? @ V@ ? p@ ? q= ףp? r@ư> $@h㈵> R@ffffff9@? f@cܥL@ $@ $@ >@ $@ 4@ I@ $@ 4@ >@ I@ $@ 4@ >@ I@ Q@ $@ .@ 4@ >@ I@ Q@ $@ .@ 4@ >@ D@ I@ Q@10^^ \.c10^^ %.4g %.6g %s 9yP Rj lj ( 8Pj @ t@ (@ffffff? @@ *@? b@ `s@? @ ?ffffff&@ N@ ? @ @Q ??333333? Q?$I$I?m۶m?ffffff?333333?= ףp=?zG?(\?? ףp= ? ףp= ?zG?Q ?333333??333333? ?? t@ |@/P Tj 'j 0Rj HyperPage.font HyperPage.fontSize HyperLink %s %ld Print Left or inside header Middle header Right or outside header: Right or outside header Left or inside footer Middle footer Right or outside footer Mirror even/odd headers 0 (= no page numbers) First page number Font Times Helvetica New Century Schoolbook Palatino Font size 12 Font size (points) Search for page a Page verticalScrollBar PostScript settings... File Print page... -- close -- Go to Search for page... Back Forward -- page -- Page up Page down 10 14 18 24 Font size... Font... < > < 1 1 > drawingArea HyperPage.c XtWindow (my drawingArea) HyperPage yP `Uj n Uj P @Vj n (Uj ?InterpreterVariable You cannot use 'e' as the name of a variable (e is the constant 2.71...). You cannot use 'pi' as the name of a variable (pi is the constant 3.14...). You cannot use 'undefined' as the name of a variable. Interpreter Include files nested too deep. Probably cyclic. include include Include file "%s" not read. form endform word real positive integer natural boolean sentence text choice optionmenu button option comment Unknown parameter type: "%s". Missing parameter: "%s". %s Script arguments $file %ld Missing matching quote. 1 yes on Yes On YES ON 0 no off No Off NO OFF Unknown value "%s" for boolean "%s". Unknown value "%s" for choice "%s". %d Unknown value "%s" for option menu "%s". Unknown label "%s". Interpreter.c type != 0 $ Editor "%s" does not exist. label Duplicate label "%s". Too many labels. %.47s newline$ tab$ shellDirectory$ defaultDirectory$ assert undefined false Script assertion fails in line %ld (%s): %s call Missing procedure name after 'call'. Missing procedure name after 'procedure'. Call to procedure "%s" has too many arguments. Call to procedure "%s" has too few arguments. Call depth greater than %d. Procedure "%s" not found. dec endif endfor Unmatched 'endfor'. endwhile while Unmatched 'endwhile'. endproc Unmatched 'endproc'. else if Unmatched 'else'. elsif elif elsif elif Unmatched 'elsif'. 'elsif' not matched with 'endif'. exit from to Missing 'to' in 'for' loop. Missing loop variable after 'for'. for Unmatched 'for'. Unmatched 'form'. goto Missing label name after 'goto'. Unmatched 'if'. The value of the 'if' condition is undefined. inc procedure Unmatched 'proc'. repeat stopwatch until Unmatched 'until'. Unmatched 'while'. Missing '=', '<', or '>' after variable %s. Missing file name after variable %s. Missing expression after variable %s. 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" j j j j j j (j ,j 7j <j Fj Nj Vj ]j hj sj ~j j j j j j j j j j j j mP j n 0 j ManPage_TYPE _ intro entry normal list_item tag definition code prototype formula picture script list_item1 list_item2 list_item3 tag1 tag2 tag3 definition1 definition2 definition3 code1 code2 code3 code4 code5 page_title ManPage ~P j lj j Uj Yj ^j cj Uj Yj ij nj oj nj ij nj tj {j Uj Yj j j Uj Yj Uj Yj j nj j nj j nj 5j nj Lj nj uj nj j nj j nj j nj j {j j {j j {j 1j {j j {j \ nj j j j j j j j j j j j j ManPages.c *p == '@' (ManPages::grind:) Link starting with "@@" is too long: %s Cannot find page title. Cannot find author. Cannot find date. Cannot find recording time. end of file Cannot find text. Cannot find sound file "%s". %s Cannot find script "%s". .man r File "%s". ManPages Page "%s" contains a dangling link to "%s". (ManPages::grind:) %ld dangling links encountered. See console window. ilinkHither == grandNlinks && ilinkThither == grandNlinks <p> </p> <h3> </h3> <dd> <dt> <code> <br></code> <table width="100%"><tr><td align=middle> </table> <dd> <dd> <dd> <dt> <dt> <dt> <code> <code> <code> <code> <code> <p><font size=-2>[sorry, no pictures yet in the web version of this manual]</font></p> <ul> <dl> <li> </ul> </dl> <table border=0 cellpadding=0 cellspacing=0><tr><td width=100 align=middle> </i> </b> </code> <a href=" \FI _ .html </a> "> <i> <i><b> </sub> <sub> <b> <b><i> </sup> <sup> </font> } <font size=-1> <td width=100 align=middle> < > & ; &# .xbm"></sub> <sub><img src="symbols/ A B Chi Delta E H Phi Gamma I K Lambda M N Omega O Ø Pi Psi P Sigma <sup>TM</sup> T Theta perp Upsilon sqrt Xi Zeta alpha beta2 <b>o</b> chi delta diamond epsilon <=> eta2 phi2 <i>f</i> phi gamma integ2 iota kappa lambda L µ nu omega2 propto omega omicron infty otimes pi psi rho2 sigma2 sigma sum theta tau upsilon xi × zeta2 - -> ± ll <= <-> <- leq => neq ident appeq gg geq ' " / div approx .gif"> <img align=middle src="symbols/ <img src="symbols/ .GIF"> <img src="greekGIF/ January February March April May June July August September October November December </title></head><body bgcolor="#FFFFFF"> <html><head><meta name="robots" content="index,follow"> <title> </b></font></table></table> <table border=0 cellpadding=0 cellspacing=0><tr><td bgcolor="#CCCC00"><table border=4 cellpadding=9><tr><td align=middle bgcolor="#000000"><font face="Palatino,Times" size=6 color="#999900"><b> <h3>Links to this page</h3> <li><a href=" </a> .html"> <hr> <address> <p>© , </p> </address> </body> </html> j j j j j j j j j j j j j ? Q? r@ $@ ?j j j j j j j j j j j j A Q /j 0Rj h @j January February March April May June July August September October November December Write to HTML file .html Write all pages as HTML files Type a directory name: directory Search for page Page Best matches The best matches to your query seem to be: \bu @@%s Links to this page @@%s@ ppgb Paul Boersma djmw David Weenink \co %s, %s %ld, %ld Print range Left or inside header Middle header Manual Right or outside header Left or inside footer Middle footer Right or outside footer Mirror even/odd headers Print all pages whose title starts with: Intro Print pages starting with 1 First page number Suppress "Links to this page" Home Record Play Copy last played to list Search: searchText Print manual... File Write page to HTML file... Write manual to HTML directory... -- close -- Search for page (list)... Go to Manual help Help Jan Feb Mar Apr Jun Jul Aug Sep Oct Nov Dec %s %ld, %ld Page %ld not found. Page "%s" not found. j j gj j j j 6j j j sj j j j ;j j j j j j ^j j j j j j Nj _j zj j j j j #j Uj j ej j Sj j j j j j j Nj j j j j /j Pj xj j j j j Lj \j j j j j j j j Jj j 7j Rj j *j tj j j j j "j j <j j j Dj j j j j %j j j ^j lj j k k The documentation system for the P\s{RAAT} program. You will get a manual window every time you choose anything from a #Help menu or press a #Help button. How to find what you are looking for You can navigate the manual in several ways: \bu To go to the Intro, use the #H button. \bu To go to the information behind a %link (a piece of blue text), #click on it. \bu To go forward and backward through a tutorial with numbered pages, use "1 >" and "< 1". \bu To %revisit previous pages, use the #< and #> buttons. \bu To browse %alphabetically, use the horizontal scroll bar and the buttons named "< 1" and "1 >", or the ##Search for page (list)...# command in the ##Go to# menu. \bu To find a page with a %%known title%, use the ##Search for page...# command. The fastest way to find what you want is often the #Search button. Search In the text field after the Search button, you can type strings, separated by spaces. When you press the #Return (or #Enter) key, or click the #Search button, all manual pages are searched for the combination of strings that you typed. The titles of the 20 best matching pages are displayed as links. ##Example:# to know how to create a pitch contour from a sound, type sou pit and press #Return. The best matches should appear on top. These should include ##Sound: To Pitch (ac)...# and ##Sound: To Pitch (cc)...#. The search is case-insensitive. For instance, the search string "$script" will give you all the pages that contain the words %script, %Script, %description, %PostScript, or %SCRIPT, and so on. #Background. The search algorithm uses the following heuristics: \bu A match in the page title is better than one in the rest of the text. \bu Pages with many matches are better than those with few. Your own man pages To create your own man pages, create @ManPages text files. You can create a documentation or education system with files that you and others can read into P\s{RAAT} (with the @@Read from file...@ command). Your files will become a hypertext system very similar to the usual @Manual. Example 1: a single document If you create a single ManPages file, it will look like a manual with a single page. Here is an example: ManPagesTextFile "Welkom" "miep" 19970820 0 <intro> "Hallo allemaal!" <entry> "Belangrijk..." <normal> "Hoogge\bse\" \" erd publiek!" <normal> "Einde." A ManPages file should start with the following information: 1. The word "ManPagesTextFile" on the first line. 2. The title of the man page, between double quotes. This will be drawn at the top of the page. The name of the ManPages file should be derived from the title (see below). 3. The author of the man page, between double quotes. This will be drawn at the bottom of the page. 4. The date you created or modified the page, in the format year \-- month (two digits) \-- day (two digits), without spaces. 5. The recording time. If this is not zero, three sound buttons (see below) will appear at the top of the page. 6. A sequence of paragraph types and texts. You put the types between < and >, and the texts between double quotes (if your text contains a double quote, you should write two double quotes). The format of a ManPages text file is rather free, as long as the first line is correct, the four required pieces of information are there in the correct order, and there is a correct alternation between paragraph texts and types. If you put multiple elements on a line, there should be at least one space between them. You may distribute texts across multiple lines, as long as you do not add any spaces: <normal> "Hoogge\bse\" \" erd publiek!" This will have exactly the same effect as above. Example 2: multiple documents The above example with a single document is not very useful. You will usually want to refer to other documents: "Welcome" "ppgb" 19970820 1.0 <intro> "Welcome to our transcription course." <entry> "Groups of speech sounds" <normal> "You can listen to the following sounds from the languages of the world, pronounced by a single speaker (me):\"r <list_item> "\@ Vowels, quite problematic for Dutch students!" <list_item> "\@ \@ Dorsal fricatives\@ , equally problematic!" With the symbol `\@ ', you create a %link to another ManPages file. A link will be drawn in blue on your screen. In this example, you have created links to the files ##Vowels.man# and ##Dorsal_fricatives.man# in the same directory as the current file (all ##.man# files have to be in the same directory; this makes it likely that their names are unique). If the link contains spaces or other non-alphanumeric symbols, you have to use three `\@ ' symbols, as shown; with a single word, you may use a single `\@ '. In resolving the file name, the ManPages system replaces spaces and other special symbols with underscores, and converts any initial lower-case character by its upper-case variant. For instance, if your link is "\@ \@ back vowels\@ ", the file name will be ##Back_vowels.man#. The %title attribute of ##Back_vowels.man# must be equal to the link name, though capitalization of the first letter is allowed. Thus, the title of ##Back_vowels.man# will probably be "Back vowels". Likewise, the starting file with the title "Welcome" should have the name ##Welcome.man# if any other files refer to it. Paragraph types A normal paragraph will have type <normal>. The hypertext system will leave a blank space between paragraphs with this type. The first paragraph of a man page will normally have the type <intro>. Though this may look the same as <normal>, the search system of the @Manual may take account of the distinction. Headings (like the title "Paragraph types" of this subsection) have type <entry>. This will be drawn in a larger character size. For lists, you use the type <list_item>. You will often combine this with %button symbols, like in the following: <normal> "Choose a colour:" <list_item> "\bsbu \@ Red." <list_item> "\bsbu \@ Green." <list_item> "\bsbu \@ Blue." For text that should appear with a fixed character width, you use the type <code>. For a paragraph that should be connected with the following paragraph without leaving a blank space (probably a list item or a definition), you use the type <tag>. For a paragraph with a blank left margin, you use the type <definition>. Special symbols and styles You can use all of P\s{RAAT}'s @@special symbols@ and @@text styles@, except that some %single text-style symbols have different meanings: \bu A single percent sign introduces a word in italic: $$\% pot$ gives %pot. \bu A single number sign introduces a word in bold: $$\# pot$ gives #pot. \bu A single dollar sign introduces a word in monospace: $$\$ pot$ gives $pot. \bu A single underscore is rendered as an underscore: $$a_b$ gives a_b. To create a single italic, bold, or subscripted letter, you revert to the usual technique for stretches of italic, bold, or subscripted text. So, to get %F__1_, you type $$\% F_\_ 1_. Sound links Your text may contain links to sound files. They are drawn in blue. The format is: <normal> "You should know that \@ \@ \bsFIct.aifc|\bsct\@ is more open than \@ \@ \bsFIo.aifc|o\@ ." On your screen, you will see an #\ct and an #o symbol, both drawn in blue. If you click on one of these sound links, one of the sound files ##ct.aifc# or ##o.aifc# will be played. The format of the sound link "$$\@ \@ \bsFIo.aifc|o\@ $" is to be understood as follows. The pipe symbol separates the link information (\bsFIo.aifc) from the viewable link text (o). The link information is introduced with a symbol (\bsFI) that tells the manual system that a sound file name follows. The manual system reads this file, sees that it contains a sound, and plays that sound. You can use relative path names, e.g., \bsFIsounds/o.aifc refers to the file ##o.aifc# in the subdirectory #sounds, which must be contained in the same directory as the ##.man# files; use the forward slash (/) if you want your man pages to run on all platforms (Windows, Macintosh, Unix). Script links Your text may contain links to Praat scripts. They are drawn in blue. The format is: <normal> "Here is a script that \@ \@ \bsSCdraw.praat|draws\@ what you have selected." On your screen, you will see the word #draws, drawn in blue. If you click on it, the script ##draw.praat# will be executed. The string "$$\bsSC$" indicates that a script file name follows. As with sounds, you can use relative file paths. The script can take arguments: <normal> "This script \@ \@ \bsSCload2files.praat hello.wav hello.TextGrid|loads\@ some files." If the script file name or any arguments except the last contain spaces, they have to be enclosed within double quotes, which have to be doubled again in the ManPage code: <normal> "Here is a script that \@ \@ \bsSC\" \" my scripts/draw.praat\" \" |draws\@ what you have selected." <normal> "This script \@ \@ \bsSC\" \" my scripts/load2files.praat\" \" \" \" my sounds/hello.wav\" \" my textgrids/hello.TextGrid|loads\@ some files." How to separate link information and link text The separation between link information and viewable link text, as seen in the above description of sound and script links, is actually a general mechanism in the hypertext system. For instance, if you want to see the text "x" in blue on your screen, and create a link from it to the page "Dorsal fricatives", you specify the link as $$\@ \@ Dorsal fricatives|x\@ $. Sound buttons If the %%Recording time% attribute is not 0, three buttons will appear at the top of the page: 1. The #%Rec button allows you to record a sound from the microphone. 2. The #%Play button allows you to play this recorded sound. In this way, you can compare your own utterances with the sounds behind the sound links, for example. 3. The #%Pub button copies the latest sound to the list of objects, allowing you to perform analyses on it, save it to disk, et cetera. The latest sound may be a sound that you recorded with the #%Rec button, a sound that you played with the #%Play button, or a sound that you played by clicking on a sound link, whichever occurred most recently. Manual ppgb ManPages ? ? 3@ @ 4@ N@1@ @ @ @ @ "@ $@ &@ (@ *@ ,@ .@ 0@ 1@ 2@ 3@ffffff @ @ ffffff@ @ #@ @ @ A,k @ A,k @ pA,k @ `A,k @ PA,k @ 0A,k @ A,k @ @,k @ pA,k @ `A,k @ PA,k @ @A,k @ `A,k @ PA,k @ @,k @ A,k @ A,k @ pA,k @ `A,k @ PA,k @ @A,k @ 0A,k @ A,k @ A,k @ A,k A A -k A A-k A `A-k A PA -k A @A,k A A-k A A,k A @-k A `A-k A PA -k A @ -k A A$-k A A(-k A pA,-k A `A0-k A PA4-k A @A8-k A A<-k A A@-k A @D-k 0A `AF-k 0A PAJ-k @A AN-k @A AP-k @A pAT-k @A `AX-k @A PA\-k @A @A`-k @A Ab-k @A Af-k PA @Aj-k `A `An-k `A @Ar-k pA At-k pA Av-k pA pAz-k pA `A~-k pA PA-k pA @A-k pA A-k pA A-k A A-k A A-k A pA-k A `A-k A PA-k A 0A-k A A-k A `A-k A PA-k A A-k A `A-k A PA-k A A-k A `A-k A PA-k @ @.k @ @.k @ @.k @ @/k A @/k A @ /k ff@ @ /k ff@ @/k A @/k @ @/k @ @/k @ @ /k @ @"/k A @&/k A @*/k @ @@,/k @ ?0/k @ @4/k @ @8/k @ @</k @ @@/k A @D/k A @H/k @ ?L/k @ P/k @ R/k A V/k A Z/k /k 10k B0k a1k 1k ]2k 2k 93k 3k 3k 4k p4k 4k 4k 5k Q5k f5k 5k "6k \6k 6k 6k 77k 7k 7k 7k 38k z8k 8k "9k ;9k p9k 9k 9k 9k :k ):k F:k c:k :k :k :k :k :k ;k 8;k R;k l;k ;k ;k ;k ;k <k <k <<k b<k }<k <k <k <k <k <k =k =k n=k w=k =k =k >k r>k >k >k >k ??k ?k ?k @k <@k N@k t@k Ak n=k pAk Ak _Bk Bk Bk Bk @ @!Q Ck Ck Ck SDk mDk &Gk Hk !Hk DHk bHk Hk Hk Hk ,Ik }Ik Ik Ik Jk >Jk fJk Jk Jk Kk Kk 9Kk eKk Kk Kk Kk 0Lk bLk Lk Lk @ @{&Q Mk Mk SDk Nk Ok Ok Pk XPk ^Pk dQk Qk Qk Qk .Rk lRk Rk Rk Sk KSk ZSk Sk Sk Sk Sk Tk LTk }Tk Tk Tk Uk Uk 8Vk BVk XPk Vk Wk Ok Xk 8Vk Xk Xk Yk Yk Yk Zk {Zk Zk [k [k \k $\k \k ]k ]k ]k B^k ^k c_k _k _k _k Ok /`k `k `k `k `k ak ak ak ak ak 8Vk ,bk bk bk &ck bck ck ck <dk }dk dk aek ek XPk !gk hk hk ik #ik _k Ok ik `k 0jk Cjk `k ak ak ak ak ak Qk jk _k Ok Ulk `k lk lk nmk ymk `k ak ak ak ak ak _k Ok 7nk `k nk nk \ok kok pk pk pk pk =qk Iqk Qk qk _k Ok sk `k nk Msk \ok sk pk pk pk pk =qk Iqk Qk tk Yk Ok xuk 8Vk uk hvk vk vk vk "wk \wk ywk wk wk wk wk wk wk xk 8xk `xk xk xk xk xk yk xk yk yk nyk yyk yk `k zk Zzk |k |k |k h}k }k S~k m~k sk k k рk k ܁k k Tk ȃk k k k 1k Nk |k 3k nk k tk rk k k Ok 0k 8Vk k XPk k k Ok ݍk k k `k Rk Uk k k k k Tk ik k k XPk k _k Ok Vk 8Vk k k Vk 8Vk k k <k Ok ~k k k 'k k k *k <k Ok ~k k k tk k k *k <k Ok ޕk Ek k Pk k Ök k Tk Ck rk k k k k 8Vk &k XPk gk Uk k .k Uk k k XPk k 8Vk k ak jk Uk ٞk XPk Kk Uk k 8Vk k XPk ek ʢk p b m \ff \bf \bc \b^ \O. \mj f v \vs \tf \dh \|1 t d n s z \rt r \fh l \d^ t^l d^l \l- \lz \rl \|2 \sh \zh \|- \t. \d. \n. \s. \z. \r. \f. \l. ! \cc \zc c \j- \nj \c, \jc j \yt \j^ \ht \wt w k \gs \ng x \gf \ml \lc \g^ q \gc \nc \cf \ri \rc \G^ \h- \9e \?- \hc \9- \?g h \h^ bilabial labiodental dental alveolar alv. lateral postalveolar retroflex alveolo-palatal palatal labial-palatal labial-velar velar uvular pharyngeal epiglottal glottal voiceless plosive voiced plosive nasal voiceless fricative voiced fricative approximant trill tap or flap lateral approx. implosive click i y \i- \u- \mt u \ic \yc \hs e \o/ \e- \o- \rh o \sw \at \ef \oe \er \kb \vt \ct \ae a \Oe \as \ab front central back close close centralized close-mid open-mid open When drawing text into the @@Picture window@ or into an editor, you can use %%backslash sequences% to display various kinds of special symbols. European symbols To get the symbol "\a^" (a-circumflex), you type "\bsa\^ ", i.e., a sequence of backslash + a + circumflex. In this way, you can get a hundred non-ASCII symbols that are used in the alphabets of many European languages. You can also use these symbols in info messages sent from scripts. \a" \bsa\" \e" \bse\" \i" \bsi\" \o" \bso\" \u" \bsu\" \y" \bsy\" \A" \bsA\" \E" \bsE\" \I" \bsI\" \O" \bsO\" \U" \bsU\" \a' \bsa' \e' \bse' \i' \bsi' \o' \bso' \u' \bsu' \y' \bsy'\A' \bsA' \E' \bsE' \I' \bsI' \O' \bsO' \U' \bsU' \Y' \bsY' \a` \bsa` \e` \bse` \i` \bsi` \o` \bso` \u` \bsu` \A` \bsA` \E` \bsE` \I` \bsI` \O` \bsO` \U` \bsU` \a^ \bsa\^ \e^ \bse\^ \i^ \bsi\^ \o^ \bso\^ \u^ \bsu\^ \A^ \bsA\^ \E^ \bsE\^ \I^ \bsI\^ \O^ \bsO\^ \U^ \bsU\^ \a~ \bsa\~ \n~ \bsn\~ \o~ \bso\~ \A~ \bsA\~ \N~ \bsN\~ \O~ \bsO\~ \ae \bsae \o/ \bso/ \ao \bsao \Ae \bsAe \O/ \bsO/ \Ao \bsAo \c, \bsc, \C, \bsC, \ss \bsss \th \bsth \Th \bsTh \!d \bs!d \?d \bs?d \cu \bscu (%currency), \Lp \bsLp (%sterling), \Y= \bsY= (%yen), \fd \bsfd (Dutch %florin), \c/ \bsc/ (%cent) \SS \bsSS (%section), \|| \bs|| (%paragraph) \co \bsco (%copyright), \re \bsre (%registered), \tm \bstm (%trademark) \a_ \bsa_ (%ordfeminine), \o_ \bso_ (%ordmasculine) \<< \bs<< (%guillemotleft), \>> \bs>> (%guillemotright) Mathematical symbols \.c \bs.c (%periodcentered), \xx \bsxx (%multiply), \:- \bs:- (%divide), \/d \bs/d (%fraction) \dg \bsdg (%degree), \'p \bs'p (%minute or %prime), \"p \bs\" p (%second or %%double prime%) - - (%minus), \-- \bs-- (%endash), \+- \bs+- (%plusminus) \<_ \bs<_ (%lessequal), \>_ \bs>_ (%greaterequal), \=/ \bs=/ (%notequal) \no \bsno (%logicalnot), \an \bsan (%logicaland), \or \bsor (%logicalor) \At \bsAt (%universal), \Er \bsEr (%existential), \.3 \bs.3 (%therefore) \oc \bsoc (%proportional), \=3 \bs=3 (%equivalence), \~~ \bs~~ (%approxequal) \Vr \bsVr (%radical) \<- \bs<- (%arrowleft), \-> \bs-> (%arrowright), \<> \bs<> (%arrowboth) \<= \bs<= (%arrowdblleft), \=> \bs=> (%arrowdblright), \eq \bseq (%arrowdblboth) \^| \bs\^ | (%arrowup), \=~ \bs=~ (%congruent), \_| \bs_| (%arrowdown) \oo \bsoo (%infinity), \Tt \bsTt (%perpendicular) \O| \bsO| (%emptyset), \ni \bsni (%intersection), \uu \bsuu (%union), \c= \bsc= (%propersubset), \e= \bse= (%element) \dd \bsdd (%partialdiff) \ox \bsox (%circlemultiply), \o+ \bso+ (%circleplus) \su \bssu (%summation), \in \bsin (%integral) Greek letters To get \ep\up\ro\et\ka\al, you type \bsep\bsup\bsro\bset\bska\bsal. \al \bsal \Al \bsAl %alpha \be \bsbe \Be \bsBe %beta \ga \bsga \Ga \bsGa %gamma \de \bsde \De \bsDe %delta \ep \bsep \Ep \bsEp %epsilon \ze \bsze \Ze \bsZe %zeta \et \bset \Et \bsEt %eta \te \bste \Te \bsTe %theta \t2 \bst2 \io \bsio \Io \bsIo %iota \ka \bska \Ka \bsKa %kappa \la \bsla \La \bsLa %lambda \mu \bsmu \Mu \bsMu %mu \nu \bsnu \Nu \bsNu %nu \xi \bsxi \Xi \bsXi %xi \on \bson \On \bsOn %omicron \pi \bspi \Pi \bsPi %pi \ro \bsro \Ro \bsRo %rho \si \bssi \Si \bsSi %sigma \s2 \bss2 \ta \bsta \Ta \bsTa %tau \up \bsup \Up \bsUp %upsilon \fi \bsfi \Fi \bsFi %phi \f2 \bsf2 \ci \bsci \Ci \bsCi %chi \ps \bsps \Ps \bsPs %psi \om \bsom \Om \bsOm %omega \o2 \bso2 Phonetic symbols See @@Phonetic symbols@ Miscellaneous \bs \bsbs %backslash \bu \bsbu %bullet \cl \bscl (%club), \di \bsdi (%diamond), \he \bshe (%heart), \sp \bssp (%spade) See also @@Text styles@ When drawing text into the @@Picture window@ or into an editor, you can use text styles other than regular Roman. Italic, bold, superscript, subscript With the following symbols, you introduce stretches of text drawn in special styles: \% : the following letter will be italic. \# : the following letter will be bold. \# \% : the following letter will be bold-italic. \^ : the following letter will be superscript: \% m\% c\^ 2 gives %mc^2. \_ : the following letter will be subscript. Example: %F__0_ is typed as \% F_0. \% \% : the following letters will be italic, until the following \% : $$Now \% \% you\% try$ gives: Now %%you% try. The same goes for \# \# , \^ \^ , and \_ \_ . \bss{...}: small: $$W\bss{ARP}$ gives: W\s{ARP} To draw a \% , \# , \^ , or \_ symbol, you type "$$\bs\% $", "$$\bs\# $", "$$\bs\^ $", or "$$\bs\_ $": a backslash, the symbol, and a space. On Xwindows machines, the font `Symbol' will never look bold or italic, but it will be printed correctly. @@Special symbols@ To draw phonetic symbols in the @@Picture window@ or in the @TextGridEditor, make sure that you have installed the SIL Doulos IPA 1993 font, e.g. from www.praat.org. You can then use backslash sequences as described in: \bu @@Phonetic symbols: consonants \bu @@Phonetic symbols: vowels \bu @@Phonetic symbols: diacritics To draw phonetic symbols for consonants in the @@Picture window@ or in the @TextGridEditor, make sure that you have installed the SIL Doulos IPA 1993 font, e.g. from www.praat.org. You can then use the backslash sequences in the following table. Other consonant symbols: \l~ \bsl~ (%%l with tilde%): velarized %l \hj \bshj (%%heng with hooktop%): the Swedish rounded post-alveolar & velar fricative How to remember the codes For most of the codes, the first letter tells you the most similar letter of the English alphabet. The second letter can be %t (%turned), %c (%capital or %curled), %s (%script), - (%barred), %l (%%with leg%), %i (%inverted), or %j (%%left tail%). Some phonetic symbols are similar to Greek letters but have special phonetic (%f) versions with serifs (\ff, \bf, \gf) or are otherwise slightly different (\tf, \cf). The codes for \ng (%engma), \dh (%eth), \sh (%esh), and \zh (%yogh) are traditional alternative spellings. The retroflexes have a period in the second place, because an alternative traditional spelling is to write a dot under them. The code for \fh is an abbreviation for %fishhook. To draw phonetic diacritical symbols in the @@Picture window@ or in the @TextGridEditor, make sure that you have installed the SIL Doulos IPA 1993 font, e.g. from www.praat.org. You can then use the backslash sequences in the following list. In line: \:f \bs:f the phonetic length sign \|f \bs|f the phonetic stroke t\cn t\bscn (%corner): unreleased plosive Understrikes: n\|v n\bs|v (%strokeunder): syllabic consonant b\0v b\bs0v (%ringunder): voiceless (e.g. lenis voiceless plosive, voiceless nasal or approximant) o\Tv o\bsTv (%lowering): lowered vowel; or turns a fricative into an approximant o\T^ o\bsT\^ (%raising): raised vowel; or turns an approximant into a fricative e\-v e\bs-v (%minusunder): backed o\+v o\bs+v (%plusunder): fronted o\:v o\bs:v (%diaresisunder): breathy voice o\~v o\bs~v (%tildeunder): creaky voice t\Nv t\bsNv (%bridgeunder): dental (as opposed to alveolar) e\3v e\bs3v (%halfringright): slightly rounded u\cv u\bscv (%halfringleft): slightly unrounded Overstrikes: \gf\0^ \bsgf\bs0\^ (%ringover): voiceless \ep\'^ \bsep\bs'\^ (%acuteover): high tone \ep\`^ \bsep\bs`\^ (%graveover): low tone \ep\-^ \bsep\bs-\^ (%minusover): mid tone (or so) \ep\~^ \bsep\bs~\^ (%tildeover): nasalized \ep\v^ \bsep\bsv\^ (%caronover, %hac\v^ek, %wedge): rising tone \ep\^^ \bsep\bs\^ \^ (%circumover): falling tone o\:^ o\bs:\^ (%diaresisover): centralized k\lip t\lis k\bslip (%ligature): simultaneous articulation, or single segment To draw phonetic symbols for vowels in the @@Picture window@ or in the @TextGridEditor, make sure that you have installed the SIL Doulos IPA 1993 font, e.g. from www.praat.org. You can then use the backslash sequences in the following table. Other vowel symbols are: \sr \bssr (%%schwa with right hook%): rhotacized schwa For most of the codes, the first letter tells you the most similar letter of the English alphabet. The second letter can be %t (%turned), %c (%capital), %s (%script), %r (%reversed), - (%barred or %retracted), or / (%slashed). One symbol (\ef) is a phonetic version of a Greek letter. The codes for \sw, \rh, \hs and \kb are abbreviations for %schwa, %%ram's horn%, %horseshoe, and %%kidney bean%. One of the commands in the #Margins and #World menus of the @@Picture window@. Purpose To view and change the current world coordinates of the horizontal and vertical axes. Usage The axes are normally changed by every drawing operation in the dynamic menu, i.e., by object-specific drawing commands with titles like ##Draw...# and ##Paint...# (the drawing commands in the Picture window, like ##Paint rectangle...#, do not change the axes). You would use the ##Axes...# command if your data are not in an object. Example The following script would draw a person's vowel triangle: \# Put F1 (between 300 and 800 Hz) along the horizontal axis, \# and F2 (between 600 and 3600 Hz) along the vertical axis. ##Axes...# 300 800 600 3600 \# Draw a rectangle inside the current viewport (selected area), \# with text in the margins, and tick marks in steps of 100 Hz along the F1 axis, \# and in steps of 200 Hz along the F2 axis. Draw inner box Text top... no Dani\bse\" l's Dutch vowel triangle Text bottom... yes \% F_1 (Hz) Text left... yes \% F_2 (Hz) Marks bottom every... 1 100 yes yes yes Marks left every... 1 200 yes yes yes \# Draw large phonetic symbols at the vowel points. Text special... 340 Centre 688 Half Times 24 0 u Text special... 481 Centre 1195 Half Times 24 0 \bso/ \# Etcetera This example would draw the texts "Dani\e"l's Dutch vowel triangle", "%F__1_ (Hz)", and "%F__2_ (Hz)" in the margins, and the texts "u" and "\o/" at the appropriate positions inside the drawing area. A command in the File menu of the @@Picture window@. It copies the selected part of the picture to the clipboard. You can then `Paste' it into any program that knows pictures. Behaviour Though all the picture data will be written to the clipboard, only the part that corresponds to the selected part of the Picture window (the %viewport) will be visible. If you have a PostScript printer, you will want to use @@Write to EPS file...@ instead. If the picture is too large, e.g. a spectrogram that does not seem to fit into the clipboard, you can try @@Write to Windows metafile...@ instead. One of the commands in the #Margins menu of the @@Picture window@. To draw a rectangle inside the drawing area, leaving @margins on all four sides for drawing text and marks. The widths of the margins depend on the current font size. a kind of PostScript file that can easily be imported into word processors and drawing programs. In Praat, you can create an Encapsulated PostScript (EPS) file by choosing @@Write to EPS file...@. A command in the #Edit menu of the @@Picture window@. It erases all your drawings. One of the menus of the @@Picture window@. It allows you to choose the default font of the text to be used in subsequent drawing, and its size (character height). Sizes You can choose any of the sizes 10, 12, 14, 18, or 24 directly from this menu, or fill in any other size in the ##Font size...# form. Unix: the font size will be rounded to the nearest size available on Xwindows, which is one from 10, 12, 14, 18, or 24 points; PostScript-printing a picture where you specified a font size of 100, however, will still give the correct 100-point character height. Macintosh and Windows: all sizes are drawn correctly (what you see on the screen is what you get on your printer). The widths of the margins depend on the current font size, so if you want to change the font size, do so before making your drawing. Fonts With these commands, you set the font in which subsequent text will de drawn: Times, Helvetica, New Century Schoolbook, Palatino, or Courier. You can mix the Symbol and IPA alphabets with the normal Roman alphabets and use sequences of backslash + digraph for @@special symbols@ (see also @@phonetic symbols@). For instance, you can get an \e" by typing \bse\" , or a \ss by typing \bsss; you can get an \ep by typing \bsep, or a \ct, which is a turned c, by typing \bsct. In a PostScript preview on the Indigo (double-click on a PostScript file), New Century Schoolbook will be replaced by Courier. If you print to a PostScript printer, all fonts will be correct. Styles You can use all graphical @@text styles@ in the Picture window. Four of the commands in the #Margins menu of the @@Picture window@. To draw a specified number of marks per decade into the @margins around the drawing area, along a logarithmic axis. Arguments %%Marks per decade the number of marks that will be drawn for every decade. %%Write numbers if on, real numbers will be written in the margin, expressed in the domain or range of your latest drawing in the horizontal or vertical direction. %%Draw ticks if on, short line pieces will be drawn in the margin. %%Draw dotted lines if on, dotted lines will be drawn through your drawing. If your vertical logarithmic axis runs from 10 to 100, and %%Marks per decade% is 1, marks will only be drawn at 10 and 100; if %%Marks per decade% is 2, marks will be drawn at 10, 30, and 100; if it is 3, marks will be drawn at 10, 20, 50, and 100; if it is 4, marks will be drawn at 10, 20, 30, 50, and 100; if it is 5, marks will be drawn at 10, 20, 30, 50, 70, and 100; if it is 6, marks will be drawn at 10, 15, 20, 30, 50, 70, and 100; if it is 7 (the maximum), marks will be drawn at 10, 15, 20, 30, 40, 50, 70, and 100. The space around most of your drawings in the @@Picture window@. World coordinates With the commands in the #Margins menu, you draw text, ticks, numbers, or a rectangle, in the margins around the latest drawing that you made, or you draw dotted lines through or text inside this last drawing. You specify the positions of these things in world coordinates, i.e., in coordinates that refer to the natural coordinate system of your last drawing. The numbers that you can mark around your drawing also refer to these coordinates. For instance, after drawing a spectrum with ##Spectrum: Draw...#, you can draw a dotted line at 2000 Hz or at 60 dB by choosing ##One mark bottom...# or ##One mark left...# and typing "2000" or "60", respectively. The margin commands work with all the drawings that leave margins around themselves, such as ##Sound: Draw...#, ##Spectrogram: Paint...#, ##Polygon: Paint...#, and more. They do not work properly, however, with the commands that draw vocal tract shapes, like ##Art & Speaker: Draw...# and ##Artword & Speaker: Draw...#, because these can only be drawn correctly into a square viewport. Limited validity The margin commands work only on the latest drawing that you made (unless you @Undo that drawing). Margin size The size of the margins depends on the font size, so be sure that you have the font size of your choice before you make your drawing. You can set the font size with the @@Font menu@. To draw any number of equally spaced marks into the @margins around the drawing area. %%Number of marks% the number of equally spaced marks (2 or more) that will be drawn; there will always be marks at the beginning and end of the domain or range. If you draw a Sound with a domain between 0 and 1 seconds to an amplitude range between -1 and 1, choosing ##Marks left...# with a number of 3 and %%Draw dotted lines% on, will give you horizontal marks and horizontal dotted lines at -1, 0, and 1; choosing ##Marks bottom...# with a number of 6 and %%Draw dotted lines% off, will give you vertical marks at 0, 0.2, 0.4, 0.6, 0.8, and 1. To draw a number of equally spaced marks into the @margins around the drawing area. %%Units the units, relative to the standard units, for writing the numbers; for example, if you want time in milliseconds instead of seconds (which is always the standard), %Units should be 0.001. %%Distance the distance between the equally spaced marks that will be drawn, expressed in %Units; for example, if you want marks every 20 milliseconds, and %Units is 0.001, this argument should be 20. To draw one mark into one of the four @margins around the drawing area, along a logarithmic axis. %%Position the %x (for top or bottom) or %y (for left or right) position of the mark, expressed in the logarithmic domain or range of your latest drawing in the horizontal or vertical direction. %%Write number if on, a real number equal to %Position will be written in the margin, at an %x (for top or bottom) or %y (for left or right) position equal to %Position. %%Draw tick if on, a short line piece will be drawn in the margin, at an %x (for top or bottom) or %y (for left or right) position equal to %Position. %%Draw dotted line if on, a dotted line will be drawn through your drawing, at an %x (for top or bottom) or %y (for left or right) position equal to %Position. %%Draw text if not empty, this text will be drawn in the margin, at an %x (for top or bottom) or %y (for left or right) position equal to %Position. After you draw a Pitch logarithmically in a range between 100 and 400 Hz, choosing ##One logarithmic mark left...# with a position of 200 and %%Draw dotted line% on, will give you a horizontal mark "200" and a horizontal dotted line at a %y position of 200, which is exactly halfway between 100 and 400 Hz. To draw one mark into one of the four @margins around the drawing area. the %x (for top or bottom) or %y (for left or right) position of the mark, expressed in the domain or range of your latest drawing in the horizontal or vertical direction. if on, a real number equal to `Position' will be written in the margin, at an %x (for top or bottom) or %y (for left or right) position equal to %Position. If you draw a Sound to an amplitude range between -1 and 1, choosing ##One mark left...# with a position of 0.0 and %%Draw dotted line% on, will give you a horizontal mark "0" and a horizontal dotted line at a y position of 0. To choose the default line type and colour to be used in subsequent drawing of lines and painted areas. The line type used by @@Draw inner box@ (plain), and the line type of the dotted lines in the ##Mark...# commands will not be affected. The commands in the @Margins menu will always draw in black. One of the two main windows in P\s{RAAT}. File menu \bu @@Read from Praat picture file...@, @@Write to Praat picture file... \bu @@Copy to clipboard@, @@Write to Windows metafile...@ \bu @@PostScript settings... \bu @@Write to EPS file... \bu @@Print... Edit menu \bu @@Undo@, @@Erase all @Margins menu \bu @@Draw inner box \bu @@Text left/right/top/bottom... \bu @@Marks left/right/top/bottom every... \bu @@One mark left/right/top/bottom... \bu @@Marks left/right/top/bottom... \bu @@Logarithmic marks left/right/top/bottom... \bu @@One logarithmic mark left/right/top/bottom... \bu @@Axes... World menu \bu @@Text... Select menu \bu @@Select inner viewport...@, @@Select outer viewport...@, @@Viewport text... @@Pen menu @@Font menu One of the commands in the File menus of many windows. The PostScript settings influence @Printing and writing to @@Encapsulated PostScript@ files. %%Allow direct PostScript printing% (Windows and Macintosh only) this determines whether Praat prints explicit PostScript commands to your printer if it is a PostScript printer. This is what you will usually want. However, if you find that some of the options that you choose in the printing dialog seem not to be supported (e.g. scaling, printing two-up...), you may switch this off; Praat will then send native Windows or Macintosh drawing commands, which the printer driver will try to translate to PostScript. If your printer does not support PostScript, this switch is ignored. On Unix, this switch is superfluous, since all printing is done directly in PostScript. %%Grey resolution you can choose from two image qualities: \bu the %finest quality for grey plots (106 spots per inch), which gives the best results directly from the printer; \bu a %photocopyable quality, which has fewer spots per inch (85) and gives the best results after photocopying. Your choice of the grey resolution influences direct PostScript printing and writing to @@Encapsulated PostScript@ files. %%Paper size% (Unix only) you can choose from A4 (210 \xx 297 mm), A3 (297 \xx 420 mm) or US Letter (8.5 \xx 11\"p). This choice applies to Unix only; on Windows, you choose the paper size in the ##Print...# dialog; on Macintosh, you choose the paper size in the ##Page setup...# dialog. %%Orientation% (Unix only) you can choose between %portrait (e.g., 297 mm high and 210 mm wide) and %landscape (e.g., 210 mm high and 297 mm wide). This choice applies to Unix only; on Windows, you choose the orientation in the ##Print...# dialog; on Macintosh, you choose the orientation in the ##Page setup...# dialog. %%Magnification% (Unix only) the relative size with which your picture will be printed; normally 1.0. This choice applies to Unix only; on Windows, you choose the scaling in the ##Print...# dialog; on Macintosh, you choose the scaling in the ##Page setup...# dialog. %%Print command% (Unix only) When printing on Unix, a temporary PostScript^\re file is created in the "/tmp" directory; it will have a name like "picXXXXXX", and is automatically removed after printing. This file is sent to the printer with the print command, which will often look like $$lp -c \% s$, where $$\% s$ stands for the file name. One of the commands in the File menu of the @@Picture window@. With this command, you send your entire picture immediately to the printer. See the @Printing tutorial for details. The best results will be obtained on PostScript printers, since these have built-in facilities for images (e.g. spectrograms) and rotated text. However, the printed page will look reasonable on colour inkjet printers as well. 1. Printing on Windows Some Windows computers are in a network that includes a PostScript printer. If a PostScript printer is available, Praat will usually write direct PostScript commands to that printer (see @@PostScript settings...@ if you want to switch this off). P\s{RAAT} also supports non-PostScript printers, such as most colour inkjet printers. 2. Indirect printing with GhostView If you don't have a PostScript printer, and you still want PostScript quality, you can save the picture to an EPS file (@@Write to EPS file...@). You can then view this file with the freely available GhostView^\tm program, which you can download from ##http://www.cs.wisc.edu/~ghost#. 3. Indirect printing with your word processor If you save your picture to an EPS file, you will be able to include it as a picture in your favourite word processor (Microsoft^\re Word^\tm, LaTeX...). See @@Write to EPS file...@. If you don't have a PostScript printer, you could again use GhostView^\tm to print your document to any printer, after you printed your document to a PostScript file. You can do the same if you are the lucky owner of Adobe^\re Acrobat^\tm Distiller^\tm, which is more reliable than GhostView but is also expensive. 4. Creating a PDF file If you have Distiller or GhostView, you can print the entire Word^\tm or LaTeX document to a PostScript file, and convert this to a PDF file, which anyone in the world can view and print with the free Adobe^\re Acrobat^\tm Reader program. Note: when creating a PDF file on Windows if you have Acrobat, ##do not use PDFWriter#, but choose Distiller as your printer. also, ##do not use "Print to PDF"# from your Microsoft Word File menu; otherwise, your EPS files will not show in the PDF file. Indirect printing without PostScript Pictures included in your word processor via @@Copy to clipboard@ or @@Write to Windows metafile...@ will print fine, though not as nicely as EPS files. To read a picture that you saved earlier with @@Write to Praat picture file...@. The picture will be drawn across whatever is currently visible in the Picture window. With the help of this command, you can transfer a picture from a Unix machine to a Macintosh. Praat for Macintosh can write the picture to an @@Encapsulated PostScript@ file with a screen preview. One of the commands in the #World menu of the @@Picture window@. To write text inside the drawing area. Scope This works with all the drawings that leave @margins around themselves. %x horizontal position, expressed in the horizontal domain of your latest drawing. %y vertical position, expressed in the vertical range or domain of your latest drawing. %%Horizontal alignment determines the horizontal alignment of the text relative to %x. %%Vertical alignment determines the vertical alignment of the text relative to %y. %%Text will be drawn in the current font and font size that you set with the @@Font menu@. With the ##Text...# command, you can use all @@special symbols@ and @@text styles@. To write text into the @margins around the drawing area. The text will be centred along the side. Text at the left or right will be turned by 90 degrees and written up and down, respectively. One of the commands in the #Edit menu of the @@Picture window@. It erases your most recently created drawing, which could have come from a command in the Objects window or from one of the drawing commands in the World and @Margins menus. This command will erase some drawings, but it will not change your settings in the #Pen and #Font menus (line type, line width, font, font size, and colour). The world window will be what it was after the latest-but-one drawing, so that you can use the @Margins menu as if the latest drawing had never happened. One of the commands in the #Select menu of the @@Picture window@. To determine where your next drawing will occur. The viewport The "viewport" is the part of the Picture window where your next drawing will occur. Its margins are pink. The %inner viewport does not include the margins, the %outer viewport does (see @@Select outer viewport...@). Normally, you select the viewport by dragging your mouse across the Picture window. However, you would use this explicit command: \bu from a script; \bu if you want a viewport that cannot be expressed in halves of an inch. The %outer viewport includes the margins, the %inner viewport does not (see @@Select inner viewport...@). To write text inside the viewport, at nine different places, with a rotation between 0 to 360 degrees. Arguments: determines the horizontal alignment of the text: \bu %Left means pushed against the left edge of the viewport; \bu %Right means pushed against the right edge of the viewport; \bu %Centre means horizontally centred in the viewport. determines the vertical alignment of the text: \bu %Top means pushed against the top of the viewport; \bu %Bottom means pushed against the bottom of the viewport; \bu %Half means vertically centred in the viewport. For rotated text, the alignment arguments will not only determine the position inside the viewport, but also the alignment in the rotated coordinate system. This gives surprises now and then; so, if you want several rotated texts that align with each other, you should do this by varying the viewport, not the alignment. You can use all @@special symbols@ and @@text styles@. It saves the picture to an @@Encapsulated PostScript@ (EPS) file, which can be imported by many other programs, such as Microsoft^\re Word^\tm. PostScript = highest possible quality! With EPS files you can use high-quality graphics in your word-processor documents. The quality is higher than if you use @@Copy to clipboard@. The big limitation EPS pictures imported in Word for Windows will show correctly only on PostScript printers, or with GhostView, or in PDF files created by Adobe^\re Acrobat^\tm Distiller^\tm. To print EPS pictures on non-PostScript printers, use a Linux or Macintosh computer. If Word cannot read your EPS files, you may have to install EPS support from the Office^\tm CD, because the standard installation of Office may not support EPS files. When you import an EPS file in an older version of Word, you may only see the file name and the date and time of creation, and a message that the picture will print correctly to a PostScript printer (it will, if the PostScript driver has been selected). Though all the contents of the Picture window are written to the EPS file, only the part that you selected in the Picture window (the %viewport) may become visible in Word (or another program). Settings The EPS picture is saved with the grey resolution and fonts that you specified with @@PostScript settings...@. It saves a picture in a format that can be imported into P\s{RAAT} later with @@Read from Praat picture file...@. With the help of this command, you can transfer the contents of the picture window between computers or even between platforms, for instance from a Macintosh to a Windows computer. It saves the selected part of the picture in an "enhanced metafile" (.EMF) format, which can be imported by many Windows programs, like Adobe^\re Illustrator^\tm or Microsoft^\re Word^\tm. Though all the picture data will be written to the file, only the part that you selected in the Picture window (the %viewport) may become visible in the other program. You will not use this command very often, because it is usually easier to copy the selection to the clipboard with the @@Copy to clipboard@ command, and `Paste' it into the other program. You may use a metafile instead of the clipboard if the clipboard is too large for the other program to read, or if you want to transfer the picture to another computer. If you have a PostScript printer, you would use @@Write to EPS file...@ instead for best printing results. Special symbols ppgb Text styles Phonetic symbols: consonants Phonetic symbols: diacritics Phonetic symbols: vowels Axes... Copy to clipboard Encapsulated PostScript Erase all Font menu Logarithmic marks left/right/top/bottom... Margins Marks left/right/top/bottom... Marks left/right/top/bottom every... One logarithmic mark left/right/top/bottom... One mark left/right/top/bottom... Pen menu Picture window PostScript settings... Print... Printing Read from Praat picture file... Text... Text left/right/top/bottom... Undo Select inner viewport... Select outer viewport... Viewport text... Write to EPS file... Write to Praat picture file... Write to Windows metafile... k Bk Mk ^k k {k k pk k ck k k :k [k Ͳk k k k ӳk Գk k k ӳk k =k dk k k k k k k ok k You can extend the functionality of the P\s{RAAT} program by adding modules written in C to it. All of P\s{RAAT}'s source code is available under the General Public Licence. 1. Warning Before trying the task of learning how to write P\s{RAAT} extensions in C, you should be well aware of the possibilities of @scripting. Many built-in commands in P\s{RAAT} have started their lives as P\s{RAAT} scripts, and scripts are easier to write than extensions in C. 2. Getting the existing source code You obtain the P\s{RAAT} source code via ##www.praat.org#, in a file with a name like ##praat4301_sources.tar.gz# (depending on the P\s{RAAT} version), and unpack this with #gunzip and ##tar xvf# (on Unix), or ##StuffIt^\re Expander^\tm# (on Macintosh), or ##Aladdin^\re Expander^\tm# (on Windows). The result will be a set of directories called #ipa, #GSL, #sys, #dwsys, #fon, #dwtools, #LPC, #FFNet, #artsynth, #main, and #makefiles, plus a makefile and a Codewarrior project for Macintosh and Windows. 3. Building P\s{RAAT} on Unix To compile and link P\s{RAAT} on Unix, you go to the directory that contains the source directories and the makefile, and copy a ##makefile.defs# file from the #makefiles directory. On Linux, for instance, you type > cp makefiles/makefile.defs.linux.dynamic ./makefile.defs The file ##makefile.defs# may require some editing after this, since the libraries in your Linux distribution may be different from mine, or your Motif library (##Xm.a# or ##Xm.so#) is in a different location. On Silicon Graphics Irix, you will use ##makefile.defs.sgi#; on Sparc Solaris, you will probably use ##makefile.defs.solaris.cde#; on HPUX, you will use ##makefile.defs.hpux#; on Intel Solaris, ##makefile.defs.solaris.cde.up.ac#. P\s{RAAT} is preferably linked with a real Motif version (Lesstif gives some minor problems), i.e., there must be a library ##Xm.so# or ##Xm.a# and an #Xm include directory. There exists a free Motif library for Linux (##openmotif-devel-2.1.30-1_ICS.i386.rpm# from ICT); on SGI, Solaris, and HPUX, Motif libraries are included with the system, and the include directory comes with the development package. 4. Building P\s{RAAT} on Macintosh Open ##praat.mcp# in CodeWarrior (version 9.0 or higher), choose the target ##praat_macx# (for MacOS X), ##praat_mac9# (for MacOS 8.5 to 9.2), and choose Make or Run. You probably have to edit the prefix (Language Settings: C/C++ Preprocessor), e.g. by changing "\# if 0" to "\# if 1". 5. Building P\s{RAAT} on Windows Open ##praat.mcp# in CodeWarrior (version 9.0 or higher), choose the target ##praat_win#, and choose Make or Run. P\s{RAAT} may compile under Visual C++ as well. 6. Extending P\s{RAAT} You can edit ##main/main_Praat.c#. This example shows you how to create a very simple program with all the functionality of the P\s{RAAT} program, and a single bit more: \# include "praat.h" DIRECT (HelloFromJane) Melder_information ("Hello, I am Jane."); END void main (int argc, char **argv) { praat_init ("Praat_Jane", argc, argv); INCLUDE_LIBRARY (praat_uvafon_init) praat_addMenuCommand ("Objects", "New", "Hello from Jane...", NULL, 0, DO_HelloFromJane); praat_run (); return 0; } 7. Learning how to program To see how objects are defined, take a look at ##sys/Thing.h#, ##sys/Data.h#, ##sys/oo.h#, the ##XXX_def.h# files in the #fon directory, and the corresponding ##XXX.c# files in the #fon directory. To see how commands show up on the buttons in the fixed and dynamic menus, take a look at the large interface description file ##fon/praat_Fon.c#. 8. Using the P\s{RAAT} shell only For building the P\s{RAAT} shell (the Objects and Picture windows) only, you need only the code in the four directories #ipa, #GSL, #sys, and #dwsys. You delete the inclusion of praat_uvafon_init from #main. You will be able to build a P\s{RAAT} shell, i.e. an Objects and a Picture window, which has no knowledge of the world, i.e., which does not know any objects that can be included in the list of objects. You could use this P\s{RAAT} shell for modelling your own world and defining your own classes of objects. For advanced programmers only. Programming with Praat ppgb Gl Gl Hl Il $Il CIl IIl Jl Jl Il ?Kl CIl \Kl Ll Ll Ll Il Ml Ml ZNl eNl Ol Ol ;Pl FPl qPl {Pl Pl Ql /Ql 9Ql Rl Rl Sl Sl Sl Sl Ul Ul Ul Vl Vl Vl NWl 0Xl AXl Xl Xl Ll JYl Il Yl Zl bZl hZl [l [l Rl \l I]l Sl P]l X]l *^l 4^l ^l ^l 9_l C_l _l _l 0Xl AXl Xl `l `l al al *al al al 2bl bl bl dl dl dl dl el <el ^el el el el fl +fl Xfl pfl fl gl gl hl hl hl hl Til il il kl ml ml &ol 8ol pl ql ql ql %rl drl rl sl Jsl sl tl tl tl ul bul }ul vl vl vl wl `wl rwl vxl xl xl xl yl ;zl zl D{l {l {l |l |l }l w}l }l }l }l r~l ~l ~l Ul l l $l `l l l Dl l Ёl l Fl l l l Hl l l l $l `l l l Dl l Ёl l Ql el l l ބl l l *l 9l ml ul l (l Wl ^l l l l ͆l &l 7l yl l χl l 8l bl kl l l Jl pl l l l l l Dl Ql l El Sl gl nl ~l Sl l l l Sl l nl l Sl (l *l Ώl Sl яl l el l (l l 5l Sl Il Nl בl l l Dl Wl gl l l l Ǔl ؓl l l l l l l l Cl al l l l l ͗l Fl fl l Θl Hl il l l ֛l l l l l l ҟl ۟l ol l l l `l l l l l ܢl l Kl l l l 4l Ol dl l l l l l %l (l Yl l l l l l Al il l l l ml l l l ¨l l l l l el l Ӫl (l l l zl l l l l /l ml l ˮl ߮l l l _l l l (l \l ڱl l ٲl l ӳl l l .l bl ôl Ӵl l յl ƶl l &l 3l ~l l l ķl l l Wl pl l l #l 3l Dl Ul ֹl l /l kl l l 1l l l l >l dl l Ҽl l !l Ll al tl l l ɽl ݽl l gl l ξl l Al ~l l l Hl fl wl l l l l l l =l Ol xl l l ll l l l 'l 9l Gl l l l l l l :l Il l l l 4l Bl fl l l l l #l bl !l &l Cl Gl al ml l l l l l l l 'l Wl cl l l l l l 0l hl yl l l l l l l l l l l 6l Dl Ol bl ql |l l l l l l l l l ;l Gl ql }l l l l l 'l 6l Ql `l l l l l l ;l l l l l 4l Ll cl rl l l l l l l l l fl l Nl hl l l l l Cl [l l l l l /l Ml l l l l l l l l Hl [l l l l l Zl ll l l l l 0l ;l l l <l Nl l l Dl al l l l l .l >l dl xl l Ul il l l l l ]l l l l ?l Tl l l l l l /l l l @l sl l l l ;l nl l l -l l l l @l l l tl l l l l l ,l Al al l l l l -l l l Tl .l Jl l l l ^l l l Gl l l l l l [l ll l l l l dl jl l l 7l =l ~l l l l hl nl (l .l l l l l l l l dl l m m m m m <m m 4m Cm m m m 0m Gm m m m m |m m m $m m m m m ~m m m m m m m | m m m ^ m { m @ m W m ]m ym Nm ^m ym m m m 3m Nm Gm dm rm m m m m m m Km pm m m m m m m m Vm hm m (m Xm Mm m m p m m m Ul m X m m m m m K"m "m #m #m >$m $m G%m u&m &m {l f'm 'm 'm (m O)m )m K*m *m F+m z+m +m +m +m Y,m ,m ,m -m vl .m =/m G/m B0m ^1m xl 1m 2m CIl 53m 3m D4m 4m ~l \5m 5m 5m %6m _6m 6m 6m 6m '7m j7m 7m 7m 7m 7m ,8m n8m 8m 9m /9m x9m 9m 9m 2:m a:m :m :m ;m :;m d;m ;m ;m ;m m m <m =m =m ?m ?m Am Am Am Bm :Cm Dm Em Fm Fm Fm Gm Gm Gm %Hm cHm Hm Im Jm Jm Jm 1Km bKm Mm 5Mm Mm Om aOm Om Om Pm Pm Qm 5Rm jRm Rm Sm Sm _Tm Tm Tm Vm Vm Wm Wm Wm Wm Wm Xm m Xm <Xm Xm Xm Xm 6Ym OYm Ym Ym Ym Zm Zm Zm $[m Q[m [m [m G\m W\m ]m 2]m :]m H]m r]m ]m ]m ]m ]m ]m ]m Q^m ^m m ^m ^m ^m ^m (_m m <_m _m _m _m `m `m am am am Gbm nbm bm am bm bm wcm cm cm cm ,dm hdm dm dm em :em Gem Uem em em fm 6m 6m '7m j7m .gm Ggm 7m qgm gm gm hm hm hm &im /im ;im Uim im im 'jm Sjm jm jm zl l l jm l 6km km km jm km km km #lm jm ]lm lm lm lm jm lm mm mm lm jm mm mm nm om *om /im eom wom om om om zpm pm pm pm :qm qm qm qm rm rm rm sm sm &sm 7sm =sm Nsm Usm }sm sm sm sm tm )um ?um Vum 2]m ]m um um mvm |vm vm wm ywm wm wm wm wm wm &xm lxm zxm xm xm ym aym ym ym xm ym ym xm ym nzm zm zm `{m {m R|m [|m |m |m |m }m *}m 2]m ]m R|m m}m }m (~m ~m ~m m +m Hm fm R|m m m 3m Om R|m qm m m m um %m m m m m m Ԃm um m im m Ãm Ƀm ރm m 7m Am ҅m }m m m φm m bm m Ήm ԉm `m wm m ,8m n8m 8m 9m /9m x9m 9m 9m 2:m .m m m m m m m m fm m m m m ޏm m m m ݐm Zm {m +m Im m m m 8m m m m m Zm hm m m m m m 2m ]m m m m $m {m m Ζm m m m *m Fm Zm nm m m m m Ɨm m m pm řm m {m m gm m m m ǚm m m m %m :m Nm m Ɨm gm m m m m m 0m Xm m ݜm (m Hm hm m 3m m m :m m m m +m Dm m m !m Gm m m im m Ƣm m m $m <m Im m m 0m Cm m m m m Jm bm m m m m Хm ۥm m 8m <m jm Xm m 2m [m m ̨m m Ym hm m ˩m m gm ~m m 8m m m m m m m 8m Pm Um em km zm ĭm ۭm wm Ѯm m m Cm Ym m үm m m Vm km m m m m m m m m m dm ձm m Ʋm m ۲m m m +m rm m m m 4m Am ״m m m Ul (m m ,m am m m m m m /m 7m Zm em m m m m /m Dm _m m m em m m <m m m ۼm m m ým m Um wm þm pm m 1m m m m m m m 2m ]m m m m pm m $m fm :m zm m m m m m Am Fm _m wm m m Tm m sm m m Qm m m m wm m Am m m Sm m m m &m tm m Hm _m nm wm m m m 4m m m m m 7m Vm qm m m m .m 7m Vm m m Fm m m wm m Am m _m wm m m m m m m :;m d;m ;m Lm al m Il %m .m m m m m m 3m %m +m fm m m m m 9m m m mm m m m m m m hm m m m m m m ym al m m fm cm zm m :m m cm m m m rm m m m fm zm .m Cm ^m Zm tm m m m m .m Fm {m *^l m mm am m m $m m m m m m m m m m m Cm m m m 6m m Nm m m m ~m m m m 9_l m m 5m Om m m Pm im m m Im 8m & n (n n Rn n n /n Bn rn n Pm n em n n n 5n Zn n n n n n An n n n <n an n n Pm n em m n bn vn n n , n E n _ n x n n n n n n n n ! n P n k n n m n n O n p n n n n n En Xn {n n n n 8n m ^n dn Gn n n n 3n en n en n n n 9n n n n ln n n n n n n &n em m +n n Fn gn tn n m n n En em n vn n n n n n n n n /n An `n zn n n n em m n n The commands in the @@Dynamic menu@ of the @@Object window@. These commands are only available if the right kinds of objects are selected. They are shown in a scrollable list, or in the #Write menu if they start with "Write to " or "Append to ". One of the hidden commands in the Praat menu of the @@Object window@. With this command, you add a button to the dynamic menu in the Object window. Arguments See @@Add to dynamic menu...@. Usage You can use this command in your @@Initialization script@, and you will see it in your @@Buttons file@ after you have added an action button with this command or with the @ScriptEditor. Normally, however, if you want to add a command to the dynamic menu, you would use the command @@Add to dynamic menu...@ of the @ScriptEditor instead. One of the hidden commands in the Praat menu of the @@Object window@. With this command, you add a button to any of the fixed menus in the Object or Picture window. See @@Add to fixed menu...@. You can use this command in your @@Initialization script@, and you will see it in your @@Buttons file@ after you have added a menu button with this command or with the @ScriptEditor. Normally, however, if you want to add a command to a fixed menu, you would use the command @@Add to fixed menu...@ of the @ScriptEditor instead. A command in the File menu of the @ScriptEditor. With this command, you add a button to the dynamic menu in the @@Object window@. This button will only be visible if the specified combination of objects is selected. Clicking the button will invoke the specified @@Praat script@. %%Class 1 the name of the class of the object to be selected. For instance, if a button should only appear if the user selects a Sound, this would be "Sound". %%Number 1 the number of objects of %class1 that have to be selected. For most built-in commands, this number is unspecified (0); e.g., the user can choose #Draw... or ##To Spectrum# regardless of whether she selected 1, 2, 3, or more Sound objects. If the number of selected objects is different from %number1, the button will be visible but insensitive. %%Class 2 the name of the class of the second object to be selected, different from %class1. Normally the empty string (""). %%Number 2 the number of selected objects of %class2. %%Class 3 the name of the class of the third object to be selected, different from %class1 and %class2. Normally the empty string (""). %%Number 3 the number of selected objects of %class3. %%Command the title of the new command button (or label, or submenu title). To get a separator line instead of a command text (only in a submenu), you specify a unique string that starts with a hyphen ('-'); the @ButtonEditor may contain some examples of this. If the command starts with "Write to ", it will be placed in the @@Write menu@. %%After command a button title in the dynamic menu or submenu where you want your new button. If you specify the empty string (""), your button will be put at the bottom. You can specify a push button, a label (subheader), or a cascade button (submenu title) here. %%Depth 0 if you want your button in the main menu, 1 if you want it in a submenu. %%Script the full path name of the script to invoke. If you saved the script you are editing, its name will already have been filled in here. If you do not specify a script, you will get a separating label or cascading menu title instead, depending on the %depth of the following command. Example If one object of class Sound is selected, you want a submenu called "Filters" after the #Convolve button, containing the commands "Autocorrelation" and "Band filter...", separated by a horizontal separator line: Add to dynamic menu... Sound 0 "" 0 "" 0 "Filters -" "Convolve" 0 Add to dynamic menu... Sound 1 "" 0 "" 0 "Autocorrelation" "Filters -" 1 /u/praats/demo/autocorrelation.praat Add to dynamic menu... Sound 0 "" 0 "" 0 "-- band filter --" "Autocorrelation" 1 Add to dynamic menu... Sound 1 "" 0 "" 0 "Band filter..." "-- band filter --" 1 /u/praats/demo/bandFilter.praat Note that "Filters -" will be a submenu title, %because it is followed by subcommands (%depth 1). Note that %number1 is 1 only for the executable buttons; for the cascade button and the separator line, this number is ignored. Usage convention Please adhere to the convention that commands that take arguments, end in three dots (...). Using this command in a script To add a dynamic button from a script (perhaps your @@Initialization script@), use the hidden shell command @@Add action command...@ instead. With this command, you add a button to any fixed menu in the @@Object window@ or in the @@Picture window@. Clicking the added button will invoke the specified @@Praat script@. %Window the name of the window ("Objects" or "Picture") that contains the menu that you want to change. %Menu the title of the menu that you want to change. If %window is "Objects", you can specify the Praat, New, Read, Help, Goodies, or Preferences menu (for the Write menu, which depends on the objects selected, you would use @@Add to dynamic menu...@ instead). If %window is "Picture", you can specify the File, Edit, Margins, World, Select, Pen, Font, or Help menu. %Command the title of the new menu button. To get a separator line instead of a command text, you specify a unique string that starts with a hyphen ('-'); the @ButtonEditor contains many examples of this. a button title in the menu or submenu after which you want your new button to be inserted. If you specify the empty string (""), your button will be put in the main menu. %Depth %Script the full path name of the script to invoke. If you saved the script you are editing, its name will already have been filled in here. If you do not specify a script, you will get a cascading menu title instead. Example 1 In the #Matrix submenu of the @@New menu@, you want a separator line followed by the command "Peaks": Add to fixed menu... Objects New "-- peaks --" "Create simple Matrix..." 1 Add to fixed menu... Objects New "Peaks" "-- peaks --" 1 /u/praats/demo/peaks.praat Example 2 In the @@New menu@, you want a submenu called "Demo", with a subitem titled "Lorenz...": Add to fixed menu... Objects New "Demo" "" 0 Add to fixed menu... Objects New "Lorenz..." "Demo" 1 /u/praats/demo/lorentz.praat To add a fixed button from a script (perhaps your @@Initialization script@), use the hidden shell command @@Add menu command...@ instead. A function that can be used in @@Formulas@. The complement of the cumulative binomial distribution. Syntax $$binomialQ (%p, %k, %n) the probability that in %n trials an event with probability %p will occur at least %k times. Calculator example A die is suspected to yield more sixes than a perfect die would do. In order to test this suspicion, you throw it 1,000 times. The result is 211 sixes. The probability that a perfect die yields at least 211 sixes is, according to @@Calculator...@, $$binomialQ (1/6, 211, 1000)$ = 0.000152. Script example You convert 1000 values of pitch targets in Hz to the nearest note on the piano keyboard. 597 of those values turn out to be in the A, B, C, D, E, F, or G regions (the white keys), and 403 values turn out to be in the A\# , C\# , D\# , F\# , or G\# regions (the black keys). Do our subjects have a preference for the white keys? The following script computes the probability that in the case of no preference the subjects would target the white keys at least 597 times. This is compared with a %\ci^2 test. a = 597 b = 403 p = 7/12 ; no preference echo *** Binomial test 'a', 'b', p = 'p:6' *** pbin = binomialQ (p, a, a+b) printline P (binomial) = 'pbin:6' \# Chi-square test with Yates correction: x2 = (a - 1/2 - p * (a+b))\^ 2/(p*(a+b)) + (b + 1/2 - (1-p) * (a+b))\^ 2/((1-p)*(a+b)) px2 = chiSquareQ (x2, 1) printline P (chi-square) = 'px2:6' The result is: *** Binomial test 597, 403, p = 0.583333 *** P (binomial) = 0.199330 P (chi-square) = 0.398365 The %\ci^2 test is two-sided (it signals a preference for the white or for the black keys), so it has twice the probability of the binomial test. We cannot conclude from this test that people have a preference for the white keys. Of course, we cannot conclude either that people do not have such a preference. An editor for viewing, hiding, showing, removing, and executing the commands in the fixed and dynamic menus of the P\s{RAAT} program. To open it, choose ##Buttons...# from the #Praat menu of the @@Object window@. What the button editor shows The button editor gives a list of: 1. The five fixed buttons. 2. The built-in and added @@fixed menu commands@, lexicographically sorted by window and menu name. 3. The built-in and added @@action commands@, sorted by the names of the selected objects. Visibility of built-in commands Most built-in commands are visible by default, but some are hidden by default (see @@Hidden commands@). The button editor shows these commands as "shown" or "hidden", respectively. You can change the visibility of a command by clicking on the blue "shown" or "hidden" text; this text will then be replaced with "HIDDEN" or "SHOWN", with capitals to signal their non-standard settings. These changes will be remembered in the @@Buttons file@ across sessions of your program. To return to the standard settings, click the blue "HIDDEN" or "SHOWN" texts again. Some built-in commands cannot be hidden. They are marked as "unhidable". The most notable example is the ##Buttons...# button (a failure to make the ##Commands...# command unhidable in Microsoft Word causes some computer viruses to be very hard to remove...). Added commands Commands that you have added to the fixed or dynamic menus (probably with @@Add to fixed menu...@ or @@Add to dynamic menu...@ in the @ScriptEditor), are marked as "ADDED". They are remembered in the @@Buttons file@. You can change the availability of these commands by clicking on the blue "ADDED" text, which will then be replaced with "REMOVED". After this, the added command will no longer be remembered in the @@Buttons file@. To make the command available again, click the blue "REMOVED" text again, before leaving the program. Start-up commands Commands that were added in an @@Initialization script@ (with @@Add menu command...@ or @@Add action command...@) are marked as "START-UP". They are %not remembered in the @@Buttons file@. You can change the visibility of these commands by clicking on the blue "START-UP" text, which will then be replaced with "HIDDEN". This setting %will be remembered in the @@Buttons file@. To make the command visible again, click the blue "HIDDEN" text again. Executing commands The button editor allows you to choose hidden commands without first making them visible in the fixed or dynamic menus. The editor shows all the executable commands in blue. These include: 1. The fixed #Remove button, if one or more objects are selected in the @@List of Objects@. 2. The other fixed buttons, if exactly one object is selected. 3. All of the fixed menu commands, hidden or not, and "removed" or not. 4. Those action commands that match the currently selected objects with respect to class and number. To execute any of these blue commands, just click on it. The file into which changes in the availability and visibility of commands in the fixed and dynamic menus are recorded. The buttons file is written to disk when you leave Praat, and it is read again when you enter Praat the next time. It is a simple @@Praat script@ that you can read (but should not edit) with any text editor. Adding buttons To add a command to a fixed or dynamic menu, you typically use the @ScriptEditor. Removing buttons To remove an added command from a fixed or dynamic menu, you typically use the @ButtonEditor. Hiding and showing buttons To hide a built-in command from a fixed or dynamic menu, or to make a hidden command visible, you typically use the @ButtonEditor. Unix If your home directory is /people/miep, the buttons file is /people/miep/.praat-dir/buttons. If the directory .praat-dir does not exist, it is created when you enter Praat. If you rename Praat, the name of the directory will also be different. MacOS X If you are Miep, the buttons file will be /Users/Miep/Library/Preferences/Praat Prefs/Buttons. Classic Macintosh The buttons file, which is called "Buttons", will be in a folder named "Praat Preferences" in the Preferences folder in your System Folder. If your hard disk is called "H\ael' sji'f", and you have a Dutch system, the complete path to your preferences file is: H\ael' sji'f:Systeemmap:Voorkeuren:Praat Preferences:Buttons Windows The buttons file may be C:\bsWINDOWS\bsPraat\bsButtons.ini. A window that allows you to calculate all kinds of simple or complicated mathematical and string expressions. To show the calculator, type Command-U or choose the @@Calculator...@ command. The result will be written to the Info window. See the @Formulas tutorial for all the things that you can calculate with this command. A command in the @Goodies submenu of the @@Praat menu@ of the @@Object window@. Shortcut: Command-U. Choosing this command brings up Praat's @calculator. A command in the Edit menu of the @ScriptEditor for clearing the remembered history. See @@History mechanism@. A routine for converting intensity difference limens into sensation level, the inverse of @phonToDifferenceLimens. Formula differenceLimensToPhon (%ndli) = ln (1 + %ndli / 30) / ln (61 / 60) The commands in the fixed menus of the @@Object window@ (#Praat, #New, #Read, #Help, #Goodies, and #Preferences) and the @@Picture window@ (#File, #Edit, #Margins, #World, #Select, #Pen, #Font, #Help). These commands are always clickable (if not hidden) and scriptable (if not added). You can use numeric expressions and string (text) expressions in many places in Praat: \bu in the @calculator in Praat's @Goodies submenu; \bu in the numeric fields of most settings windows; \bu in a @@Praat script@. For some types of objects (mainly Sound and Matrix), you can also apply formulas to all their contents at the same time: \bu when you create a Sound or a Matrix from the @@New menu@; \bu when you choose @@Formula...@ from the @Modify menu for a selected object. You can read this tutorial sequentially with the help of the "< 1" and "1 >" buttons. 1. @@Formulas 1. My first formulas|My first formulas@ (where to use) 1.1. @@Formulas 1.1. Formulas in the calculator|Formulas in the calculator@ 1.2. @@Formulas 1.2. Numeric expressions|Numeric expressions@ 1.3. @@Formulas 1.3. String expressions|String expressions@ 1.4. @@Formulas 1.4. Representation of numbers|Representation of numbers@ 1.5. @@Formulas 1.5. Representation of strings|Representation of strings@ 1.6. @@Formulas 1.6. Formulas in settings windows|Formulas in settings windows@ 1.7. @@Formulas 1.7. Formulas for creation|Formulas for creation@ 1.8. @@Formulas 1.8. Formulas for modification|Formulas for modification@ 1.9. @@Formulas 1.9. Formulas in scripts|Formulas in scripts@ 2. @@Formulas 2. Operators|Operators@ (+, -, *, /, \^ ) 3. @@Formulas 3. Constants|Constants@ (pi, e, undefined) 4. @@Formulas 4. Mathematical functions|Mathematical functions@ 5. @@Formulas 5. String functions|String functions@ 6. @@Formulas 6. Control structures|Control structures@ (if then else fi, semicolon) 7. @@Formulas 7. Attributes of objects|Attributes of objects@ 8. @@Formulas 8. Data in objects|Data in objects@ To use the Praat @calculator, go to the @@Praat menu@ and choose @@Calculator...@ from the @Goodies submenu. Or simply type Command-U anywhere in Praat. Calculating numbers You can do arithmetic computations. Type the formula 8*17 and click OK. The Info window will pop up and show the result: 136 Calculating strings You can also do text computations. Type the formula "see" + "king" and click OK. The Info window will show the result: seeking All the formulas whose outcome is a number are called numeric expressions. For the following examples, all the outcomes can be checked with the @calculator. Examples with numbers Some numeric expressions involve numbers only: ##8*17 computes a multiplication. Outcome: 136. ##2\^ 10 computes the tenth power of 2. Outcome: 1024. ##sqrt (2) / 2 computes the square root of 2, and divides the result by 2. Outcome: 0.7071067811865476. ##sin (1/4 * pi) computes the sine of %\pi/4. Outcome: 0.7071067811865476 (again). Examples with strings Some numeric expressions compute numeric properties of strings: ##length ("internationalization") computes the length of the string "internationalization". Outcome: 20. ##index ("internationalization", "ation") computes the location of the first occurrence of the string "ation" in the string "internationalization". Outcome: 7, because the first letter of "ation" lines up with the seventh letter of "internationalization". If the substring does not occur, the outcome is 0. All the formulas whose outcome is a text string are called string expressions. Again, the outcomes of the following examples can be checked with the @calculator. ##"see" + "king" concatenates two strings. Outcome: seeking. ##left\$ ("internationalization", 6) computes the leftmost six letters of the string; the dollar sign is used for all functions whose result is a string. Outcome: intern. ##mid\$ ("internationalization", 6, 8) computes the 8-letter substring that starts at the sixth letter of "internationalization". Outcome: national. ##date\$ ( ) computes the current date and time. Outcome at the time I am writing this: Mon Dec 2 02:23:45 2002. Formulas can work with integer numbers as well as with real numbers. Real numbers You can type many real numbers by using a decimal notation, for instance 3.14159, 299792.5, or -0.000123456789. For very large or small numbers, you can use the %e-notation: 6.022\.c10^^23^ is typed as 6.022e23 or 6.022e+23, and -1.6021917\.c10^^-19^ is typed as -1.6021917e-19. You can use also use the percent notation: 0.157 can be typed as 15.7\% . There are some limitations as to the values that real numbers can have in Praat. The numbers must lie between -10^^308^ and +10^^308^. If you type 1e200 * 1e100 the outcome will be 1e+300 but if you type 1e300 * 1e100 --undefined-- Another limitation is that the smallest non-zero numbers lie near -10^^-308^ and +10^^-308^. If you type 1e-200 / 1e100 1e-300 1e-300 / 1e100 0 Finally, the precision of real numbers is limited by the number of bits that every real number is stored with in the computer, namely 64. For instance, if you type pi 3.141592653589793 because only 16 digits of precision are stored. This can lead to unexpected results caused by rounding. For instance, the formula 0.34999999999999999 - 0.35 will result in rather than the correct value of 1e-17. This is because the numbers 0.34999999999999999 and 0.35 cannot be distinguished in the computer's memory. If you simply type 0.34999999999999999 0.35 (as in this example, the calculator will always come up with the minimum number of digits needed to represent the number unambiguously). Another example of inaccuracy is the formula 1 / 7 / 59 * 413 Because of rounding errors, the result will be 0.9999999999999999 Integer numbers Formulas can work with integer (whole) numbers between -1,000,000,000,000,000 and +1,000,000,000,000,000. You type them without commas and without the plus sign: 337, -848947328345289. You %can work with larger numbers than that (up to 10^^308^), but there will again be rounding errors. For instance, the formula 1000000000000000 + 1 correctly yields 1000000000000001 but the formula 10000000000000000 + 1 yields an incorrect outcome: 1e16 Formulas can work with strings that are put between two double quotes, as in "goodbye" or "how are you doing?". If a string has to contain a double quote, you have to type it twice. For instance, if you type "I asked: \" \" how are you doing?\" \" " into the calculator, the outcome will be I asked: "how are you doing?" Into numeric fields in settings windows you usually simply type a number. However, you can use any numeric expression instead. For instance, suppose you want to create a Sound that contains exactly 10000 samples. If the sampling frequency is 22050 Hz, the duration will be 10000/22050 seconds. You can create such a Sound by choosing @@Create Sound...@ from the @@New menu@, then typing 10000/22050 into the ##%%Finishing time#% field. Into text fields in settings windows, you can only type text directly; there is no way to use string expressions (except if you use scripts; see @@Formulas 1.9. Formulas in scripts@). With some commands in the @@New menu@, you can supply a formula that Praat will apply to all elements of the new object. Creating a Sound from a formula Choose @@Create Sound...@ and type the following into the #%Formula field: 1/2 * sin (2 * pi * 377 * x) When you click OK, a new @Sound object will appear in the list. After you click #%Edit and zoom in a couple of times, you will see that the sound is a sine wave with a frequency of 377 Hertz (cycles per second). This worked because the %x in the formula represents the time, i.e. the formula was applied to every sample separately, with a different value of %x for each sample. Creating a Matrix from a formula Choose @@Create simple Matrix...@ and type the following into the #%Formula field: 8 When you click OK, a new @Matrix object will appear in the list. When you click Info, you will see that it is a matrix with 10 rows and 10 columns, and that all the 100 cells contain the value 8 (you can see this because both the minimum and the maximum are reported as being 8). A more interesting example is the formula row * col For the resulting Matrix, choose @@Matrix: Paint cells...|Paint cells...@ and click OK. The Picture window will show a 10\xx10 matrix whose elements are the product of the row and column numbers, i.e., they have values between 1 and 100. Beside %row and %col, you can use %x for the distance along the horizontal axis and %y for the distance along the vertical axis; see the following page for examples. Analogously to the formulas that you can use for creating new objects (see the previous page), you can use formulas for modifying existing objects. You do this with the command ##%Formula...%# that you can find in the @Modify menu when you select an object. Modifying a Sound with a formula Record a sound with your microphone and talk very lowly. If you don't know how to record a sound in Praat, consult the @Intro. Once the Sound objetc is in the list, click #%Play. The result will sound very soft. Then choose ##%%Formula...#% from the #%Modify menu and type self * 3 Click OK, then click #%Play again. The sound is much louder now. You have multiplied the amplitude of every sample in the sound with a factor of 3. Replacing the contents of a Sound with a formula If you don't use $self in your formula, the formula does not refer to the existing contents of the Sound. Hence, the formula will simply replace your recorded speech with a 377-Hz sine wave. Modifying a Matrix with a formula Many objects can be thought of as matrices: they consist of a number of rows and columns with data in every cell: @Sound: one row; columns represent samples. @Spectrum: two rows (first row is real part, second row is imaginary part); columns represent frequencies. @Spectrogram, @Cochleagram: rows represent frequencies; columns represent times. @Excitation: one row; columns represent frequency bands. @Harmonicity: one row; columns represent time frames. The formula is performed on every column of every row. The formula self\^ 2$ will square all matrix elements. The formula first works on the first row, and in that row from the first column on; this can work recursively. The formula self + self [row, col - 1] integrates each row. Referring to the current position in the object You can refer to the current position in a Matrix (or Sound, etc.) by index or by %x and %y values: #row the current row #col the current column #x the %x value associated with the current column: for a Sound, Spectrogram, Cochleagram, or Harmonicity: time for a Spectrum: frequency (Hertz) for an Excitation: frequency (Bark) #y the %y value associated with the current row: for a Spectrogram: frequency (Hertz) for a Cochleagram: frequency (Bark) Referring to the contents of the object itself You can refer to values in the current Matrix (or Sound, etc.) by index. ##self refers to the value in the current Matrix at the current row and column, or to the value in the current Sound at the current sample. ##self [%%column-expression%] refers to the value in the current Sound (or Intensity etc.) at the current sample (or frame). The %%column-expression% is rounded to the nearest integer. If the index is out of range (less than 1 or greater than %n__%x_), the expression evaluates as 0. #Example. An integrator is self [col - 1] + self * dx ##self [%%row-expression%, %%column-expression%] refers to the value in the current Matrix (or Spectrogram etc.) at the specified row and column. The expressions are rounded to the nearest integers. You can refer to values in the current Matrix (or Spectrogram, etc.) by %x and %y position: \bu ##self (%%x-expression%, %%y-expression%) the expressions are linearly interpolated between the four nearest matrix points. You can refer to values in the current Sound (or Intensity etc.) by %x position: \bu ##self (%%x-expression%) the expression is linearly interpolated between the two nearest samples (or frames). In scripts, you can assign numeric expressions to numeric variables, and string expressions to string variables. You can also use numeric and string variables in expressions. Example: report a square Choose @@New Praat script@ from the @@Praat menu@. A script editor window will become visible. Type the following lines into that window: x = 99 x2 = x * x echo The square of 'x' is 'x2'. This is an example of a simple @@Praat script@; it assigns the results of the numeric formulas $$99$ and $$x * x$ to the numeric variables %x and %x2. Note that the formula $$x * x$ itself refers to the variable %x. To run (execute) this script, type Command-R or choose #%Run from the %#Run menu. Praat will then write the following text into the Info window: The square of 99 is 9801. For more information on scripts, see the @Scripting tutorial. Example: rename the city of Washington Type the following text into the script editor window: current\$ = "Bush" previous\$ = "Clinton" famous\$ = "Lincoln" newCapital\$ = current\$ + mid\$ (famous\$ , 2, 3) + right\$ (previous\$ , 3) echo The new capital will be 'newCapital\$ '. This script assigns the results of four string expressions to the four string variables %%current\$ %, %%previous\$ %, %%famous\$ %, and %%newCapital\$ %. The dollar sign is the notation for a string variable or for a function whose result is a string (like ##left\$ #). Note that the formula in the fourth line refers to three existing variables. To see what the new name of the capital will be, choose #%Run. Example: numeric expressions in settings in scripts As in real settings windows, you can use numeric expressions in all numeric fields. The example of the previous page becomes: Create Sound... sine 0 10000/22050 22050 0.9 * sin (2*pi*377*x) If the numeric field is not the last field of the settings window, you will want to write the formula without any spaces, e.g. as 10000/22050, since spaces are used to separate the fields. Example: string expressions in settings in scripts As in real settings windows, you cannot use string expressions in text fields directly, but you can still use the trick of variable substitution with single quotes (see @@Scripting 5.1. Variables@): soundName\$ = "hello" fileName\$ = soundName\$ + ".wav" Read from file... 'fileName\$ ' Example: numeric expressions in creation in scripts Suppose you want to generate a sine wave whose frequency is held in a variable. This is the way: frequency = 377 Create Sound... sine 0 1 22050 0.9 * sin (2*pi*frequency*x) In this example, Praat will protest if %x is a variable as well, because that would be ambiguous with the %x that refers to the time in the sound (see @@Formulas 1.8. Formulas for modification@). In formulas you can use the numerical and logical operators that are described on this page. The order of evaluation of the operators is the order that is most usual in programming languages. To force a different order, you use parentheses. The operators with the highest precedence are #negation (-) and #exponentation (\^ ): --6 \-> 6 2\^ 6 \-> 64 Sequences of negation and exponentiation are evaluated from right to left: 2\^ -6 \-> 0.015625 -(1+1)\^ 6 \-> -64 4\^ 3\^ 2 \-> 4\^ 9 \-> 262144 Note that changing the spacing does not change the meaning: 4\^ 3 \^ 2 \-> 262144 To change the order of evaluation, you have to use parentheses: (4 \^ 3) \^ 2 \-> 4096 The following construction is not allowed because of an ambiguity between a negative number and negation of a positive number: -2\^ 6 \-> ? Instead, you use any of the following: (-2)\^ 6 \-> 64 -(2\^ 6) \-> -64 -(2)\^ 6 \-> -64 The operators with the next highest precedence are #multiplication (*) and #division (/). They are evaluated from left to right: 1/4*5 \-> 1.25 (from left to right) 1 / 4*5 \-> 1.25 (spacing does not help) 1 / (4*5) \-> 0.05 (use parentheses to change the order) 3 * 2 \^ 4 \-> 48 (exponentiation before multiplication) 3*2 \^ 4 \-> 48 (this spacing does not matter and is misleading) (3 * 2) \^ 4 \-> 1296 (use parentheses to change the order) ##Integer division# operators (#div and #mod) have the same precedence as * and /, and are likewise evaluated from left to right: 54 div 5 \-> 10 (division rounded down) 54 mod 5 \-> 4 (the remainder) 54.3 div 5.1 \-> 10 (works for real numbers as well) 54.3 mod 5.1 \-> 3.3 (the remainder) -54 div 5 \-> -11 (division rounded down; negation before division) -54 mod 5 \-> 1 (the remainder) -(54 div 5) \-> -10 (use parentheses to change the order) -(54 mod 5) \-> -4 3 * 18 div 5 \-> 10 (from left to right) 3 * (18 div 5) \-> 9 3 * 18 mod 5 \-> 4 3 * (18 mod 5) \-> 9 54 div 5 * 3 \-> 30 (from left to right) 54 div (5 * 3) \-> 3 54 mod 5 * 3 \-> 12 54 mod (5 * 3) \-> 9 The operators with the next highest precedence are #addition (+) and #subtraction (-), evaluated from left to right: 3 - 8 + 7 \-> 2 (from left to right) 3 - (8 + 7) \-> -12 (use parentheses to change the order) 3 + 8 * 7 \-> 59 (multiplication before addition) (3 + 8) * 7 \-> 77 (use parentheses to change the order) 3 + - 2 \^ 4 \-> -13 (exponentiation, negation, addition) 3 + 5 / 2 + 3 \-> 8.5 (3 + 5) / (2 + 3) \-> 1.6 The operators with the next highest precedence are the #comparison operators (= <> < > <= >=). These operators always yield 0 (%false) or 1 (%true): 5 + 6 = 10 \-> 0 (equal) 5 + 6 = 11 \-> 1 5 + 6 <> 10 \-> 1 (unequal) 5 + 6 <> 11 \-> 0 5 + 6 < 10 \-> 0 (less than) 5 + 6 < 11 \-> 0 5 + 6 > 10 \-> 1 (greater than) 5 + 6 > 11 \-> 0 5 + 6 <= 10 \-> 0 (less than or equal) 5 + 6 <= 11 \-> 1 5 + 6 >= 10 \-> 1 (greater or equal) 5 + 6 >= 11 \-> 1 The comparison operators are mainly used in #if, #while, and #until conditions. The operators of lowest precedence are the #logical operators (#not, #and, and #or), of which #not has the highest precedence and #or the lowest: not 5 + 6 = 10 \-> 1 x > 5 and x < 10 (is x between 5 and 10?) not x <= 5 and not x >= 10 (same as previous line) not (x <= 5 or x >= 10) (same as previous line) String comparison ##a\$ = b\$ gives the value %true (= 1) if the strings are equal, and %false (= 0) otherwise. ##a\$ <> b\$ gives the value %true if the strings are unequal, and %false otherwise. ##a\$ < b\$ gives %true if the string %%a\$ % precedes the string %%b\$ % in ASCII sorting order. Thus, "ha" < "hal" and "ha" < "ja" are true, but "ha" < "JA" is false, because all capitals precede all lower-case characters in the ASCII sorting order. ##a\$ > b\$ %true if %%a\$ % comes after %%b\$ % in ASCII sorting order. ##a\$ <= b\$ gives the value %true if the string %%a\$ % precedes the string %%b\$ % in ASCII sorting order, or if the strings are equal. ##a\$ >= b\$ %true if %%a\$ % comes after %%b\$ % or the two are equal. String concatenation and truncation ##a\$ + b\$ concatenates the two strings. After text\$ = "hallo" + "dag" The variable %%text\$ % contains the string "hallodag". ##a\$ - b\$ subtracts the second string from the end of the first. After soundFileName\$ = "hallo.aifc" textgridFileName\$ = soundFileName\$ - ".aifc" + ".TextGrid" the variable %%textgridFileName\$ % contains the string "hallo.TextGrid". If the first string %%a\$ % does not end in the string %%b\$ %, the result of the subtraction is the string %%a\$ %. ##pi %\pi, 3.14159265358979323846 ##e %e, 2.7182818284590452354 ##undefined a special value, see @undefined ##abs (%x) absolute value ##round (%x) nearest integer; round (1.5) = 2 ##floor (%x) round down: highest integer value not greater than %x ##ceiling (%x) round up: lowest integer value not less than %x ##sqrt (%x) square root: \Vr%x, %x \>_ 0 ##min (%x, ...) the minimum of a series of numbers, e.g. min (7.2, -5, 3) = -5 ##max (%x, ...) the maximum of a series of numbers, e.g. max (7.2, -5, 3) = 7.2 ##imin (%x, ...) the location of the minimum, e.g. imin (7.2, -5, 3) = 2 ##imax (%x, ...) the location of the maximum, e.g. imax (7.2, -5, 3) = 1 ##sin (%x) sine ##cos (%x) cosine ##tan (%x) tangent ##arcsin (%x) arcsine, -1 \<_ %x \<_ 1 ##arccos (%x) arccosine, -1 \<_ %x \<_ 1 ##arctan (%x) arctangent ##arctan2 (%y, %x) argument angle ##exp (%x) exponentiation: %e^%x; same as ##e\^ %x ##ln (%x) natural logarithm, base %e ##log10 (%x) logarithm, base 10 ##log2 (%x) logarithm, base 2 ##sinh (%x) hyperbolic sine: (%e^%x - %e^^-%x^) / 2 ##cosh (%x) hyperbolic cosine: (%e^%x + %e^^-%x^) / 2 ##tanh (%x) hyperbolic tangent: sinh (%x) / cosh (%x) ##arcsinh (%x) inverse hyperbolic sine: ln (%x + \Vr(1+%x^2)) ##arccosh (%x) inverse hyperbolic cosine: ln (%x + \Vr(%x^2\--1)) ##arctanh (%x) inverse hyperbolic tangent ##sigmoid (%x) #R \-> (0,1): 1 / (1 + %e^^\--%x^) or 1 \-- 1 / (1 + %e^%x) ##erf (%x) the error function: 2/\Vr%\pi __0_\in^%x exp(-%t^2) %dt ##erfc (%x) the complement of the error function: 1 - erf (%x) ##randomUniform (%min, %max) uniform random deviate between %min (inclusive) and %max (exclusive) ##randomInteger (%min, %max) uniform random deviate between %min and %max (inclusive) ##randomGauss (%\mu, %\si) Gaussian random deviate with mean %\mu and standard deviation %\si ##randomPoisson (%mean) Poisson random deviate ##lnGamma (%x) logarithm of the \Ga function ##gaussP (%z) the area under the Gaussian distribution between \--\oo and %z ##gaussQ (%z) the area under the Gaussian distribution between %z and +\oo: the one-tailed "statistical significance %p" of a value that is %z standard deviations away from the mean of a Gaussian distribution ##invGaussQ (%q) the value of %z for which $gaussQ (%z) = %q ##chiSquareP (%chiSquare, %df) the area under the %\ci^2 distribution between 0 and %chiSquare, for %df degrees of freedom ##chiSquareQ (%chiSquare, %df) the area under the %\ci^2 distribution between %chiSquare and +\oo, for %df degrees of freedom: the "statistical significance %p" of the %\ci^2 difference between two distributions in %df+1 dimensions ##invChiSquareQ (%q, %df) the value of %\ci^2 for which $chiSquareQ (%\ci^2, %df) = %q ##studentP (%t, %df) the area under the student T-distribution from -\oo to %t ##studentQ (%t, %df) the area under the student T-distribution from %t to +\oo ##invStudentQ (%q, %df) the value of %t for which $studentQ (%t, %df) = %q ##fisherP (%f, %df1, %df2) the area under Fisher's F-distribution from 0 to %f ##fisherQ (%f, %df1, %df2) the area under Fisher's F-distribution from %f to +\oo ##invFisherQ (%q, %df1, %df2) the value of %f for which $fisherQ (%f, %df1, %df2) = %q ##binomialP (%p, %k, %n) the probability that in %n experiments, an event with probability %p will occur at most %k times @binomialQ (%p, %k, %n) the probability that in %n experiments, an event with probability %p will occur at least %k times; equals 1 - $binomialP (%p, %k - 1, %n) ##invBinomialP (%P, %k, %n) the value of %p for which $binomialP (%p, %k, %n) = %P ##invBinomialQ (%Q, %k, %n) the value of %p for which $binomialQ (%p, %k, %n) = %Q ##hertzToBark (%x) from acoustic frequency to Bark-rate (perceptual spectral frequency; place on basilar membrane): 7 ln (%x/650 + \Vr(1 + (%x/650)^2)) ##barkToHertz (%x) 650 sinh (%x / 7) ##hertzToMel (%x) from acoustic frequency to perceptual pitch: 550 ln (1 + %x / 550) ##melToHertz (%x) 550 (exp (%x / 550) - 1) ##hertzToSemitones (%x) from acoustic frequency to a logarithmic musical scale, relative to 100 Hz: 12 ln (%x / 100) / ln 2 ##semitonesToHertz (%x) 100 exp (%x ln 2 / 12) ##erb (%f) the perceptual %%equivalent rectangular bandwidth% (ERB) in Hertz, for a specified acoustic frequency (also in Hertz): 6.23\.c10^^-6^ %f^2 + 0.09339 %f + 28.52 ##hertzToErb (%x) from acoustic frequency to ERB-rate: 11.17 ln ((%x + 312) / (%x + 14680)) + 43 ##erbToHertz (%x) (14680 %d - 312) / (1 - %d) where %d = exp ((%x - 43) / 11.17) @phonToDifferenceLimens (%x) from perceptual loudness (intensity sensation) level in phon, to the number of intensity difference limens above threshold: 30 \.c ((61/60)^^ %x^ \-- 1). @differenceLimensToPhon (%x) the inverse of the previous: ln (1 + %x / 30) / ln (61 / 60). ##beta (%x, %y) ##besselI (%n, %x) ##besselK (%n, %x) String functions are functions that either return a text string or have at least one text string as an argument. Since string computations are not very useful in the @calculator, in settings windows, or in creation and modification formulas, this page only gives examples of strings in scripts, so that the example may contain string variables. ##length (a\$ ) gives the length of the string. After string\$ = "hallo" length = length (string\$ + "dag") the variable %length contains the number 8 (by the way, from this example you see that variables can have the same names as functions, without any danger of confusing the interpreter). ##left\$ (a\$ , n) gives a string consisting of the first %n characters of %%a\$ %. After head\$ = left\$ ("hallo", 3) the variable %%head\$ % contains the string "hal". ##right\$ (a\$ , n) gives a string consisting of the last %n characters of %%a\$ %. After english\$ = "he" + right\$ ("hallo", 3) the variable %%english\$ % contains the string "hello". ##mid\$ ("hello" , 3, 2) gives a string consisting of 2 characters from "hello", starting at the third character. Outcome: ll. ##index (a\$ , b\$ ) gives the index of the first occurrence of the string %%b\$ % in the string %%a\$ %. After where = index ("hallo allemaal", "al") the variable %where contains the number 2, because the first "al" starts at the second character of the longer string. If the first string does not contain the second string, %index returns 0. ##rindex (a\$ , b\$ ) gives the index of the last occurrence of the string %%b\$ % in the string %%a\$ %. After where = rindex ("hallo allemaal", "al") the variable %where contains the number 13, because the last "al" starts at the 13th character. If the first string does not contain the second string, %rindex returns 0. ##startsWith (a\$ , b\$ ) determines whether the string %%a\$ % starts with the string %%b\$ %. After where = startsWith ("internationalization", "int") the variable %where contains the number 1 (true). ##endsWith (a\$ , b\$ ) determines whether the string %%a\$ % ends with the string %%b\$ %. After where = endsWith ("internationalization", "nation") the variable %where contains the number 0 (false). ##index_regex (a\$ , b\$ ) determines where the string %%a\$ % first matches the @@regular expressions|regular expression@ %%b\$ %. After where = index_regex ("internationalization", "a.*n") the variable %where contains the number 7. If there is no match, the outcome is 0. ##rindex_regex (a\$ , b\$ ) determines where the string %%a\$ % last matches the @@regular expressions|regular expression@ %%b\$ %. After where = rindex_regex ("internationalization", "a.*n") the variable %where contains the number 16. If there is no match, the outcome is 0. ##fixed\$ (number, precision) formats a number as a string with %precision digits after the decimal point. Thus, $$fixed\$ (72.65687, 3)$ becomes the string $$72.657$, and $$fixed\$ (72.65001, 3)$ becomes the string $$72.650$. In these examples, we see that the result can be rounded up and that trailing zeroes are kept. At least one digit of precision is always given, e.g. $$fixed\$ (0.0000157, 3)$ becomes the string $$0.00002$. The number 0 always becomes the string $0. ##percent\$ (number, precision) the same as ##fixed\$ #, but with a percent sign. For instance, $$percent\$ (0.157, 3)$ becomes $$15.700\% $, $$percent\$ (0.000157, 3)$ becomes $$0.016\% $, and $$percent\$ (0.000000157, 3)$ becomes $$0.00002\% $. The number 0 always becomes the string $0. ##date\$ () gives the date and time in the following format: Mon Jun 24 17:11:21 2002 To write the day of the month into the Info window, you type: date\$ = date\$ () day\$ = mid\$ (date\$ , 9, 2) echo The month day is 'day\$ '. ##extractNumber ("Type: Sound'newline\$ 'Name: hello there'newline\$ 'Size: 44007", "Size:") looks for a number after the first occurrence of "Size:" in the long string. Outcome: 44007. This is useful in scripts that try to get information from long reports, as the following script that runs in the Sound editor window: report\$ = Settings report maximumFrequency = extractNumber (report\$ , "Spectrogram maximum frequency:") ##extractWord\$ ("Type: Sound'newline\$ 'Name: hello there'newline\$ 'Size: 44007", "Type:") looks for a word without spaces after the first occurrence of "Type:" in the long string. Outcome: Sound. ##extractLine\$ ("Type: Sound'newline\$ 'Name: hello there'newline\$ 'Size: 44007", "Name: ") looks for the rest of the line (including spaces) after the first occurrence of "Name: " in the long string. Outcome: hello there. Note how "Name: " includes a space, so that the `rest of the line' starts with the %h. if ... then ... else ... fi You can use conditional expressions in all formulas. For example, 3 * if 52\% * 3809 > 2000 then 5 else 6 fi evaluates to 15. Instead of %fi, you can also use %endif. Another example: you can clip the absolute amplitude of a Sound to 0.5 by supplying the following formula: if abs(self)>0.5 then if self>0 then 0.5 else -0.5 fi else self fi The semicolon The semicolon ends the evaluation of the formula. This can be convenient if you do not want to overwrite a long formula in your text field: the formula 800;sqrt(2)*sin(2*pi*103*0.5)+10\^ (-40/20)*randomGauss(0,1) evaluates to 800. You can refer to several attributes of objects that are visible in the @@List of Objects@. To do so, use the type and the name of the object, connected with an underscore. Thus, $$Sound_hallo$ refers to an existing Sound object whose name is "hallo" (if there is more than one such object, it refers to the one that was created last). To refer to an attribute, you use the period ( `.'). Thus, $$Sound_hallo.nx$ is the number of samples of Sound_hallo, and $$1 / Sound_hallo.dx$ is the sampling frequency of Sound_hallo. Attributes in the calculator Record a Sound (read the @Intro if you do not know how to do that), name it "mysound" (or anything else), and type the following formula into the @calculator: Sound_mysound.nx After you click OK, the Info window will show the number of samples. Since you could have got this result by simply choosing ##%%Get number of samples#% from the @Query menu, these attribute tricks are not very useful in the calculator. We will see that they are much more useful in creation and modification formulas and in scripts. List of possible attributes The following attributes are available: #xmin the start of the time domain (usually 0) for a @Sound, @Pitch, @Formant, @Spectrogram, @Intensity, @Cochleagram, @PointProcess, or @Harmonicity object, in seconds; the lowest frequency (always 0) for a @Spectrum object, in Hertz; the lowest frequency (usually 0) for an @Excitation object, in Bark; the left edge of the %x domain for a @Matrix object. #xmax the end of the time domain (usually the duration, if %xmin is zero) for a Sound, Pitch, Formant, Spectrogram, Intensity, Cochleagram, PointProcess, or Harmonicity object, in seconds; the highest frequency (@@Nyquist frequency@) for a Spectrum object, e.g. 11025 Hertz; the highest frequency for an Excitation object, often 25.6 Bark; the right edge of the %x domain for a Matrix object. #ncol the number of columns in a @Matrix, @TableOfReal, or @Table object. #nrow the number of rows in a @Matrix, @TableOfReal, or @Table object. #nx the number of samples in a Sound object; the number of analysis frames in a Pitch, Formant, Spectrogram, Intensity, Cochleagram, or Harmonicity object; the number of frequency bins in a Spectrum or Excitation object; the number of divisions of the %x domain for a Matrix object (= %ncol). #dx the sample period (time distance between consecutive samples) in a Sound object (the inverse of the sampling frequency), in seconds; the time step between consecutive frames in a Pitch, Formant, Spectrogram, Intensity, Cochleagram, or Harmonicity object, in seconds; the width of a frequency bin in a Spectrum object, in Hertz; the width of a frequency bin in an Excitation object, in Bark; the horizontal distance between cells in a Matrix object. #ymin the lowest frequency (usually 0) for a Spectrogram object, in Hertz; the lowest frequency (usually 0) for a Cochleagram object, in Bark; the bottom of the %y domain for a Matrix object. #ymax the highest frequency for a Spectrogram object, e.g. 5000 Hertz; the highest frequency for a Cochleagram object, often 25.6 Bark; the top of the %y domain for a Matrix object. #ny the number of frequency bands in a Spectrogram or Cochleagram object; for a Spectrum object: always 2 (first row is real part, second row is imaginary part) the number of divisions of the %y domain for a Matrix object (= %nrow). #dy the distance between adjacent frequency bands in a Spectrogram object, in Hertz; the distance between adjacent frequency bands in a Cochleagram object, in Hertz; the vertical distance between cells in a Matrix object. Attributes in a creation formula In formulas for creating a new object, you can refer to the attributes of any object, but you will often want to refer to the attributes of the object that is just being created. You can do that in two ways. The first way is to use the name of the object, as above. Choose @@Create Sound...@, supply %hello for its name, supply arbitrary values for the starting and finishing time, and type the following formula: (x - Sound_hello.xmin) / (Sound_hello.xmax - Sound_hello.xmin) When you edit this sound, you can see that it creates a straight line that rises from 0 to 1 within the time domain. The formula above will also work if the Sound under creation is called %goodbye, and a Sound called %hello already exists; of course, in such a case $$Sound_hello.xmax$ refers to a property of the already existing sound. If a formula refers to an object under creation, there is a shorter way: you do not have to supply the name of the object at all, so you can simply write (x - xmin) / (xmax - xmin) The attributes that you can use in this implicit way are %xmin, %xmax, %ncol, %nrow, %nx, %dx, %ny, and %dy. Attributes in a modification formula In formulas for modifying an existing object, you refer to attributes in the same way as in creation formulas, i.e., you do not have to specify the name of the object that is being modified. The formula self * 20 \^ (- (x - xmin) / (xmax - xmin)) causes the sound to decay exponentially in such a way that it has only 5 percent of its initial amplitude at the end. If you apply this formula to multiple Sound objects at the same time, %xmax will refer to the finishing time of each Sound separately as it is modified. More examples of the use of attributes are on the next page. With square brackets, you can get the values inside some objects. Object contents in the calculator The outcomes of the following examples can be checked with the @calculator. ##Matrix_hello [10, 3] gives the value in the cell at the third column of the 10th row of the Matrix called %hello. ##Sound_hello [10000] gives the value (in Pa) of the 1000th sample of the Sound %hello. ##TableOfReal_tokens [5, 12] gives the value in the cell at the fifth row of the 12th column of the TableOfReal called %tokens. ##TableOfReal_tokens [5, "F1"] gives the value in the cell at the fifth row of the column labelled %F1 of the TableOfReal %tokens. ##TableOfReal_tokens ["\bsct", "F1"] gives the value in the cell at the row labelled %%\bsct% of column %F1 of the TableOfReal %tokens. ##Table_listeners [3, "m3ae"] gives the numeric value in the cell at the third row of column %m3ae of the Table %listeners. ##Table_listeners [3, 12] gives the numeric value in the cell at the third row of the 12th column of the Table %listeners. Cells outside the objects are considered to contain zeroes. Interpolation The values inside some objects can be interpolated. ##Sound_hallo (0.7) gives the value (in Pa) at a time of 0.7 seconds in the Sound "hallo", by linear interpolation between the two samples that are nearest to 0.7 seconds. ##Spectrogram_hallo (0.7, 2500) gives the value at a time of 0.7 seconds and at a frequency of 2500 Hz in the Spectrogram "hallo", by linear interpolation between the four samples that are nearest to that point. In the interpolation, cells outside the objects are considered to contain zeroes. Object contents in a modification formula Suppose you want to do the difficult way of reversing the contents of a Sound called %hello (the easy way is to choose #%Reverse from the @Modify menu). You select this sound, then choose @@Copy...@ to duplicate it to a new Sound, which you name %%hello_reverse%. You select this new Sound and choose ##Formula...# from the @Modify menu. The formula will be Sound_hello [ncol + 1 - col] From this example, you see that the indices between [ ] may be formulas themselves, and that you can use implicit attributes like %ncol and position references like %col. An alternative formula is Sound_hello (xmax - x) at least if %xmin is zero. The advantage of the second method is that is also works correctly if the two sounds have different sampling frequencies; the disadvantage is that it may do some interpolation between the samples, which deteriorates the sound quality. Object contents in a script In scripts, the indices between [ ] and the values between ( ) may be formulas themselves and contain variables. The following script computes the sum of all the cells along the diagonal of a Matrix named %hello. sumDiagonal = 0 for i to Matrix_hello.ncol sumDiagonal += Matrix_hello [i, i] endfor echo The sum of cells along the diagonal is 'sumDiagonal'. This example could have been written completely with commands from the dynamic menu: select Matrix hello ncol = Get number of columns for i to ncol value = Get value in cell... i i sumDiagonal += value The first version, which accesses the contents directly, is not only three lines shorter, but also three times faster. Some commands in P\s{RAAT}'s fixed and dynamic menus are hidden by default. You can still call hidden commands from scripts, run them by clicking on them in a @ButtonEditor, or make them visible with the help of the @ButtonEditor. To hide commands that are visible by default, use the @ButtonEditor. What commands are hidden by default? Commands that are expected to be of very limited use, are hidden by default. Examples are: 1. The commands @@Add menu command...@, ##Hide menu command...#, ##Show menu command...#, @@Add action command...@, ##Hide action command...#, and ##Show action command...# in the #Praat menu of the @@Object window@. These are used in the @@Buttons file@ and could be used by an @@Initialization script@ as well; in an interactive session, however, the functionality of these commands is part of the @ScriptEditor and the @ButtonEditor. 2. The command ##Read from old Praat picture file...# in the #File menu of the @@Picture window@. For reading a file format that was in use before May, 1995. 3. In the Praat program, the action ##Sound: Write to Sesam file...#. Writes a file format in common use in the Netherlands on Vax machines. In the Dutch phonetics departments, the plugs were pulled from the Vaxes in 1994. 4. In the Praat program, the action ##Sound: To Cochleagram (edb)...#. Needed by one person in 1994. An interesting, but undocumented procedure (De Boer's gamma-tone filter bank plus Meddis & Hewitt's synapse model), which does not create a normally interpretable Cochleagram object. The easiest way to do @@scripting@. The %history is the sequence of all menu commands (in the Objects or Picture window or in the editors), action commands (in the dynamic menu), or mouse clicks on objects (in the list of objects), that you performed during your Praat session, together with the settings that you specified in the settings windows that popped up as a result of those commands. Viewing the history To view your history, you first open a @ScriptEditor with @@New Praat script@ or @@Open Praat script...@. You then choose @@Paste history@ from the Edit menu. Recording a macro To record a sequence of mouse clicks for later re-use, perform the following steps: 1. Choose @@Clear history@ from the Edit menu. This makes the history mechanism forget all previous clicks. 2. Perform the actions that you want to record. 3. Choose @@Paste history@ from the Edit menu. Because you cleared the history before you started, the resulting script contains only the actions that you performed in step 2. You can now already re-run the actions that you performed in step 2. 4. You can save the recorded actions to a script file by choosing #Save from the File menu. 5. You can put this script file under a button in the @@dynamic menu@ by choosing @@Add to dynamic menu...@ from the File menu, or under a button in a fixed menu by choosing @@Add to fixed menu...@. This button will be preserved across Praat sessions. This macro mechanism is much more flexible than the usual opaque macro mechanism used by most programs, because you can edit the script and make some of the arguments variable by putting them in the #form clause at the top of the script. In this way, the script will prompt the user for these arguments, just as with all the menu and action commands that end in the three dots (...). See the @Scripting tutorial for all the things that you can do in scripts. Your initialization script is a normal @@Praat script@ that is run as soon as you start Praat. On Windows NT or XP, you create an initialization script by creating a file named "praat-user-startUp" in your home directory, which on my Windows XP computer is C:\bsDocuments and Settings\bsPaul. If you have both of these files, they are run in the above order. If you like to be greeted by your husband when Praat starts up, you could put the following lines in your initialization script: Read from file... C:\bsDocuments and Settings\bsMiep\bshelloMiep.wav Play Remove What not to use an initialization script for You could set preferences like the default font in your initialization script, but these will be automatically remembered between invocations of Praat anyway (in your @@Preferences file@), so this would often be superfluous. Added and removed commands are also remembered across Praat sessions (in your @@Buttons file@), but you may want to call a changeable list of them. Using an initialization script for site-wide customization If your research group shares a number of Praat scripts, these can be included in everybody's version of the program in the following way: 1. Create a script that adds buttons to the fixed and dynamic menus, using the commands @@Add menu command...@ and @@Add action command...@. This script could be a slightly edited copy of someone's @@Buttons file@. 2. Have everyone call this script from her own start-up file (with @@Run script...@). This procedure allows all members of the group to automatically enjoy all the later changes in the custom command set. A command in the @@Praat menu@ for creating a new Praat script. It creates a @ScriptEditor with an empty script that you can edit, run, and save. A command in the @@Praat menu@ for editing an existing @@Praat script@. It creates a @ScriptEditor and asks you to select a file. If you click #%OK, the file is read into the ScriptEditor window, and you can run and edit it; if you click #%Cancel, you get an empty script, as with @@New Praat script@. A command in the Edit menu of a @ScriptEditor, for inserting the history of commands. See @@History mechanism@. A routine for converting sensation level in phons into intensity difference limen level, the inverse of @differenceLimensToPhon. phonToDifferenceLimens (%phon) = 30 \.c ((61/60)^^ %phon^ \-- 1) Derivation In first approximation, humans can detect an intensity difference of 1 phon, i.e. if two sounds that differ only in intensity are played a short time after each other, people can generally detect their intensity difference if it is greater than 1 phon. But the sensitivity is somewhat better for louder sounds. According to @@Jesteadt, Wier & Green (1977)@, the relative difference limen of intensity is given by DLI = \De%I / %I = 0.463 \.c (%I / %I__0_)^^ \--0.072^ In this formula, %I is the intensity of the sound in Watt/m^2, %I__0_ is the intensity of the auditory threshold (i.e. 10^^\--12^ Watt/m^2 at 1000 Hz), and \De%I is the just noticeable difference. @@Boersma (1998)|Boersma (1998: 109)@ calculates a difference-limen scale from this. Given an intensity %I, the number of difference limens above threshold is \in__%I0_^%I %dx \De%I(%x) = (1 / 0.463) \in__%I0_^%I %dx %I__0_^^\--0.072^ %x^^0.072\--1^ = (1 / (0.463\.c0.072)) ((%I/%I__0_)^^0.072^ \-- 1) The sensation level in phon is defined as SL = 10 log__10_ (%I/%I__0_) so that the number of difference limens above threshold is (1 / (0.463\.c0.072)) (10^^(0.072/10)(10log(%I/%I__0_))^ \-- 1) = 30 \.c (1.0167^^SL^ \-- 1) An executable text that consists of menu commands and action commands. See the @Scripting tutorial. The file into which some of your preferences are saved across your sessions with P\s{RAAT}. For instance, if you change the font used by the Picture window to Palatino and leave P\s{RAAT}, the Picture-window font will still be Palatino when you enter P\s{RAAT} again. The preferences file is written to disk when you leave P\s{RAAT}, and it is read when you enter P\s{RAAT}. It is a simple text file that you can read (but should not edit) with any text editor. If your home directory is /people/miep the preferences file is /people/miep/.praat-dir/prefs. If the directory .praat-dir does not exist, it is created when you enter P\s{RAAT}. Macintosh In MacOS X, the preferences file is called %Prefs, and it will be in the folder %%Praat Prefs% in the %Preferences folder of your personal %Library folder. On my iBook, the preferences file is ##/Users/pboersma/Library/Preferences/Praat Prefs/Prefs#. In MacOS 7, 8, or 9, the preferences file is also called %Prefs, and it will be in the folder %%Praat Preferences% in the Preferences folder in your System Folder. If your hard disk is called "H\ael' sji'f", and you have a Dutch system, the complete path to your preferences file is: H\ael' sji'f:Systeemmap:Voorkeuren:Praat Preferences:Prefs The preferences file is called %%Preferences.ini%, and it will be in the directory %Praat in your Windows directory, or in the directory %Praat in your home directory if you work on a shared computer. On my Virtual PC Windows XP Home Edition computer, the preferences file is ##C:\bsDocuments and Settings\bsPaul Boersma\bsPraat\bsPreferences.ini#. A hidden command in the @@Praat menu@. Runs a @@Praat script@. This command is hidden because you would normally open a script with @@Open Praat script...@, so that you can run it several times without selecting a file each time. In scripts, the command ##%%Run script...#% is automatically replaced by the script directive #execute. This is one of the tutorials of the P\s{RAAT} program. It assumes you are familiar with the @Intro. A %script is a text that consists of menu commands and action commands. If you %run the script (perhaps from a @ScriptEditor), the commands are executed as if you clicked on them. @@Scripting 1. My first script@ (how to create, how to run) @@Scripting 2. Arguments to commands@ (numeric, check, radio, text, file) @@Scripting 3. Layout@ (white space, comments, continuation lines) @@Scripting 4. Object selection@ (selecting and querying) @@Scripting 5. Language elements@ @@Scripting 5.1. Variables@ (numeric, string, copy, substitution) @@Scripting 5.2. Formulas@ (numeric, string) @@Scripting 5.3. Jumps@ (if, then, elsif, else, endif) @@Scripting 5.4. Loops@ (for/endfor, while/endwhile, repeat/until) @@Scripting 5.5. Procedures@ (call, procedure) @@Scripting 5.6. Arrays @@Scripting 5.7. Including other scripts @@Scripting 5.8. Quitting@ (exit) @@Scripting 6. Communication outside the script @@Scripting 6.1. Arguments to the script@ (form/endform, execute) @@Scripting 6.2. Calling system commands@ (system, system_nocheck) @@Scripting 6.3. Writing to the Info window@ (echo, print, printtab, printline) @@Scripting 6.4. Query commands@ (Get, Count) @@Scripting 6.5. Files@ (fileReadable, <, >, >>, filedelete, fileappend) @@Scripting 6.6. Controlling the user@ (pause) @@Scripting 6.7. Sending a message to another program@ (sendsocket) @@Scripting 6.8. Messages to the user@ (exit, assert, nowarn, nocheck) @@Scripting 6.9. Calling from the command line @@Scripting 7. Scripting the editors @@Scripting 7.1. Scripting an editor from a shell script@ (editor/endeditor) @@Scripting 7.2. Scripting an editor from within @@Scripting 8. Controlling Praat from another program @@Scripting 8.1. The sendpraat subroutine @@Scripting 8.2. The sendpraat program @@Scripting 8.3. The sendpraat directive Also see the @@scripting examples@. Suppose that you want to create a script that allows you to play a selected Sound object twice. You first create an empty script, by choosing @@New Praat script@ from the Praat menu. A @ScriptEditor will appear on your screen. In this editor, you type Now select a #Sound in the object menu. As you expect from selecting a Sound, a #Play button will appear in the dynamic menu. If you now choose #Run in the ScriptEditor, the sound will be played twice. What commands can I put into my script? In the above example, you could use the "Play" command because that was the text on a button currently available button in the dynamic menu. Apart from these selection-dependent (dynamic) commands, you can also use all fixed commands in the menus of the @@Object window@ and the @@Picture window@. For how to proceed with commands that need %arguments (i.e. the commands that end in "..." and present a settings window), see @@Scripting 2. Arguments to commands|\SS2@. Faster ways of getting a script text Instead of manually typing the command lines, as described above, it may be easier to create a script text from a %%macro recording%, with the @@History mechanism@. This allows you to create script texts without typing. For instance, if you choose @@Clear history@ in your ScriptEditor, then click the #%Play button twice (after selecting a Sound), and then choose @@Paste history@, your new script text contains exactly two lines that read "Play". To edit a script that is already contained in a file on disk, use @@Open Praat script...@. How to run a script You can run scripts from the @ScriptEditor. If you will have to use the script very often, it is advisable to create a button for it in the fixed menu or in a dynamic menu. See the @ScriptEditor manual page. On Unix and Windows, you can also run scripts from the command line. See @@Scripting 6.9. Calling from the command line@. This chapter describes how your script should represent commands that need %arguments, i.e. commands whose button has a title that ends in "...". Clicking such a button normally presents a %%settings window%, which asks the user to supply %arguments (settings) and then press the OK button. In a script, all of these arguments should be supplied on the same line as the command, in the same order as in the settings window, counted from top to bottom. Numeric arguments The command ##Draw line...# from the World menu in the Picture window, normally presents a settings window that asks the user to supply values for the numeric parameters %%From x%, %%From y%, %%To x%, and %%To y% (from top to bottom). To draw a line from the point (0, 0.5) to the point (1, 1), the values of the arguments would be 0, 0.5, 1, and 1, respectively. In a script, the command would read Draw line... 0 0.5 1 1 Check buttons In a script, you represent a %%check button% (yes/no choice) by "true" or "false", which may be abbreviated to "t" etc., or written with a capital; "yes" or "no" can also be used, as well as "1" or "0": Marks left every... 1.0 100 yes yes no Radio boxes You represent a %%radio box% (multiple choice) by the text on the button that you want to select: Print picture to PostScript printer... Finest A4 Portrait 1.0 If the choice (in a non-final argument) contains spaces, it should be enclosed within double quotes: Print picture to PostScript printer... Finest "US Letter" Portrait 1.0 Using these double quotes is necessary because spaces are normally used for separating the arguments. Putting quotes around "US Letter" ensures that the second argument consists of both words. If you forget the quotes, the interpreter will think that the second argument is "US", the third argument is "Letter", and the fourth argument is the rest of the line, namely "Portrait 1.0", and the command will fail with the message `Paper size' cannot have the value "US". Text arguments A text argument at the end should be typed without any quotes: Text... 400 Centre 1.5 Bottom This is the summit Though spaces separate the arguments, the last argument is always written without surrounding quotes, even if it contains spaces. This is possible because the interpreter knows that the ##Text...# command takes five arguments. The fifth argument is simply everything that follows the first four arguments. With this strategy, you will not suffer from %%quote paranoia%, which would occur if your text itself contains quotes: Text... 0.5 Centre 0.5 Half "hello world" In this case, the quotes around "hello world" will be written to the Picture window as well. For these reasons, nearly all texts in settings windows appear in the last (bottom) field, so that it can be scripted without using quotes. The exceptions are those few commands that have more than a single text parameter. A text argument that is not at the end should then be enclosed in double quotes if it is empty or contains spaces (otherwise, the quotes are optional): Add menu command... Objects New "Create a Bicycle..." "" 0 /u/miep/createBicycle.script If you want to include a double quote in such a text, use %two double quotes: Add menu command... Objects New "Create a \"l\"lBicycle\"r\"r..." (etc.) This doubling of quotes is what you want to avoid in your scripts, especially if your texts come from the expansion of string variables. File arguments The commands from the Read and Write menus, and several other commands whose names start with Read, Open, or Write, present a %%file selector window% instead of a typical Praat settings window. File selector windows ask the user to supply a single argument: the file name. In a script, you can supply the complete %path, including the directory (folder) hierarchy and the name of the file. In Windows, it goes like this: Read from file... D:\bsSounds\bsAnimals\bsmiauw.aifc Instead of these complete path names, you can use %relative path names. These are taken as relative to the directory in which your script resides. In Windows, a relative path name starts without a backslash. So if your script is C:\bsSounds\bsAnalysis.praat, the sound file is read by Read from file... Animals\bsmiauw.aifc Finally, your script may not be in a directory %above the directory from which you like to read, but in a directory on the side, like D:\bsScripts. The commands would then read Read from file... ..\bsAnimals\bsmiauw.aifc How to supply arguments automatically If you dislike manually copying arguments from settings windows into your script, you can use the @@history mechanism@ to automate this process: choose @@Clear history@ from the Edit menu in your @ScriptEditor, click your command button, edit the arguments, and click OK. The command will be executed. Then choose @@Paste history@, and the command line, including the arguments (with correct quotes), appears in a the ScriptEditor. You can build a new script on the basis of this line. This chapter handles the way you use white space, comments, and continuation lines in a Praat script. White space All white space (spaces and tabs) at the beginning of lines is ignored. This means that you can use indenting to make your script readable. You are advised to use three spaces for each level of indenting: sum = 0 for i to 10 for j to 10 sum += i\^ j endfor echo The sum of the products is 'sum' Lines that are empty or consist solely of white space, are also ignored. Comments Comments are lines that start with !, \# , or ;. These lines are ignored when your script is running: \# Create 1 second of a sine wave with a frequency of 100 Hertz, \# sampled at 22050 Hz: Create Sound... sine 0 1 22050 sin (2*pi*100*x) Continuation lines There is normally one line per command, and one command per line. But you can chop up long lines by using continuaton lines that start with three dots ("..."). You will normally want to follow this %ellipsis with a space, unless you want to concatenate the parts of a long word: Viewport... 0 10 0 4 Text top... yes It's a long way to Llanfairpwllgwyngyll ...gogerychwyrndrobwllllantysiliogogogoch, ... unless you start from Tyddyn-y-felin. This chapter is about how to select objects from your script, and how to find out what objects are currently selected. Selecting objects To simulate the mouse-clicked and dragged selection in the list of objects, you have the following commands: #select %object selects one object, and deselects all others. If there are more objects with the same name, the most recently created one (i.e., the one nearest to the bottom of the list of objects) is selected: #select Sound hallo Play #plus %object adds one object to the current selection. #minus %object removes one object from the current selection. ##select all selects all objects: ##select all Remove In the Praat shell, newly created objects are automatically selected. This is also true in scripts: ! Generate a sine wave, play it, and draw its spectrum. Create Sound... sine377 0 1 10000 0.9 * sin (2*pi*377*x) To Spectrum ! Draw the Spectrum: Draw... 0 5000 20 80 yes ! Remove the created Spectrum and Sound: #plus Sound sine377 Instead of by name, you can also select objects by their sequential ID: #select 43 This selects the 43rd object that you created since you started the program (see below). Querying selected objects You can get the name of a selected object into a string variable. For instance, the following reads the name of the second selected Sound (as counted from the top of the list of objects) into the variable %name\$ : name\$ = ##selected\$ # ("Sound", 2) If the Sound was called "Sound hallo", the variable %name\$ will contain the string "hallo". To get the name of the topmost selected Sound object, you can leave out the number: name\$ = ##selected\$ # ("Sound") Negative numbers count from the bottom. Thus, to get the name of the bottom-most selected Sound object, you say name\$ = ##selected\$ # ("Sound", -1) You would use ##selected\$ # for drawing the object name in a picture: Draw... 0 0 0 0 yes Text top... no This is sound 'name\$ ' For identifying previously selected objects, this method is not very suitable, since there may be multiple objects with the same name: \# The following two lines are OK: soundName\$ = ##selected\$ # ("Sound", -1) pitchName\$ = ##selected\$ # ("Pitch") \# But the following line is questionable, since it doesn't \# necessarily select the previously selected Sound again: #select Sound 'soundName\$ ' Instead of this error-prone approach, you should get the object's unique ID. The correct version of our example becomes: sound = #selected ("Sound", -1) pitch = #selected ("Pitch") \# Correct: #select sound To get the number of selected objects into a variable, use numberOfSelectedSounds = numberOfSelected ("Sound") In a Praat script, you can use variables, expressions, and functions, of numeric as well as string type, and most of the control structures known from other procedural computer languages. The way the distinction between numbers and strings is made, may remind you of the programming language Basic. @@Scripting 5.1. Variables@ (numeric, string, copy, expansion) @@Scripting 5.6. Arrays@ @@Scripting 5.7. Including other scripts@ In a Praat script, you can use numeric variables as well as string variables. Numeric variables Numeric variables contain integer numbers between -1,000,000,000,000,000 and +1,000,000,000,000,000 or real numbers between -10^^308^ and +10^^308^. The smallest numbers lie near -10^^-308^ and +10^^-308^. You can use %%numeric variables% in your script: %variable = %formula evaluates a numeric formula and assign the result to a variable. Example: length = 10 Draw line... 0 length 1 1 Names of numeric variables must start with a lower-case letter, optionally followed by a sequence of letters, digits, and underscores. String variables You can also use %%string variables%, which contain text: title\$ = "Dutch nasal place assimilation" As in the programming language Basic, the names of string variables end in a dollar sign. Variable substitution Existing variables are substituted when put between quotes: This will write the following text to the Info window: You can reduce the number of digits after the decimal point by use of the colon: root = sqrt (2) echo The square root of 2 is approximately 'root:3'. The square root of 2 is approximately 1.414. By using ":0", you round to whole values: echo The square root of 2 is very approximately 'root:0'. The square root of 2 is very approximately 1. By using ":3\% ", you give the result in a percent format: jitter = 0.0156789 echo The jitter is 'jitter:3\% '. The jitter is 1.568\% . The number 0, however, will always be written as 0, and for small numbers the number of significant digits will never be less than 1: jitter = 0.000000156789 The jitter is 0.00002\% . ##Predefined string variables# are $$newline\$ $, $$tab\$ $, and $$shellDirectory\$ $. The last one specifies the directory that was the default directory when Praat started up; you can use it in scripts that run from the Unix or DOS command line. In a Praat script, you can use numeric expressions as well as string expressions. Numeric expressions You can use a large variety of @@Formulas@ in your script: height = length/2 area = length * height You can use numeric variables and formulas in arguments to commands: Draw line... 0 length 0 length/2 Of course, all arguments except the last should either not contain spaces, or be enclosed in double quotes. So you would write either Draw line... 0 height*2 0 height or Draw line... 0 "height * 2" 0 height You can use numeric expressions in assignments (as above), or after #if, #elsif, #while, #until, and twice after #for. On how to get information from commands that normally write to the Info window, see @@Scripting 6.4. Query commands@. You can use conditional jumps in your script: #if %expression #elsif %expression if the expression evaluates to zero or %false, the execution of the script jumps to the next #elsif or after the next #else or #endif at the same depth.. The following script computes the preferred length of a bed for a person 'age' years of age: #if age <= 3 length = 1.20 #elsif age <= 8 length = 1.60 #else length = 2.00 #endif A variant spelling for #elsif is #elif. "For" loops #for %variable #from %expression__1_ #to %expression__2_ #for %variable #to %expression the statements between the #for line and the matching #endfor will be executed while a variable takes on values between two expressions, with an increment of 1 on each turn of the loop. The default starting value of the loop variable is 1. The following script plays nine sine waves, with frequencies of 200, 300, ..., 1000 Hz: #for i #from 2 #to 10 frequency = i * 100 Create Sound... tone 0 0.3 22050 0.9*sin(2*pi*frequency*x) #endfor The stop value of the #for loop is evaluated on each turn. If the second expression is already less than the first expression to begin with, the statements between #for and #endfor are not executed even once. "Repeat" loops #until %expression the statements between the matching preceding #repeat and the #until line will be executed again if the expression evaluates to zero or %false. The following script measures the number of trials it takes me to throw 12 with two dice: throws = 0 #repeat eyes = randomInteger (1, 6) + randomInteger (1, 6) throws = throws + 1 #until eyes = 12 #echo It took me 'throws' trials to throw 12 with two dice. The statements in the #repeat/#until loop are executed at least once. "While" loops #while %expression if the expression evaluates to zero or %false, the execution of the script jumps after the matching #endwhile. #endwhile execution jumps back to the matching preceding #while line, which is then evaluated again. The following script forces the number %x into the range [0; 2\pi): #while x < 0 x = x + 2 * pi #while x >= 2 * pi x = x - 2 * pi If the expression evaluates to zero or %false to begin with, the statements between #while and #endwhile are not executed even once. In a Praat script, you can define and call %procedures (subroutines). #call %procedureName [%argument1 [%argument2 [...]]] the execution of the script jumps to the line after the matching #procedure line, which can be anywhere in the script. #procedure %procedureName [%parameter1 [%parameter2 [...]]] introduces a procedure definition (when the execution of the script happens to arrive here, it jumps after the matching #endproc, i.e., the statements in the procedure are ignored). #endproc the execution of the script jumps to the line after the #call line that invoked this procedure. The following script plays three notes: #call play_note 440 #call play_note 400 #procedure play_note frequency Create Sound... note 0 0.3 22050 0.9 * sin (2*pi*'frequency'*x) #call play_note 500 The variable %frequency is a normal variable, global to the script. The procedure uses the same name space as the rest of the script, so beware of possible conflicts. For arguments that contain spaces, you use double quotes, except for the last argument, which is the rest of the line: #call Conjugate be "I am" "you are" she is #procedure Conjugate verb\$ first\$ second\$ third\$ #echo Conjugation of 'to 'verb\$ '': #printline 1sg 'first\$ ' #printline 2sg 'second\$ ' #printline 3sg 'third\$ ' Arguments (except for the last) that contain double quotes should also be put between double quotes, and the double quotes should be doubled: #procedure texts top\$ bottom\$ Text top... yes 'top\$ ' Text bottom... yes 'bottom\$ ' #call texts \" \" \" hello\" \" at the top\" \" goodbye\" at the bottom Quote substitution allows you to simulate arrays of variables: #for i #from 1 #to 5 square'i' = i * i After this, the variables %square1, %square2, %square3, %square4, and %square5 contain the values 1, 4, 9, 16, and 25, respectively. You can use any number of variables in a script, but you can also use Matrix or Sound objects for arrays. You can substitute variables with the usual single quotes, as in $$'square3'$. If the index is also a variable, however, you may need a dummy variable: #echo Some squares: #hop = square'i' #printline The square of 'i' is 'hop' The reason for this is that the following line would not work, because of the required double substitution: #print The square of 'i' is 'square'i'' You can include other scripts within your script: a = 5 include square.praat echo 'a' The Info window will show the result 25 if the file square.praat is as follows: a = a * a The inclusion is done before any other part of the script is considered, so you can use the #form statement and all variables in it. Usually, however, you will put some procedure definitions in the include file, that is what it seems to be most useful for. Watch out, however, for using variable names in the include file: the example above shows that there is no such thing as a separate name space. Since including other scripts is the first thing Praat will do when considering a script, you cannot use variable substitution. For instance, the following will not work: scriptName\$ = "myscript.praat" \# This will *not* work: include 'scriptName\$ ' \# That did *not* work!!! You can use full or relative file names. For instance, the file square.praat is expected to be in the same directory as the script that says %%include square.praat%. If you use the ScriptEditor, you will first have to save the script that you are editing before any relative file names become meaningful (this is the same as with other uses of relative file names in scripts). You can %nest include files, i.e., included scripts can include other scripts. However, relative file names are always evaluated relative to the directory of the outermost script. Usually, the execution of your script ends when the interpreter has executed the last line that is not within a procedure definition. However, you can also explicitly stop the script: #exit stops the execution of the script in the normal way, i.e. without any messages to the user. Any settings window is removed from the screen. #exit %%error-message% stops the execution of the script while sending an error message to the user. Any settings window will stay on the screen. For an example, see @@Scripting 6.8. Messages to the user@. You can cause a Praat script to prompt for arguments. The file $$playSine.praat$ may contain the following: #form Play a sine wave #positive Sine_frequency_(Hz) 377 #positive Gain_(0..1) 0.3 (= not too loud) #endform Create Sound... sine'sine_frequency' 0 1 10000 'gain' * sin (2*pi*'sine_frequency'*x) When running this script, the interpreter puts a settings window (%form) on your screen, entitled "Play a sine wave", with two fields, titled "Sine frequency (Hz)" and "Gain", that have been provided with the standard values "377" and "0.3 (= not too loud)", which you can change before clicking #OK. As you see, the underscores have been replaced with spaces: that looks better in the form. Inside the script, the field names can be accessed as variables: these do contain the underscores, since they must not contain spaces, but the parentheses (Hz) have been chopped off. Note that the first letter of these variables is converted to lower case, so that you can assign to them in your script. Inside the script, the value "0.3 (= not too loud)" will be known as "0.3", because this is a numeric field. You can use the following field types in your forms: #real %variable %initialValue for real numbers. #positive %variable %initialValue for positive real numbers: the form issues an error message if the number that you enter is negative or zero; further on in the script, the number may take on any value. #integer %variable %initialValue for whole numbers: the form reads the number as an integer; further on in the script, the number may take on any real value. #natural %variable %initialValue for positive whole numbers: the form issues an error message if the number that you enter is negative or zero; further on in the script, the number may take on any real value. #word %variable %initialValue for a string without spaces: the form only reads up to the first space ("oh yes" becomes "oh"); further on in the script, the string may contain spaces. #sentence %variable %initialValue for any short string. #text %variable %initialValue for any possibly long string (the variable name will not be shown in the form). #boolean %variable %initialValue a check box will be shown; the value is 0 if off, 1 if on. #choice %variable %initialValue a radio box will be shown; the value is 1 or higher. This is followed by a series of: #button %text a button in a radio box. #comment %text a line with any text. Inside the script, strings are known as string variables, numbers as numeric variables: #form Sink it #sentence Name_of_the_ship Titanic #real Distance_to_the_iceberg_(m) 500.0 #natural Number_of_people 1800 #natural Number_of_boats 10 In this script, the variables are known as %%name_of_the_ship\$ %, %distance_to_the_iceberg, %number_of_people, and %number_of_boats. The variable associated with a radio box will get a numeric as well as a string value: #form Fill attributes #comment Choose any colour and texture for your paintings #choice Colour: 5 #button Dark red #button Sea green #button Navy blue #button Canary yellow #button Black #button White #choice Texture: 1 #button Smooth #button Rough #button With holes #echo You chose the colour 'colour\$ ' and texture 'texture\$ '. This shows two radio boxes. In the Colour box, the fifth button (Black) is the standard value here. If you click on "Navy blue" and then #%OK, the variable %colour will have the value "3", and the variable %%colour\$ % will have the value "Navy blue". Note that the trailing colon is chopped off, and that the button and comment texts may contain spaces. So you can test the value of the Colour box in either of the following ways: if colour = 4 if colour\$ = "Canary yellow" The field types #optionmenu and #option are completely analogous to #choice and #button, but use up much less space on the screen: #optionmenu Colour: 5 #option Dark red #option Sea green #option Navy blue #option Canary yellow #option Black #option White #optionmenu Texture: 1 #option Smooth #option Rough #option With holes You can combine two short fields into one by using %left and %right: #form Get duration #natural left_Year_range 1940 #natural right_Year_range 1945 duration = right_Year_range - left_Year_range #echo The duration is 'duration' years. The interpreter will only show the single text "Year range", followed by two small text fields. Calling a script from another script Scripts can be nested: the file %%doremi.praat% may contain the following: #execute playSine.praat 550 0.9 #execute playSine.praat 615 0.9 #execute playSine.praat 687 0.9 With the #execute command, Praat will not display a form window, but simply execute the script with the two arguments that you supply on the same line (e.g. 550 and 0.9). Arguments (except for the last) that contain spaces must be put between double quotes, and values for #choice must be passed as strings: #execute "fill attributes.praat" "Navy blue" With holes You can pass values for #boolean either as "yes" and "no" or 1 and 0. You can call system commands from a Praat script on Unix, Windows, and MacOS X computers. #system %command executes a Unix or Windows shell command, interpreting non-zero return values as errors: #system cd /u/miep/sounds; sfplay hallo.aifc #system_nocheck %command executes a Unix or Windows shell command, ignoring return values: #system_nocheck rm dummy.aifc In the last example, using $$#system rm dummy.aifc$ would cause the script to stop if the file $$dummy.aifc$ does not exist. ##environment\$ (#%%symbol-string%#) returns the value of an environment variable under Unix, e.g. homeDirectory\$ = ##environment\$ # ("HOME") With the @Info button and several commands in the #Query menus, you write to the @@Info window@. If your program is run from batch (on Unix or Windows), the text goes to %stdout. The following commands allow you to write to the Info window from a script only: #echo %text clears the Info window and writes some text to it: #echo Starting simulation... #clearinfo clears the Info window. #print %text appends some text to the Info window, without clearing it and without going to a new line. #printtab appends a %tab character to the Info window. This allows you to create table files that can be read by some spreadsheet programs. #printline [%text] causes the following text in the Info window to begin at a new line. You can add text, just like with #print. The following script builds a table with statistics about a pitch contour: #printline Minimum Maximum Create Sound... sin 0 0.1 10000 sin(2*pi*377*x) To Pitch... 0.01 75 600 minimum = Get minimum... 0 0 Hertz Parabolic #print 'minimum' maximum = Get maximum... Hertz #print 'maximum' #printline You could combine the last four print statements into: #printline 'minimum''tab\$ ''maximum' or: #print 'minimum''tab\$ ''maximum''newline\$ ' If you click the "Get mean..." command for a Pitch object, the Info window will contain a text like "150 Hz" as a result. In a script, you would rather have this result in a variable instead of in the Info window. The solution is simple: mean = Get mean... 0 0 Hertz Parabolic The numeric variable "mean" now contains the number 150. When assigning to a numeric variable, the interpreter converts the part of the text before the first space into a number. You can also assign to string variables: mean\$ = Get mean... 0 0 Hertz Parabolic The string variable "mean\$ " now contains the entire string "150 Hz". This works for every command that would otherwise write into the Info window. You can read from and write to text files from a Praat script. Reading a file You can check the availability of a file for reading with the function #fileReadable (fileName\$ ) which returns #true if the file exists and can be read, and #false otherwise. To read the contents of an existing text file into a string variable, you use text\$ ##<# %fileName where $$text\$ $ is any string variable and $$%fileName$ is an unquoted string. If the file does not exist, the script terminates with an error message. Example: reading a settings file Suppose that the file ##height.inf# may contain an appropriate value for a numeric variable called $height, which we need to use in our script. We would like to read it with height\$ < height.inf height = 'height\$ ' However, this script will fail if the file ##height.inf# does not exist. To guard against this situation, we could check the existence of the file, and supply a default value in case the file does not exist: fileName\$ = "height.inf" if fileReadable (fileName\$ ) height\$ < 'fileName\$ ' height = 'height\$ ' else height = 180 endif Writing a file To write the contents of an existing string into a new text file, you use text\$ ##># %fileName where $$text\$ $ is any string variable and $$%fileName$ is an unquoted string. If the file cannot be created, the script terminates with an error message. To append the contents of an existing string at the end of an existing text file, you use text\$ ##>># %fileName If the file does not yet exist, it is created first. You can delete an existing file with #filedelete %fileName If the file does not exist, #filedelete does nothing. The simplest way to append text to a file is by using #fileappend: #fileappend out.txt Hello world! Example: writing a table of squares Suppose that we want to create a file with the following text: The square of 1 is 1 The square of 2 is 4 The square of 3 is 9 ... The square of 100 is 10000 We can do this by collecting each line in a variable: filedelete squares.txt for i to 100 square = i * i fileappend squares.txt The square of 'i' is 'square''newline\$ ' Note that we delete the file before appending to it, in order that we do not append to an already existing file. If you put the name of the file into a variable, make sure to surround it with double quotes when using #fileappend, since the file name may contain spaces and is not at the end of the line: name\$ = "Hard disk:Desktop Folder:squares.text" filedelete 'name\$ ' square = i * i fileappend "'name\$ '" The square of 'i' is 'square''newline\$ ' Finally, you can append the contents of the Info window to a file with #fappendinfo %fileName Directory listings To get the names of the files if a certain type in a certain directory, use @@Create Strings as file list...@. You can temporarily halt a Praat script: #pause %text suspends execution of the script, and allows the user to interrupt it. A message window will appear with the %text and the buttons Continue and Stop: #pause The next file will be beerbeet.TextGrid To send messages to running programs that use the Praat shell, use $sendpraat (see @@Scripting 8. Controlling Praat from another program@). To send a message to another running program that listens to a socket, you can use the $sendsocket directive. This works on Unix and Windows only. Suppose we are in the Praat-shell program #Praat, which is a system for doing phonetics by computer. From this program, we can send a message to the %%non%-Praat-shell program #MovieEdit, which does know how to display a sound file: Write to file... hallo.wav sendsocket fonsg19.hum.uva.nl:6667 display hallo.wav In this example, $$fonsg19.hum.uva.nl$ is the computer on which MovieEdit is running; you can specify any valid Internet address instead, as long as that computer allows you to send messages to it. If MovieEdit is running on the same computer as Praat, you can specify $localhost instead of the full Internet address. The number 6667 is the port number on which MovieEdit is listening. Other programs will use different port numbers. If the user makes a mistake (e.g. types conflicting settings into your form window), you can use the #exit directive (@@Scripting 5.8. Quitting|\SS5.7@) to stop the execution of the script with an error message: form My analysis real Starting_time_(s) 0.0 real Finishing_time_(s) 1.0 endform if finishing_time <= starting_time #exit The finishing time should exceed 'starting_time' seconds. \# Proceed with the analysis... For things that should not normally go wrong, you can use the #assert directive: power = Get power assert power > 0 This is the same as: if (power > 0) = undefined exit Assertion failed in line xx (undefined): power > 0 elsif not (power > 0) exit Assertion failed in line xx (false): power > 0 You can prevent Praat from issuing warning messages: nowarn Write to WAV file... hello.wav This prevents warning messages about clipped samples, for instance. You can also prevent Praat from showing a progress window: noprogress To Pitch... 0 75 500 This prevents the progress window from popping up during lengthy operations. Use this only if you want to prevent the user from stopping the execution of the script. Finally, you can make Praat ignore error messages: nocheck Remove This would cause the script to continue even if there is nothing to remove. On most computers, you can call a Praat script from the command line. Command lines on Unix and MacOS X On Unix or MacOS X, you call Praat scripts from the command line like this: > /people/mietta/praat doit.praat 50 hallo > /Applications/Praat.app/Contents/MacOS/Praat doit.praat 50 hallo This opens P\s{RAAT}, runs the script ##doit.praat# with arguments "50" and "hallo", and closes P\s{RAAT}. You also have the possibility of running the program interactively from the command line: > /people/mietta/praat - You can then type in any of the fixed and dynamic commands, and commands that handle object selection, like #select. This method also works in pipes: > echo "Statistics..." | /people/mietta/praat - Command lines on Windows On Windows, you call Praat scripts from the command line like this: e:\bspraatcon.exe e:\bsdoit.praat 50 hallo Note that you use ##praatcon.exe# instead of ##praat.exe#. The script will write to the console output, and its output can be used in pipes. How to get arguments into the script In the above example, the script ##doit.praat# requires two arguments. In the script ##doit.praat#, you use #form and #endform to receive these arguments. See @@Scripting 6.1. Arguments to the script@. As with the #execute command, Praat will not present a form window, but simply execute the script with the arguments given on the command line. The example given in @@Scripting 6.1. Arguments to the script@ will be called in the following way: > /people/mietta/praat playSine.praat 550 0.9 e:\bspraatcon.exe playSine.praat 550 0.9 With a Praat script, you can automatize your work in the editors. #Warning: if the purpose of your script is to get information about analyses (pitch, formants, intensity, spectrogram) from the Sound, we do %not advise to script the Sound editor window. It is much simpler, faster, and more reproducible to create the analyses with the commands of the @@dynamic menu@, then use the Query commands of the dynamic menu to extract information from the analyses. This also applies if you want to use a TextGrid to determine the times at which you want to query the analyses. See @@Scripting examples@. @@Scripting 7.2. Scripting an editor from within@ From a Praat shell script, you can switch to an editor and back again: sound\$ = "hallo" start = 0.3 finish = 0.7 Read from file... 'sound\$ '.aifc Edit #editor Sound 'sound\$ ' Zoom... start finish #endeditor This script reads a sound file from disk, pops up an editor for the resulting object, makes this editor zoom in on the part between 0.3 and 0.7 seconds, and returns to the Praat shell to play the entire sound. This section will show how you can permanently extend the functionality of an editor. As an example, consider the following problem: you want to see a graphic representation of the spectrum of the sound around the cursor position in the SoundEditor. To achieve this, follow these steps: 1. Create a Sound. 2. View it in a SoundEditor by clicking @Edit. 3. Choose ##New editor script# from the @@File menu@ in the SoundEditor. The resulting @ScriptEditor will have a name like "untitled script [Sound hallo]". 4. Type the following lines into the ScriptEditor: cursor = Get cursor Select... cursor-0.02 cursor+0.02 Extract windowed selection... slice Kaiser2 2 no To Spectrum (fft) If you choose Run from the Run menu in the ScriptEditor, a region of 40 milliseconds around the current cursor position in the SoundEditor will become selected. This piece will be copied to the list of objects, after applying a double Kaiser window (total length 80 ms). Thus, a Sound named "slice" will appear in the list. Subsequently, a Spectrum object also called "slice" will appear in the list, and a SpectrumEditor titled "Spectrum slice" will finally appear on your screen. 5. Save the script to disk, e.g. as /us/miep/spectrum.praat. The title of the ScriptEditor will change accordingly. 6. Since you will want this script to be available in all future SoundEditors, you choose ##Add to menu...# from the File menu. For the %Window, you specify "SoundEditor" (this is preset). For the %Menu, you may want to choose "Spec." instead of the preset value ("File"). For the name of the %Command, you type something like "Show spectrum at cursor" (instead of "Do it..."). Then you click OK. The command will be visible in every SoundEditor that you create from now on. To see this, close the one visible SoundEditor, select the original Sound, choose Edit again, and inspect the "Spec." menu. You can now view the spectrum around the cursor just by choosing this menu command. After you leave Praat and start it again, the command will continue to appear in the SoundEditor. If you don't like the command any longer, you can remove it with the @ButtonEditor, which you can start by choosing #Buttons from the Preferences submenu of the @@Praat menu@. Improving your script The above spectrum-viewing example has a number of disadvantages. It clutters the object list with a number of indiscriminable Sounds and Spectra called "slice", and the spectrum is shown up to the Nyquist frequency while we may just be interested in the lower 5000 Hz. Furthermore, the original selection in the SoundEditor is lost. To improve the script, we open it again with ##Open editor script...# from the File menu in the SoundEditor. After every change, we can run it with Run from the Run menu again; alternatively, we could save it (with Save from the File menu) and choose our new "Show spectrum at cursor" button (this button will always run the version on disk, never the one viewed in a ScriptEditor). To zoom in on the first 5000 Hz, we add the following code at the end of our script: #editor Spectrum slice Zoom... 0 5000 To get rid of the "Sound slice", we can add: select Sound slice Note that #endeditor is needed to change from the environment of a SpectrumEditor to the environment of the object & picture windows. If you now choose the "Show spectrum at cursor" button for several cursor positions, you will notice that all those editors have the same name. To remedy the ambiguity of the line $$#editor Spectrum slice$, we give each slice a better name. For example, if the cursor was at 635 milliseconds, the slice could be named "635ms". We can achieve this by changing the extraction in the following way: milliseconds = round (cursor*1000) Extract windowed selection... 'milliseconds'ms Kaiser2 2 no The names of the Sound and Spectrum objects will now have more chance of being unique. Two lines will have to be edited trivially. Finally, we will reset the selection to the original. At the top of the script, we add two lines to remember the positions of the selection markers: begin = Get begin of selection end = Get end of selection At the bottom, we reset the selection: #editor Select... begin end Note that the #editor directive if not followed by the name of an editor, returns the script to the original environment. The complete script is: \# Create a name. E.g. "670ms" means at 670 milliseconds. #editor Spectrum 'milliseconds'ms select Sound 'milliseconds'ms This script is useful as it stands. It is good enough for safe use. For instance, if the created Sound object has the same name as an already existing Sound object, it will be the newly created Sound object that will be removed in the $Remove line, because #select always selects the most recently created object in case of ambiguity. See @@Scripting 8. Controlling Praat from another program@. A subroutine for sending messages to a %running P\s{RAAT}. Also a Unix, MacOS, or DOS console program with the same purpose. ##sendpraat (void *#%display##, const char *#%program##, long #%timeOut##, char *#%text##); %display the display pointer if the subroutine is called from a running X program; if NULL, sendpraat will open the display by itself. On Windows and Macintosh, this argument is ignored. %program the name of a running program that uses the Praat shell, e.g. "Praat" or "ALS". The first letter may be specified as lower or upper case; it will be converted to lower case for Unix and to upper case for Macintosh and Windows. %message a sequence of Praat shell lines (commands and directives). %timeOut (Unix and Macintosh only) the number of seconds that sendpraat will wait for an answer before writing an error message. A %timeOut of 0 means that the message will be sent asynchronously, i.e., that sendpraat will return immediately without issuing any error message. %text the script text to be sent. Sendpraat may alter this text! Example 1: killing a program char message [100], *errorMessage; strcpy (message, "Quit"); errorMessage = #sendpraat (NULL, "praat", 0, message); if (errorMessage != NULL) fprintf (stderr, "\% s", errorMessage); This causes the program #Praat to quit (gracefully), because #Quit is a fixed command in one of the menus of that program. On Unix and Macintosh, sendpraat returns immediately; on Windows, you the %timeOut argument is ignored. The return value %errorMessage is a statically allocated string internal to sendpraat, and is overwritten by the next call to sendpraat. Example 2: playing a sound file in reverse Suppose you have a sound file whose name is in the variable $fileName, and you want the program #Praat, which can play sounds, to play this sound backwards. char message [1000], *errorMessage; sprintf (message, "Read from file... \% s\bsnPlay reverse\bsnRemove", fileName); This will work because ##Play reverse# is an action command that becomes available in the dynamic menu when a Sound is selected. On Unix, sendpraat will allow #Praat at most 1000 seconds to perform this. Example 3: executing a large script file Sometimes, it may be unpractical to send a large script directly to #sendpraat. Fortunately, the receiving program knows the #execute directive: strcpy (message, "doAll.praat 20"); This causes the program #Praat to execute the script ##doAll.praat# with an argument of "20". How to download You can download the source code of the sendpraat subroutine and program via ##www.praat.org# or from ##http://www.fon.hum.uva.nl/praat/sendpraat.html#. See also To start a program from the command line instead and sending it a message, you would not use #sendpraat, but instead run the program with a script file as an argument. See @@Scripting 6.9. Calling from the command line@. A Unix or DOS console program for sending messages to a %running P\s{RAAT} program. #sendpraat [%timeOut] %program %message... For the meaning of the arguments, see @@Scripting 8.1. The sendpraat subroutine|the sendpraat subroutine@. sendpraat 0 praat Quit Causes the program #Praat to quit (gracefully), because #Quit is a fixed command in one of its menus. On Unix, #sendpraat returns immediately; on Windows, you leave out the %timeOut argument. sendpraat 1000 praat "Read from file... hello.wav" "Play reverse" "Remove" This works because ##Play reverse# is an action command that becomes available in the dynamic menu of the #Praat program when a Sound is selected. On Unix, sendpraat will allow #Praat at most 1000 seconds to perform this. Each line is a separate argument. Lines that contain spaces should be put inside double quotes. Example 3: drawing sendpraat als "for i from 1 to 5" "Draw circle... 0.5 0.5 i" "endfor" This causes the program #Als to draw five concentric circles into the Picture window. Example 4: executing a large script sendpraat praat "execute doAll.praat 20" Besides being a subroutine (@@Scripting 8.1. The sendpraat subroutine@) and a program (@@Scripting 8.2. The sendpraat program@), @sendpraat can also be called from within a Praat script. Suppose we are in the Praat-shell program #Als, which is a browser for dictionaries, and we want to kill the Praat-shell program #Praat, which is a program for phonetics research: sendpraat Praat Quit Example 2: playing a sound Suppose we are in the Praat-shell program #Als, which is a browser for dictionaries, and has no idea of what a %sound is. From this program, we can play a sound file by sending a message to the Praat-shell program #Praat, which does know about sounds: fileName\$ = "hallo.wav" sendpraat Praat ...'newline\$ ' Read from file... 'fileName\$ ' ...'newline\$ ' Play ...'newline\$ ' Remove The first $$newline\$ $ is superfluous, but this format seems to read nicely. An aid to @@scripting@. The #ScriptEditor is a text editor that allows you to edit, save, and run any @@Praat script@. You could type such a script from scratch, but it is easier to use the @@History mechanism@, which automatically records all your commands and mouse clicks, and which can paste these directly into a #ScriptEditor. To add a script as a button to a fixed or dynamic menu, use @@Add to fixed menu...@ or @@Add to dynamic menu...@ from the @@File menu@. In this example, we create a fixed button that will play a 1-second sine wave with a specified frequency. First, we create a ScriptEditor by choosing @@New Praat script@ from the @@Praat menu@. Then, we choose @@Clear history@ from the Edit menu in the ScriptEditor. We then perform some actions that will create a sine wave, play it, and remove it: 1. Choose ##Create Sound...# from the @@New menu@ and type the formula of a sine wave (i.e. remove the "randomGauss" term). 2. Click #Play in the dynamic menu. 3. Click the fixed #Remove button. We then choose @@Paste history@ from the Edit menu in the ScriptEditor (or type Command-H). The text will now contain at least the following lines (delete any other lines): Create Sound... sine 0 1 22050 1/2*sin(2*pi*377*x) We can run this script again by choosing #Run from the #Run menu (or typing Command-R). However, this always plays a sine with a frequency of 377 Hz, so we will add the variable "Frequency" to the script, which then looks like: #positive Frequency Create Sound... sine'frequency' 0 1 22050 1/2*sin(2*pi*frequency*x) When we choose #Run, the ScriptEditor will ask us to supply a value for the "Frequency" variable. We can now play 1-second sine waves with any frequency. Note that the name of the temporary Sound is now "sine356" if %Frequency is "356": any occurrence of the string "'Frequency'" is replaced with the supplied argument. It is advisable to supply a standard value for each argument in your script. If the duration should be variable, too, the final script could look like: #positive Frequency 440 #positive Duration 1 Create Sound... sine'frequency' 0 'Duration' 22050 0.9*sin(2*pi*frequency*x) When you run this script, the ScriptEditor will ask you to supply values for the two variables, but the values "440" and "1" are already visible in the form window, so that you will get a sensible result if you just click #OK. If this script is useful to you, you may want to put a button for it in the @@New menu@, in the ##Create Sound# submenu: 1. Save the script to a file, with #Save from the #File menu. The file name that you supply, will be shown in the title bar of the ScriptEditor window. 2. Choose @@Add to fixed menu...@ from the #%File menu. Supply #Objects for the %window, #New for the %menu, "Play sine wave..." for the %command, ##Create Sound...# for %%after command%, and "1" for the depth (because it is supposed to be in a submenu); the %script argument has already been set to the file name that you supplied in step 1. 3. Click #OK and ensure that the button has been added in the @@New menu@. This button will still be there after you leave the program and enter it again; to remove it from the menu, use the @ButtonEditor. In this example, we will create a shortcut for the usual complex pitch-analysis command. First, we perform the required actions: 1. Select a Sound object. 2. Click ##To Pitch...# and set the arguments to your personal standard values. 3. Click #OK. A new #Pitch object will appear. We then paste the history into the ScriptEditor, after which this will contain at least a line like (delete all the other lines): To Pitch... 0.01 150 900 You can run this script only after selecting one or more Sound objects. If this script is useful to you, you may want to put a button for it in the dynamic menu: 1. Save the script to a file, with #Save from the #File menu. 2. Choose @@Add to dynamic menu...@ from the #File menu. Supply "Sound" for %class1 (because the button is supposed to be available only if a Sound is selected), "0" for %number1 (because the command is supposed to work for any number of selected Sound objects), "To Pitch (child)" for the %command, "To Spectrum" for %%after command%, and "0" for the depth (because it is not supposed to be in a submenu); the %script argument has already been set to the file name that you supplied in step 1. 3. Click #OK and ensure that the button is clickable if you select one or more Sound objects. This button will still be available after you leave the program and enter it again; to remove it from the dynamic menus, use the @ButtonEditor. When you give a query command for a numeric value, Praat sometimes writes the numeric value ##--undefined--# into the @@Info window@ (two hyphens at both sides of the word). This happens if the value you ask for is not defined, as in the following examples: \bu You select a Sound with a finishing time of 1.0 seconds and ask for the minimum point in the wave form between 1.5 and 2.0 seconds (with the query command ##Get minimum...#). \bu You ask for a pitch value in a voiceless part of the sound (select a #Pitch, then choose ##Get value at time...#). \bu You type into the @Calculator the following formula: 10\^ 400. Usage in a script In a Praat script, this value is simply represented as "undefined". You use it to test whether a query command returned a valid number: select Pitch hallo meanPitch = Get mean... 0.1 0.2 Hertz Parabolic if meanPitch = undefined \# Take some exceptional action. \# Take the normal action. Details for hackers In text files, this value is written as ##--undefined--#. In binary files, it is written as a big-endian IEEE positive infinity. In memory, it is the ANSI-C constant HUGE_VAL, which equals infinity on IEEE machines. Here is a number of examples of how to use scripting in the Praat program. Refer to the @scripting tutorial when necessary. @@Script for listing time\--F0 pairs @@Script for listing time\--F0\--intensity @@Script for listing F0 statistics @@Script for creating a frequency sweep @@Script for onset detection @@Script for TextGrid boundary drawing @@Script for analysing pitch with a TextGrid "I wish to have a list of time markers in one column and F0 in the other. Those times that have no voiced data should be represented as \"l.\"r in the F0 column." echo Time: Pitch: numberOfFrames = Get number of frames for iframe to numberOfFrames time = Get time from frame... iframe pitch = Get value in frame... iframe Hertz if pitch = undefined printline 'time:6' . printline 'time:6' 'pitch:3' If you want to see this in a text file, you can copy and paste from the Info window, or save the Info window, or add a line to the script like fappendinfo out.txt "I want a list of pitch and intensity values at the same times." Since @@Sound: To Pitch...@ and @@Sound: To Intensity...@ do not give values at the same times, you create separate pitch and intensity contours with high time resolution, then interpolate. In the following example, you get pitch and intensity values at steps of 0.01 seconds by interpolating curves that have a time resolution of 0.001 seconds. sound = selected ("Sound") tmin = Get starting time tmax = Get finishing time To Pitch... 0.001 75 300 Rename... pitch select sound To Intensity... 75 0.001 Rename... intensity echo Here are the results: for i to (tmax-tmin)/0.01 time = tmin + i * 0.01 select Pitch pitch pitch = Get value at time... time Hertz Linear select Intensity intensity intensity = Get value at time... time Cubic printline 'time:2' 'pitch:3' 'intensity:3' "I need to split the wave into 50 msec sections, and then for each of those sections get the F0 statistics. That is, for each 50 msec section of speech I want to get the average F0, min, max, and standard deviation." First you create the complete pitch contour, i.e., you select the Sound and choose @@Sound: To Pitch...|To Pitch...@. You can then use the commands from the #Query menu in a loop: startingTime = Get starting time finishingTime = Get finishing time numberOfTimeSteps = (finishingTime - startingTime) / 0.05 echo tmin tmax mean fmin fmax stdev for step to numberOfTimeSteps tmin = startingTime + (step - 1) * 0.05 tmax = tmin + 0.05 mean = Get mean... tmin tmax Hertz minimum = Get minimum... tmin tmax Hertz Parabolic maximum = Get maximum... tmin tmax Hertz Parabolic stdev = Get standard deviation... tmin tmax Hertz printline 'tmin:6' 'tmax:6' 'mean:2' ... 'minimum:2' 'maximum:2' 'stdev:2' Notes One should not cut the sound up into pieces of 50 ms and then do ##To Pitch...# on each of them, because Praat will not compute F0 values in the first or last 20 ms (or so) of each piece. This is because the analysis requires a window of 40 ms (or so) for every pitch frame. Instead, one typically does the analysis on the whole sound, then queries the resulting large Pitch object. In that way, the information loss of windowing only affects the two 20 ms edges of the whole sound. The example writes lines to the Info window. If you want to write to a file instead, you start with something like filedelete ~/results/out.txt and add lines in the following way: fileappend ~/results/out.txt 'tmin:6' 'tmax:6' 'mean:2' ... 'minimum:2' 'maximum:2' 'stdev:2''newline\$ ' "I have to find a formula for a sinewave that sweeps from 1 kHz to 12 kHz in 60 seconds while ramping the amplitude from 1 to 12 volts in the same amount of time." The absolute amplitude in volts cannot be handled, of course, but linear crescendo is easy: Create Sound... sweep 0 60 44100 ... 0.05 * (1 + 11 * x/60) * sin (2*pi * (1000 + 11000/2 * x/60) * x) Note the "/2" in this formula. Here is the derivation of the formula: %frequency (%t) = 1000 + 11000 %t / 60 %phase (%t) = \in %frequency (%t) %dt = 1000 %t + 11000 (%t^2/2) / 60 %signal (%t) = sin (%phase (%t)) "Can anybody provide me with a script that detects the onset of sound (i.e. the end of silence)." You can create an Intensity contour and look for the first frame that is above some predefined threshold: To Intensity... 100 0 n = Get number of frames for i to n intensity = Get value in frame... i if intensity > 40 time = Get time from frame... i echo Onset of sound at: 'time:3' seconds. exit Since the intensity is computed with rather long windows, the result may be 0.01 or 0.02 seconds before the actual start of sound. "I want only the dotted lines of the textgrid marked on top of another analysis (e.g. pitch, intensity or so) without the labels being shown below it." n = Get number of intervals... 1 for i to n-1 t = Get end point... 1 i One mark bottom... t no no yes "I want the mean pitch of every interval that has a non-empty label on tier 5." if numberOfSelected ("Sound") <> 1 or numberOfSelected ("TextGrid") <> 1 exit Please select a Sound and a TextGrid first. textgrid = selected ("TextGrid") echo Result: To Pitch... 0.0 75 600 pitch = selected ("Pitch") select textgrid n = Get number of intervals... 5 tekst\$ = Get label of interval... 5 i if tekst\$ <> "" t1 = Get starting point... 5 i t2 = Get end point... 5 i select pitch f0 = Get mean... t1 t2 Hertz printline 't1:3' 't2:3' 'f0:0' 'tekst\$ ' plus textgrid Action commands ppgb Add action command... Add menu command... Add to dynamic menu... Add to fixed menu... binomialQ ButtonEditor Buttons file Calculator Calculator... Clear history differenceLimensToPhon Fixed menu commands Formulas Formulas 1. My first formulas Formulas 1.1. Formulas in the calculator Formulas 1.2. Numeric expressions Formulas 1.3. String expressions Formulas 1.4. Representation of numbers Formulas 1.5. Representation of strings Formulas 1.6. Formulas in settings windows Formulas 1.7. Formulas for creation Formulas 1.8. Formulas for modification Formulas 1.9. Formulas in scripts Formulas 2. Operators Formulas 3. Constants Formulas 4. Mathematical functions Formulas 5. String functions Formulas 6. Control structures Formulas 7. Attributes of objects Formulas 8. Data in objects Hidden commands History mechanism Initialization script New Praat script Open Praat script... Paste history phonToDifferenceLimens Praat script Preferences file Run script... Scripting Scripting 1. My first script Scripting 2. Arguments to commands Scripting 3. Layout Scripting 4. Object selection Scripting 5. Language elements Scripting 5.1. Variables Scripting 5.2. Formulas Scripting 5.3. Jumps Scripting 5.4. Loops Scripting 5.5. Procedures Scripting 5.6. Arrays Scripting 5.7. Including other scripts Scripting 5.8. Quitting Scripting 6. Communication outside the script Scripting 6.1. Arguments to the script Scripting 6.2. Calling system commands Scripting 6.3. Writing to the Info window Scripting 6.4. Query commands Scripting 6.5. Files Scripting 6.6. Controlling the user Scripting 6.7. Sending a message to another program Scripting 6.8. Messages to the user Scripting 6.9. Calling from the command line Scripting 7. Scripting the editors Scripting 7.1. Scripting an editor from a shell script Scripting 7.2. Scripting an editor from within sendpraat Scripting 8. Controlling Praat from another program Scripting 8.1. The sendpraat subroutine Scripting 8.2. The sendpraat program Scripting 8.3. The sendpraat directive ScriptEditor undefined Scripting examples Script for listing time\--F0 pairs Script for listing time\--F0\--intensity Script for listing F0 statistics Script for creating a frequency sweep Script for onset detection Script for TextGrid boundary drawing Script for analysing pitch with a TextGrid 6Q %7Q 67Q G7Q S7Q j7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q @@ ? 4&k C mB eA .A $@ Y@{Gz?%n %n %n %n &%n <%n I%n %n b%n n%n ~%n %n %n %n %n %n %n Pause: %s Press 'q' to stop, or anyother key to continue. %s Do not know how to find help on "%s". Do not know how to search. Warning: %s You interrupted User interrupt: %s Error: %s Fatal error: %s Casual info %s melderProgress Work in progress label scale Interrupt Interrupted! melderMonitor drawingArea equal to not equal to less than less than or equal to greater than greater than or equal to is equal to is not equal to contains does not contain starts with does not start with ends with does not end with matches (regex) %ld - %d, %03d, %03d %d yes no --undefined-- %.15g %.16g %.17g %.8g %.4g 0 %.*f %.*fE%d %.*f%% undefined inf INF Inf nan NAN NaN melder.c foregroundBuffer != NULL && infos != NULL infos != NULL Praat cannot start up Praat will crash. Notify the author (paul.boersma@uva.nl) with the following information: Assertion failed in file "%s" at line %d: %s melderPause Pause rc text Continue Stop Warning Fatal error Message (Melder_malloc:) Can never allocate %ld bytes. Out of memory: there is not enough room for another %ld bytes. (Melder_realloc:) Can never allocate %ld bytes. Out of memory. Could not extend room to %ld bytes. (Melder_calloc:) Can never allocate %ld elements. (Melder_calloc:) Can never allocate elements whose size is %ld bytes. Out of memory: there is not enough room for %ld more elements whose sizes are %ld bytes each. Out of memory: there is not enough room to duplicate a text of %ld characters. ? @@Audio.maximumAsynchronicity Audio.useInternalSpeaker Audio.outputGain Audio.zeroPadding (Melder_play16:) Previous sound is still playing? Should not occur! Report bug to the author: %ld; wasPlaying: %d (Melder_play16:) Cannot play a sound. Perhaps another program is playing a sound at the same time? (Melder_play16:) This machine probably has no sound card. (Melder_play16:) Not enough free memory to play any sound at all. (Melder_play16:) Bad sound format? Should not occur! Report bug to the author! (Melder_play16:) Unknown error %ld while trying to play a sound? Report bug to the author! (Melder_play16:) No device? Should not occur! (Melder_play16:) No driver? Should not occur! (Melder_play16:) Not enough free memory to play this sound. Remove some objects, play a shorter sound, or buy more memory. (Melder_play16:) Unknown error %ld while preparing header? Should not occur! (Melder_play16:) Error %d while writing. t5n 74n K4n y5n }5n 5n 5n 5n 74n K4n Z4n 5n 5n 5n 5n 5n 5n 5n 5n 5n 5n DDDDDDDD$d$d$d$d4Tt4Tt ,<L\l| |} |y |u |q |m |i |e |a |] |Y |U |Q |M |I |E |A |> |< |: |8 |6 |4 |2 |0 |. |, |* |( |& |$ |" | < < < < < < < < \ \ \ \ l L , l L , t d T D 4 $ x p h ` X P H @ 8 0 ( @@@@@@@@ ˨(8hxHX(8hxHX ` ` ` `Pp0Pp0 @ @ @ @ @@ @ @ V R ^ Z F B N J v r ~ z f b n j + ) / - # ! ' % ; 9 ? = 3 1 7 5XHxh8(X H x h 8 ( ` ` ` ` 0pP0pP ? @ < ; ? ? 8 7 4 3 0 / C ? `@ G K A AFORM AIFF FVER COMM SSND AIFC NONE RIFF WAVE fmt data .snd NIST_1A 1024 channel_count -i %d sample_count -i %d sample_n_bytes -i 2 sample_byte_format -s2 01 sample_coding -s3 pcm sample_rate -i %d sample_min -i -32768 sample_max -i 32767 end_head Cannot yet write Sound Designer II files. Unknown audio file type %d. none WAV NeXT/Sun NIST Sound Designer II unknown ULAW Sd2f .aiff .aifc .wav .au .nist .sd2 PpgB (Melder_writeAudioFile16:) File not written. File too small: no FORM statement. Not an AIFF or AIFC file (FORM statement expected). File too small: no size of FORM chunk. File too small: no file type info (expected AIFF or AIFC). Not an AIFF or AIFC file (wrong file type info). Ha! a buggy SGI "soundeditor" file... %d sound channels is too few. %d sound channels is too many. Too few samples (%ld). Too many samples (%ld). %d bits per sample is too many (maximum is 32). Wrong sampling frequency (%.17g Hz). File too small: no compression info. sowt Cannot read compressed AIFC files (compression type %c%c%c%c). File too small: expected chunk of %ld bytes, but found %ld. File too small: expected %ld bytes, but found %ld. Found no Common Chunk. Found no Data Chunk. File too small: no RIFF statement. Not a WAV file (RIFF statement expected). File too small: no size of RIFF chunk. File too small: no file type info (expected WAVE statement). CDDA Not a WAVE or CD audio file (wrong file type info). %d bits per sample is too few (minimum is 4). Unsupported Windows audio encoding %d. File too small: expected %ld bytes in fmt chunk, but found %ld. Found no Format Chunk. melder_audiofiles.c numberOfBitsPerSamplePoint != -1 && dataChunkSize != -1 Not a Sun audio file. Sorry, cannot read header of audio file. Length %ld. Sorry, cannot translate audio file encoding %ld. Impossible sampling frequency %ld Hertz. Wrong number of channels in audio file (%d). %s%s%s -i -r -s Cannot read NISTheader. NIST_1A Not a NIST sound file. sample_count Incorrect number of samples in NIST file. sample_n_bytes Incorrect number of bytes per sample (should be 1 or 2). channel_count Incorrect number of channels. Too many channels in NIST file. sample_rate Incorrect sampling frequency %f Hz. sample_byte_format 01 sample_coding ulaw embedded-shorten-v database_id POLYPHONE-NL alaw File too small (mono 8-bit). File too small (stereo 8-bit). (Melder_readAudioToFloat:) Unknown encoding %d. Audio file too short. Missing samples were set to zero. (Melder_readAudioToFloat:) Error reading audio samples from file. (Melder_readAudioToShort:) Unknown encoding %d. (Melder_readAudioToShort:) Error reading audio samples from file. (Melder_writeShortToAudio:) Unknown encoding %d. (Melder_writeShortToAudio:) Early end of audio file. (Melder_writeShortToAudio:) Error writing audio samples to file. (Melder_writeFloatToAudio:) Unknown format. (Melder_writeFloatToAudio:) %ld out of %ld samples have been clipped. Advice: you could scale the amplitudes or write to a binary file. <stdout> :// %s%s %s\%s USERPROFILE HOMEDRIVE HOMEPATH open append to create Cannot %s file "%.200s". Hint: empty file name. Hint: file name starts with a space. Hint: file name ends in a space. Error closing file "%.200s". rb r Error reading file "%s". w Error closing file "%s". a Cannot create directory "%s". (MelderFile_readLine:) No room even for a string buffer of 100 bytes. (MelderFile_readLine:) No memory to extend string buffer to %ld bytes. wb Cannot seek in file %s. Cannot tell in file %s. Bn Bn Bn Bn Bn Cn Cn Cn Cn Cn #Cn *Cn /Cn #Cn 3Cn ;Cn ECn LCn OCn RCn UCn XCn [Cn ^Cn aCn dCn gCn kCn oCn Bn Bn Bn Bn sCn wCn {Cn ~Cn Cn Cn Cn Cn Cn Cn *Cn /Cn Cn Cn Cn Cn LCn OCn RCn UCn XCn [Cn ^Cn aCn dCn gCn kCn oCn Bn Bn Bn Praatwulg menuBar Help Left Right Up Down Pause Delete Insert BackSpace Tab Return Home End Page_Up Page_Down Escape F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 <- -> UP DOWN Backspace Enter PageUp PageDown Esc Ctrl Ctrl- Shift Shift- Mod1 Alt- <Key> question ? bracketleft [ bracketright ] menuSeparator tLn |Ln Ln Ln Ln Ln Ln Ln Ln Ln Mn &Mn .Mn 6Mn EMn QMn ^Mn tMn Mn Mn Mn Mn Mn Mn Mn Mn Nn Nn *Nn :Nn LNn aNn wNn Nn Nn Nn Nn Nn Nn Nn On On +On 7On BOn ZOn lOn On On On On On On Pn Pn 0Pn BPn KPn ^Pn mPn |Pn Pn Pn Pn Pn Pn Pn Pn Pn Qn Qn 3Qn @Qn PQn aQn mQn {Qn Qn Qn Qn Qn Qn Qn Qn Qn Rn !Rn 7Rn NRn cRn mRn yRn Rn Rn Rn Rn Rn Rn Rn Rn Rn Sn Sn *Sn HSn XSn aSn rSn Sn Sn Sn Sn Sn Sn Sn Sn Tn Tn %Tn 7Tn ETn UTn cTn wTn Tn Tn Tn Tn Tn Tn Tn Un Un -Un ;Un JUn WUn fUn tUn Un Un Un Un Un Un Un Un Un Vn Vn (Vn 5Vn HVn SVn _Vn kVn ~Vn Vn Vn Vn Vn Vn Vn Wn Wn &Wn 8Wn DWn SWn aWn oWn Wn Wn Wn Wn Wn Wn Wn Xn Xn &Xn 6Xn MXn bXn tXn Xn Xn Xn Xn Xn Xn Xn Xn Yn Yn &Yn 5Yn FYn NYn cYn pYn Yn Yn Yn Yn Yn Yn Yn Zn 'Zn :Zn LZn ]Zn oZn ~Zn Zn Zn Zn Zn Zn Zn [n [n +[n 2[n E[n S[n a[n r[n [n [n [n [n [n [n [n [n [n \n \n +\n :\n N\n _\n o\n \n \n \n \n \n \n \n \n \n ]n ]n ,]n =]n I]n R]n j]n x]n ]n ]n ]n ]n ]n ]n ]n ]n ^n ^n ^n ,^n 8^n F^n K^n P^n @ @@ _n _n _n _n _n _n _n _n _n _n _n _n _n _n _n _n _n _n _n `n `n `n `n `n `n `n `n `n `n $`n &`n (`n *`n ,`n .`n 0`n 2`n 4`n 6`n 8`n :`n <`n >`n @`n B`n D`n F`n H`n J`n L`n N`n P`n R`n T`n V`n X`n Z`n \`n ^`n ``n b`n d`n f`n h`n j`n l`n n`n p`n r`n t`n v`n x`n z`n |`n ~`n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n `n _n `n `n :`n ``n >`n `n X`n <`n `n \`n 0`n } XmNnull XmNaccelerator XmNaccelerators XmNacceleratorText XmNactivateCallback XmNadjustLast XmNadjustMargin XmNalignment XmNallowOverlap XmNallowShellResize XmNancestorSensitive XmNargc XmNargv XmNarmCallback XmNarmColor XmNarmPixmap XmNautomaticSelection XmNautoShowCursorPosition XmNautoUnmanage XmNbackground XmNbackgroundPixmap XmNbaseHeight XmNbaseWidth XmNblinkRate XmNborderColor XmNborderPixmap XmNborderWidth XmNbottomAttachment XmNbottomOffset XmNbottomPosition XmNbottomShadowColor XmNbottomShadowPixmap XmNbottomWidget XmNbrowseSelectionCallback XmNbuttonFontList XmNcancelButton XmNcancelCallback XmNcancelLabelString XmNcascadePixmap XmNcascadingCallback XmNchildren XmNclipWindow XmNcolormap XmNcolumns XmNcreatePopupChildProc XmNcursorPosition XmNcursorPositionVisible XmNdecimalPoints XmNdecrementCallback XmNdefaultActionCallback XmNdefaultButton XmNdefaultButtonType XmNdefaultButtonShadowThickness XmNdefaultFontList XmNdefaultPosition XmNdeleteResponse XmNdepth XmNdestroyCallback XmNdialogStyle XmNdialogTitle XmNdialogType XmNdisarmCallback XmNdragCallback XmNeditable XmNeditMode XmNentryAlignment XmNentryBorder XmNentryCallback XmNentryClass XmNexposeCallback XmNextendedSelectionCallback XmNfillOnArm XmNfillOnSelect XmNfocusCallback XmNfontList XmNforeground XmNfractionBase XmNgainPrimaryCallback XmNgeometry XmNheight XmNheightInc XmNhelpCallback XmNhelpLabelString XmNhighlightColor XmNhighlightOnEnter XmNhighlightPixmap XmNhighlightThickness XmNhorizontalScrollBar XmNhorizontalSpacing XmNiconic XmNiconMask XmNiconName XmNiconNameEncoding XmNiconPixmap XmNiconWindow XmNiconX XmNiconY XmNincrement XmNincrementCallback XmNindicatorOn XmNindicatorSize XmNindicatorType XmNinitialDelay XmNinitialResourcesPersistent XmNinitialState XmNinput XmNinputCallback XmNinsertPosition XmNisAligned XmNisHomogeneous XmNitemCount XmNitems XmNkeyboardFocusPolicy XmNlabelFontList XmNlabelInsensitivePixmap XmNlabelPixmap XmNlabelString XmNlabelType XmNleftAttachment XmNleftOffset XmNleftPosition XmNleftWidget XmNlistMarginHeight XmNlistMarginWidth XmNlistSizePolicy XmNlistSpacing XmNlosePrimaryCallback XmNlosingFocusCallback XmNmapCallback XmNmappedWhenManaged XmNmappingDelay XmNmarginBottom XmNmarginHeight XmNmarginLeft XmNmarginRight XmNmarginTop XmNmarginWidth XmNmaxAspectX XmNmaxAspectY XmNmaxHeight XmNmaximum XmNmaxLength XmNmaxWidth XmNmenuAccelerator XmNmenuHelpWidget XmNmenuHistory XmNmessageAlignment XmNmessageString XmNminAspectX XmNminAspectY XmNminHeight XmNminimizeButtons XmNminimum XmNminWidth XmNmnemonic XmNmnemonicCharSet XmNmodifyVerifyCallback XmNmotionVerifyCallback XmNmoveCallback XmNmultiClick XmNmultipleSelectionCallback XmNmwmDecorations XmNmwmFunctions XmNmwmInputMode XmNmwmMenu XmNnavigationType XmNnoResize XmNnumChildren XmNnumColumns XmNokCallback XmNokLabelString XmNorientation XmNoverrideRedirect XmNpacking XmNpageDecrementCallback XmNpageIncrement XmNpageIncrementCallback XmNpendingDelete XmNpopdownCallback XmNpopupCallback XmNpopupEnabled XmNprocessingDirection XmNpushButtonEnabled XmNradioAlwaysOne XmNradioBehavior XmNrecomputeSize XmNrepeatDelay XmNresizable XmNresizeCallback XmNresizeHeight XmNresizePolicy XmNresizeWidth XmNrightAttachment XmNrightOffset XmNrightPosition XmNrightWidget XmNrowColumnType XmNrows XmNrubberPositioning XmNsaveUnder XmNscaleHeight XmNscaleMultiple XmNscaleWidth XmNscreen XmNscrollBarDisplayPolicy XmNscrollBarPlacement XmNscrolledWindowMarginHeight XmNscrolledWindowMarginWidth XmNscrollHorizontal XmNscrollingPolicy XmNscrollLeftSide XmNscrollTopSide XmNscrollVertical XmNselectColor XmNselectedItemCount XmNselectedItems XmNselectInsensitivePixmap XmNselectionArray XmNselectionArrayCount XmNselectionPolicy XmNselectPixmap XmNselectThreshold XmNsensitive XmNset XmNshadowThickness XmNshadowType XmNshowArrows XmNshowAsDefault XmNshowValue XmNsingleSelectionCallback XmNsliderSize XmNsource XmNspacing XmNstringDirection XmNsubMenuId XmNsymbolPixmap XmNtextFontList XmNtextTranslations XmNtitle XmNtitleEncoding XmNtitleString XmNtoBottomCallback XmNtopAttachment XmNtopCharacter XmNtopItemPosition XmNtopOffset XmNtopPosition XmNtopShadowColor XmNtopShadowPixmap XmNtopWidget XmNtoTopCallback XmNtransient XmNtransientFor XmNtranslations XmNtraversalOn XmNtroughColor XmNunmapCallback XmNuserData XmNvalue XmNvalueChangedCallback XmNverifyBell XmNverticalScrollBar XmNverticalSpacing XmNvisibleItemCount XmNvisibleWhenOff XmNvisual XmNvisualPolicy XmNwaitForWm XmNwidth XmNwidthInc XmNwindowGroup XmNwinGravity XmNwmTimeout XmNwordWrap XmNworkWindow XmNx XmNy XmNend motifEmulator.c scrolledWindow -> motif.scrolledWindow.clipWindow != NULL - Help XmScrollBar: maximum (%d) less than minimum (%d). XmScrollBar: slider size (%d) greater than maximum (%d) minus minimum (%d). XmScrollBar: value (%d) less than minimum (%d). XmScrollBar: value (%d) greater than maximum (%d) minus slider size (%d). <- -> Up Down PAUSE Del Ins Backspace Tab LineFeed Home End Enter PageUp PageDown Esc F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 Space ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~ ??? Shift- Alt- Ctrl- %s %s%s%s%s bulletinBoard drawingArea form rowColumn list listbox messageBox OK Cancel text static button msctls_progress32 verticalScrollBar scrollbar scrolledWindow horizontalScrollBar clipWindow my widgetClass == xmToggleButtonWidgetClass my widgetClass == xmListWidgetClass ! my shell || ! my shell -> nat.shell.duringMoveWindow <Key> MEMBER (me, PushButton) Ctrl Shift Mod1 Return BackSpace question bracketleft bracketright Left Right Pause Delete Insert Page_Up Page_Down Escape MEMBER3 (me, Form, BulletinBoard, MessageBox) MEMBER (me, MessageBox) MEMBER (me, Text) MEMBER (my defaultButton, PushButton) MEMBER (me, Shell) MEMBER (me, RowColumn) MEMBER (me, ScrollBar) MEMBER3 (me, Label, CascadeButton, PushButton) MEMBER3 (me, RowColumn, ScrollBar, Scale) MEMBER (me, Scale) MEMBER (me, List) MEMBER (me, CascadeButton) edit (XtVaSetValues:) Resource out of range (%d). (XtVaSetValues:) Unknown resource "%s". MEMBER2 (my parent, Form, ScrolledWindow) my widgetClass == xmScrolledWindowWidgetClass i < MAXNUM_CALLBACKS my widgetClass == xmMessageBoxWidgetClass my widgetClass == xmScrollBarWidgetClass my widgetClass == xmTextWidgetClass my widgetClass == xmDrawingAreaWidgetClass False (XtAddCallback:) Callback name out of range (%d). (XtAddCallback:) Unknown callback "%s". i < 10 my widgetClass != xmPulldownMenuWidgetClass (XtRemoveCallback:) Callback name out of range (%d). (XtRemoveCallback:) Unknown callback "%s". Unknown PraatShell%d %s PraatChildWindow%d %s PraatDrawingArea%d %s my widgetClass == xmShellWidgetClass my widgetClass == xmLabelWidgetClass || my widgetClass == xmCascadeButtonWidgetClass || my widgetClass == xmScaleWidgetClass my widgetClass == xmFormWidgetClass || my widgetClass == xmBulletinBoardWidgetClass || my widgetClass == xmMessageBoxWidgetClass my widgetClass == xmRowColumnWidgetClass my widgetClass == xmRowColumnWidgetClass || my widgetClass == xmScrollBarWidgetClass my widgetClass == xmCascadeButtonWidgetClass my widgetClass == xmFormWidgetClass || my widgetClass == xmBulletinBoardWidgetClass my parent -> widgetClass == xmFormWidgetClass (XtVaGetValues:) Resource out of range (%d). (XtVaGetValues:) Unknown resource "%s". WM_DELETE_WINDOW my widgetClass == xmScaleWidgetClass MEMBER (me, ToggleButton) dummy %ld %d MEMBER4 (child, PushButton, ToggleButton, CascadeButton, Separator) -DT!@-DT! @-DT! ? @tHZr?Ix?2t?,?N?03@$ @;^p?UL+ߐZ? 'TPÂ?JNYՒ+Hub? -5? e3E?Ӱ٩=5?.h?Z9?*O?(z?Y ? ?;PJ4qqJ:N?P⥝' 8`?< Q tZOZ??Vm .k*ꂰ >3. ?~%-e?.ܡ?ƻe?Uv? xYtioA?~?-d{GHx?_F ?6k?4 > ?mJWq}aRv'=ǿnv忉#h?07\FUTٞj?}.K"N'UΎ?*~?;f?-DT! @ @ :0yE>|= cANUMincompleteBeta status %d NUM.c x > 0 n >= 2 (NUMviterbin:) Number of tracks (%d) should not exceed number of candidates (%ld). (NUMviterbin:) Unrealistically high number of combinations (%ld). jcomb == ncomb (NUMvector:) Not created. NUMarrays.c v != NULL && to != NULL v1 != NULL && v2 != NULL m != NULL && to != NULL m1 != NULL && m2 != NULL (empty) %s []: %s %s [%ld] (NUMbvector_readAscii:) Could not read %s [%ld]. %s [] []: %s %s [%ld]: %s [%ld] [%ld] (NUMbmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMsvector_readAscii:) Could not read %s [%ld]. (NUMsmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMivector_readAscii:) Could not read %s [%ld]. (NUMimatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMlvector_readAscii:) Could not read %s [%ld]. (NUMlmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMubvector_readAscii:) Could not read %s [%ld]. (NUMubmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMusvector_readAscii:) Could not read %s [%ld]. (NUMusmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMuivector_readAscii:) Could not read %s [%ld]. (NUMuimatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMulvector_readAscii:) Could not read %s [%ld]. (NUMulmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMfvector_readAscii:) Could not read %s [%ld]. (NUMfmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMdvector_readAscii:) Could not read %s [%ld]. (NUMdmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMfcvector_readAscii:) Could not read %s [%ld]. (NUMfcmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMdcvector_readAscii:) Could not read %s [%ld]. (NUMdcmatrix_readAscii:) Could not read %s [%ld] [%ld]. (NUMcvector_readAscii:) Could not read %s [%ld]. (NUMcmatrix_readAscii:) Could not read %s [%ld] [%ld]. P@ ? @DDDDDD? >@h㈵> 4@ V@ @ @ @ @ ? 0@ Y@ (@9B.??:\i!>* 3h?Q <@ @ s@ףp= W&@ E@ (@ ?Q '@{Gz?q= ף'@ffffff@ R@ ?? 8@ ? 9@@ أ@ @%d wb PraatPictureFile Picture_writeToPraatPictureFile: error while writing file %.200s rb Picture_readFromPraatPictureFile: file %.200s is not a Praat picture file. Praat Cannot create metafile. DEVICE CAPS: y aspect x vert res(pixels) hor size(mm) hor pixels/inch hor physicalOffset(pixels) hor PRINTER: dmFields y resolution print quality paper width paper length paper size orientation Picture_writeToPostScriptFile: error opening file %.200s Picture not printed. No %s #%d selected. No %s selected. praat_onlyScreenObject: found %d objects instead of 1. %.50s.%s praat.Collection praat.%s praat.c iobject >= 1 && iobject <= praat.n No object was put into the list. %.50s untitled %s %s The Object Window cannot contain more than %d objects. You could remove some objects. FULL_NAME == NULL FULL_NAME != NULL select %s plus %s %s_%s w # Buttons (1). # This file is generated automatically when you quit the %s program. # It contains the buttons that you added interactively to the fixed or dynamic menus, # and the buttons that you hid or showed. (praat_installEditor:) Cannot have more than %d editors with one object. (praat_installEditor2:) Cannot have more than %d editors with one object. (praat_installEditor3:) Cannot have more than %d editors with one object. Cannot view the same object in more than %d windows. iPraatObject <= praat.n ieditor < praat_MAXNUM_EDITORS Cannot view manual from batch. help: no help on "%s". (Melder_publish:) not published. Quit Confirm Quit You have objects in your list! label You have objects and unsaved scripts! Do you still want to quit %s? You have unsaved scripts! Do you still want to quit %s? You have objects in your list! Do you still want to quit %s? %s: message not completely handled. Read from file... %s praat %s Preferences.ini Buttons.ini Message.txt Praatwulg %s objects WM_DELETE_WINDOW raam Objects: list r %s: start-up file "%s" not completed. -- quit -- Praat Objects %s-user-startUp %s: command line session interrupted. %s: command file "%s" not completed. praat_addAction: command with callback has no title. Classes: %s %s %s. praat_addAction: command "%s" has no first class. praat_addAction: the command "%s" cannot be put after "%s", because the latter command does not exist. praat_addAction: too many loose commands. Write praat_actions.c className1 && className2 && className3 && title && after && script praat_addActionScript: command with callback has no title. Classes: %s %s %s. praat_addActionScript: command "%s" has no first class. praat_addActionScript: too many loose commands. %s & %s : %s (praat_removeAction:) Action command "%s" not found. className1 && className2 && className3 && title (praat_hideAction:) Action command "%s" not found. (praat_showAction:) Action command "%s" not found. one two three any number of object objects No class1??? Selection changed! It should be: %s %s %s Selection changed! %s Command not executed. execute Script not executed. Write Append to menu Write to binary file... separator dynamicSubmenuBar menuWindow "" Add action command... %s %d %s %d %s %d "%s" "%s" %d %s Hide Show %s action command... %s %s %s %s ? ???ffffff??333333? ?ffffff9@ V@ D@xR \s{Built on the} %%Praat shell%\s{,\co Paul Boersma, 1992-2004 logo About WM_DELETE_WINDOW drawingArea praat_menuCommands.c callback != NULL History to script... %s Command not executed. execute Script not executed. Picture Objects praat_addMenuCommand: command with callback has no title. Window "%s", menu "%s". praat_addMenuCommand: the command "%s" cannot be put after "%s", in the menu "%s" in the window "%s" because the latter command does not exist. praat_addMenuCommand: too many menu commands. window && menu && title && after && script praat_addMenuCommand: command with script has no title. Window "%s", menu "%s". Add menu command... "%s" "%s" "%s" "%s" %d %s Hide Show %s menu command... "%s" "%s" %s To fix this, go to Praat:Preferences:Buttons:Editors, and remove the script from this menu. You may want to install the script in a different menu. Rename... Rename object New name: rename object newName Selection changed! No object selected. Cannot rename. Selection changed! Cannot rename more than one object at a time. %s %s Copy... Copy object Name of new object: copy object Selection changed! No object selected. Cannot copy. Selection changed! Cannot copy more than one object at a time. Selection changed! No object selected. Cannot query. Selection changed! Cannot query more than one object at a time. Selection changed! No object selected. Cannot inspect. Cannot inspect data from batch. Praat Control New Create Read Help Goodies Preferences ApplicationHelp Set debugging options Setting the following to anything other than zero will alter the behaviour of this program in inpredictable ways. 0 Debug option Add menu command... Add menu command Objects Window Menu Hallo... Command After command Depth Script file: /u/miep/hallo.praat Script Hide menu command... Hide menu command Show menu command... Show menu command Add action command... Add action command Sound Class 1 Number 1 Class 2 Number 2 Class 3 Number 3 Play reverse Play /u/miep/playReverse.praat Hide action command... Hide action command Show action command... Show action command Calculator... Calculator 5*5 expression These pages contain links to executable scripts. Only navigate these pages if you trust their author! Read Object(s) from file Write Object(s) to text file Write Object(s) to short text file Write Object(s) to binary file Write Object to LISP file lsp Manual Search manual Search for strings (separate with spaces): query Cannot view manual from batch. Intro Go to manual page Page Write all pages as HTML files Type a directory name: directory Remove Info Inspect .praat .html About %s... Debug... Statistics... -- script -- Run script... New Praat script Open Praat script... -- buttons -- Buttons... Read from file... Write to console Write to text file... Write to short text file... Write to binary file... -- manual -- Go to manual page... Write manual to HTML directory... Search %s manual... -- about -- @ @ (@ @ R@ffffff@? (@ @ ? ? {Gz? $@ ?R n lj 0 dn Font menu Praat picture: Font size 10 Font size (points) Font size Select inner viewport... Praat picture: Select inner viewport The viewport is the selected rectangle in the Picture window. It is where your next drawing will appear. The rectangle you select here will not include the margins. 0.0 left Horizontal range (inches) 6.0 right Horizontal range (inches) left Vertical range (inches) right Vertical range (inches) left Horizontal range right Horizontal range left Vertical range right Vertical range The left and right edges of the viewport cannot be equal. Please change the horizontal range. The top and bottom edges of the viewport cannot be equal. Please change the vertical range. Select outer viewport... Praat picture: Select outer viewport The rectangle you select here will include the margins. Viewport text... Praat picture: Viewport text Horizontal alignment Left Centre Right Vertical alignment Bottom Half Top 0 Rotation (degrees) text Rotation Praat picture: Line width 1.0 Line width Read picture from praat picture file Read picture from old praat picture file Write to EPS file praat.eps Write to fontless EPS file Write to Praat picture file praat.prapic Write to Windows metafile praat.emf Text... Praat picture: Text Horizontal position Vertical position Text: Praat picture: Text special Font Times New_Century_Schoolbook Helvetica Courier Rotation (degrees or dx;dy) From x From y To x To y Praat picture: Draw line Praat picture: Draw arrow Praat picture: Draw double arrow PraatPictureFunction Praat picture: Draw function 0.0 (= all) 1000 Number of horizontal steps Formula: x^2 - x^4 formula Praat picture: Draw rectangle Praat picture: Paint rectangle 0.5 Colour (0-1 or name) Colour Praat picture: Draw rounded rectangle 3.0 Radius (mm) Radius Praat picture: Paint rounded rectangle Praat picture: Draw arc Centre x Centre y Radius (along x) From angle (degrees) 90.0 To angle (degrees) To angle From angle Praat picture: Draw ellipse Praat picture: Paint ellipse Praat picture: Draw circle Praat picture: Paint circle Praat picture: Draw circle (mm) 5.0 Diameter (mm) Diameter Praat picture: Paint circle (mm) Axes... Praat picture: Axes left Left and right right Left and right left Bottom and top right Bottom and top Left and right must not be equal. %s Top and bottom must not be equal. Text left/right/top/bottom... Praat picture: Text left Far Praat picture: Text right Praat picture: Text top Praat picture: Text bottom Units 0.1 Distance Write numbers Draw ticks Draw dotted lines Marks left/right/top/bottom every... Praat picture: Marks left every... Praat picture: Marks right every... Praat picture: Marks bottom every... Praat picture: Marks top every... 6 Number of marks `Number of marks' must be at least 2. Marks left/right/top/bottom... Praat picture: Marks left Praat picture: Marks right Praat picture: Marks bottom Praat picture: Marks top 3 Marks per decade Logarithmic marks left/right/top/bottom... Praat picture: Logarithmic marks left Praat picture: Logarithmic marks right Praat picture: Logarithmic marks bottom Praat picture: Logarithmic marks top Position Write number Draw tick Draw dotted line Draw text: One mark left/right/top/bottom... Praat picture: One mark left `Position' must be between %.15g and %.15g. Praat picture: One mark right Praat picture: One mark top Praat picture: One mark bottom One logarithmic mark left/right/top/bottom... Praat picture: One logarithmic mark left Praat picture: One logarithmic mark right Praat picture: One logarithmic mark top Praat picture: One logarithmic mark bottom Compute horizontal distance in world coordinates 10.0 Distance (mm) %.17g Compute horizontal distance in millimetres Distance (wc) %.17g mm Compute vertical distance in world coordinates Compute vertical distance in millimetres Text width in world coordinates Hello world Text width in millimetres PostScript text width in world coordinates Phonetic font XIPA SILIPA PostScript text width in millimetres Picture window Special symbols Text styles Phonetic symbols praat_picture.c p == praat_picture Select inner viewport... %g %g %g %g Select outer viewport... %g %g %g %g File Edit Margins World Select Pen Help %s picture Picture picture Read from praat picture file... Read from old praat picture file... Read from old Windows praat picture file... Write to praat picture file... Write to Windows metafile... Copy to clipboard -- print -- PostScript settings... Write to EPS file... Write to fontless EPS file (XIPA)... Write to fontless EPS file (SILIPA)... Print... Undo -- erase -- Erase all Draw inner box -- text -- Text left... Text right... Text top... Text bottom... -- marks every -- Marks left every... Marks right every... Marks bottom every... Marks top every... -- one mark -- One mark left... One mark right... One mark bottom... One mark top... -- marks -- Marks Marks left... Marks right... Marks bottom... Marks top... Logarithmic marks Logarithmic marks left... Logarithmic marks right... Logarithmic marks bottom... Logarithmic marks top... One logarithmic mark One logarithmic mark left... One logarithmic mark right... One logarithmic mark bottom... One logarithmic mark top... -- axes -- Text special... -- line -- Draw line... Draw arrow... Draw two-way arrow... -- function -- Draw function... -- rectangle -- Draw rectangle... Paint rectangle... Draw rounded rectangle... Paint rounded rectangle... -- arc -- Draw arc... Draw ellipse... Paint ellipse... Draw circle... Paint circle... Draw circle (mm)... Paint circle (mm)... Measure Horizontal mm to wc... Horizontal wc to mm... Vertical mm to wc... Vertical wc to mm... -- text measure -- Text width (wc)... Text width (mm)... PostScript text width (wc)... PostScript text width (mm)... Mouse selects inner viewport Mouse selects outer viewport -- select -- Viewport... -- viewport drawing -- Plain line Dotted line Dashed line -- line width -- Line width... -- colour -- Black White Red Green Blue Yellow Cyan Magenta Maroon Lime Navy Teal Purple Olive Silver Grey 12 14 18 24 Font size... -- font --- New Century Schoolbook Palatino Picture window help About special symbols About text styles -- manual -- Search %s manual... scrolledWindow drawingArea Picture.font Picture.fontSize Picture.mouseSelectsInnerViewport %s %s Object "%s" does not exist. select all plus minus echo %s clearinfo print printtab printline %s fappendinfo a unix Unix command "%s" returned error status; if you want to ignore this, use `unix_nocheck' instead of `unix'. unix_nocheck system System command "%s" returned error status; if you want to ignore this, use `system_nocheck' instead of `system'. system_nocheck nowarn noprogress nocheck pause You interrupted the script. execute editor Editor "%s" does not exist. No editor specified. endeditor sendpraat Missing program name after `sendpraat'. Missing command after `sendpraat'. %s Message to %s not completed. sendsocket Missing host name after `sendsocket'. Missing command after `sendsocket'. filedelete Missing file name after `filedelete'. fileappend Missing file name after `fileappend'. getinfostring Command "getinfostring" no longer supported. Consult scripting tutorial or the author. getinfonumber Command "getinfonumber" no longer supported. Consult scripting tutorial or the author. getnameofselected Command "getnameofselected" no longer supported. Instead use things like: name$ = selected$ ("Sound") getidofselected Command "getidofselected" no longer supported. Instead use things like: id = selected ("Sound") getnumberofselected Command "getnumberofselected" no longer supported. Instead use things like: n = numberOfSelected ("Sound") getnumber Command "getnumber" no longer supported. Instead use things like: "variable = Menu command". getstring Command "getstring" no longer supported. Instead use things like: "variable$ = Menu command". let Command "let" no longer supported. Instead use things like: "variable = numeric-formula" or "variable$ = string-formula". proc Command "proc" no longer supported. Instead use "procedure", and distinguish between numeric variables and string variables. copy Command "copy x y" no longer supported. Instead use normal assignments, i.e. y = x. Unknown command: %s ... ARGS Command "ARGS" no longer supported. Instead use "form" and "endform". Command "%s" not recognized. Probable cause: you are trying to use a variable name that starts with a capital. Command "%s" not available for current selection. %s > %s: command "%s" not executed. Script "%s" not completed. Script not completed. $file Praat: run script PraatShell.batchSessions PraatShell.interactiveSessions PraatShell.dateOfFirstSession PraatShell.memory Currently allocated: ) (objects in list: Things: Arrays: bytes) ( History of this session: Allocation: Deallocation: until today: History of all sessions from batch sessions: Interactive sessions: bytes Total memory use: X ? A 0A A 0A 0A A A 0A A `A @ A @ (A,;AHAHA,;AHA,;A,@HAz A^AJ@!A A PAnAu:-A A `A 0A A A 0A x@ A @ A @ &APrinter.paperSize Printer.allowDirectPostScript Printer.spots Printer.fontChoiceStrategy Printer.epsFilesHavePreview /PraatPictureSaveObject save def initmatrix initclip PraatPictureSaveObject restore Allow direct PostScript Grey resolution Font choice strategy PostScript settings... PostScript settings Finest Photocopyable Automatic Linotype Monotype PS Monotype Cannot initialize printer. Cannot print from a script on this computer. Praatjes Cannot open printer. Cannot print page. :S n lj n Resource : w %s: %d %ld %u %lu %c %.9g %s [>S `n lj n Script BKS n n hn Script untitled script [ ] \"l \"r (modified) No text selected. Add to fixed menu... Add to menu ? Window File Menu Do it... Command After command 0 Depth Script file: (please save your script first) Add to fixed menu Objects Picture New Add to dynamic menu... Add to dynamic menu Sound Class 1 Number 1 Class 2 Number 2 Class 3 Number 3 No history. ScriptEditor Scripting Scripting examples Praat script Formulas History mechanism Initialization script Add to menu... -- close -- -- history -- Edit Clear history Paste history About ScriptEditor Help Scripting tutorial Formulas tutorial -- help history -- The History mechanism Initialization scripts -- help add -- Adding to a fixed menu Adding to a dynamic menu Run Run selection Cannot send to socket because the host-name-and-port string is too long. Cannot send to socket because a colon is missing. Host name and port should be in the format "hostName:port". Cannot send to socket because the socket library (WINSOCK.DLL) is not available, too old, or otherwise unusable. Cannot send to socket because the hostname "%s" is invalid. Cannot send to socket because the host "%s" is unknown. Cannot send to socket because the socket cannot be created. Cannot send to socket because the connection cannot be made. Data not sent to socket. dn dn j n qn qn j n YRS dn lj Իn RS qn lj tn number string Trying to read "%s". SimpleInt SimpleShort SimpleLong SimpleFloat SimpleDouble SimpleString lp -c %s Site.printCommand aS bn 'j n , modified (untitled%s) (modified) File \"l%s\"r%s * %s(untitled) %s%s Open Save info.txt dirtyOpenDialog Discard & Open Save & Open Save changes? Text changed dirtyNewDialog Discard & New Save & New Save as... File dirtyCloseDialog Discard & Close Save & Close TextEditor.c left <= strlen (text) right <= strlen (text) The cursor is on line %ld. The selection is on line %ld. The selection runs from line %ld to line %ld. Go to line 1 Line Text window: Font size 12 Font size (points) Font size New Open... Clear -- save -- -- close -- Undo Edit Redo -- cut copy paste -- Cut Copy Paste Erase Search Where am I? Go to line... text TextEditor TextEditor.fontSize bS n n <no name> Object: %s %.200s Date: %s Thing (Thing_new:) Out of memory. (Thing_recognizeClassesByName:) Too many (1001) readable classes. (Thing_classFromClassName:) Class "%s" not recognized. (Thing_newFromClassName:) Thing not created. (Thing_member:) Found NULL object. (_Thing_check:) NULL object passed to a function in file %.100s at line %d. (_Thing_check:) Object of wrong class (%.50s) passed to a function in file %.100s at line %d. Thing.c my methods == thy methods 3fS Dn n X n gS Ln n n ?n n n n n n n n n n n n n n n n guS -n n n UiField UiOption Ui.c my type == UI_RADIO || my type == UI_OPTIONMENU %d "%s" black white red green blue yellow cyan magenta maroon lime navy teal purple olive silver grey %s .0 `%s' must be greater than 0.0. %ld `%s' must be a positive whole number. No option chosen for `%s'. No items selected. More than one item selected. Argument `%s' empty. `%s' must be greater than 0. Empty argument for toggle button. Field `%s' cannot have the value "%s". %s %ld "%s" yes no %.6g black UiForm Cannot execute dialog `%s'. Please correct dialog `%s' or cancel. Please You could Selection changed! Please change the selection in the object list, or click Cancel in the window `%s'. Please change something in the window `%s', or click Cancel in that window. right left WM_DELETE_WINDOW UiLabelledRange_textLeft UiLabelledRange_textRight UiLabelledText_text UiText_text UiOptionMenu choice UiEnum_list UiList_list Help Standards Cancel Apply OK Missing matching quote. Wrong argument "%s". Wrong field in dialog "%s". %.6g Cannot find field "%s" in form. The script may have changed while the form was open. Please click Cancel in the form and try again. Cannot find a real value in field "%s" in the form. The script may have changed while the form was open. Please click Cancel in the form and try again. Cannot find an integer value in field "%s" in the form. The script may have changed while the form was open. Please click Cancel in the form and try again. Cannot find a string in field "%s" in the form. The script may have changed while the form was open. Please click Cancel in the form and try again. S n n , n nS n n , n S 8n n 4 n UiFile UiInfile File "%s" not finished. %s UiOutfile Dialog `%s' cancelled. pn n n n n n 2n Pn zn n n n n n !n 9n Kn tn n n n n n n )n @n Rn gn n n n n n n n n $n ?n [n un n n n n n n n 3n In _n on n n n n n n n n n 7n Jn bn un n n n n n n n n $n 5n En Un pn n n n n n n n n 1n Hn [n jn yn n n n n n n n n n (n 7n Fn Zn mn }n n n n n n n n n n n 1n Kn cn yn n n n n n n n n n n -n =n Mn ]n mn }n n n n n n n n n n n -n En _n tn n n n n n n n $n :n On jn n n n n n n n n #n ;n Pn en |n n n n n n n n .n Kn an yn n n n n n n n $n <n Nn _n rn n n n n n n n n n 4n Hn Xn in ~n n n n n n n n $n 6n Fn Zn jn n n n n n n o o 5 o Q o f o v o o o o o o o o +o ?o To ho o o o o o o o #o <o Oo do }o o o o o o o o *o ?o To no o o o o o o o o #o 3o Ho Vo eo o o o o o Oo o o o Wo o o o _o o o %o go o o - o o o o o 5 o w o o o = o o o o E o o o o M o o o o Uo o o o ]o o o #o eo o o +o mo o o 3o uo o o ;o }o o o Co o o o Ko o o o So o o o [o o o !o co o o )o ko o o 1o so o o 9o 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o Go o o o Oo o o o Wo o o o _o o o %o go o o -o oo o o 5o wo o o =o o o o Eo o o o Mo o o o Uo o o o ]o o o #o eo o o +o mo o o 3o uo o o ;o }o o o Co o o o Ko o o o So o o o [o o o !o co o o )o ko o o 1o so o o 9o {o o o Ao o o o Io o o o Qo o o o Yo o o o ao o o 'o io o o /o qo o o 7o yo o o ?o o o o Go o o o Oo o o o Wo o o o _o o o %o go o o -o oo o o 5o wo o o =o o o o Eo o o o Mo o o o Uo o o o ]o o o #o eo o o +o mo o o 3o uo o o ;o }o o o Co o o o Ko o o o So o o o [o o o !o co o o ) p k p p p 1p sp p p 9p {p p p Ap p p p Ip p p p Qp p p p Yp p p p ap p p 'p ip p p / p q p p p 7 p y p p p ? p p p p G p p p p O p p p p Wp p p p _p p p %p gp p p -p op p p 5p wp p p =p p p p Ep p p p Mp p p p Up p p p ]p p p #p ep p p +p mp p p 3p up p p ;p }p p p C p p p p K p p p p S p p p p [ p p p ! p c p p p )!p k!p !p !p 1"p s"p "p "p 9#p {#p #p #p A$p $p $p %p I%p %p %p &p Q&p &p &p 'p Y'p 'p 'p (p a(p (p (p ')p i)p )p )p /*p q*p *p *p 7+p y+p +p +p ?,p ,p ,p -p G-p -p -p .p O.p .p .p /p W/p /p /p 0p _0p 0p 0p %1p g1p 1p 1p -2p o2p 2p 2p 53p w3p 3p 3p =4p 4p 4p 5p E5p 5p 5p 6p M6p 6p 6p 7p U7p 7p 7p 8p ]8p 8p 8p #9p e9p 9p 9p +:p m:p :p :p 3;p u;p ;p ;p ;<p }<p <p =p C=p =p =p >p K>p >p >p ?p S?p ?p ?p @p [@p @p @p !Ap cAp Ap Ap )Bp kBp Bp Bp 1Cp sCp Cp Cp 9Dp {Dp Dp Dp AEp Ep Ep Fp IFp Fp Fp Gp QGp Gp Gp Hp YHp Hp Hp Ip aIp Ip Ip 'Jp iJp Jp Jp /Kp qKp Kp Kp 7Lp yLp Lp Lp ?Mp Mp Mp Np GNp Np Np Op OOp Op Op Pp WPp Pp Pp Qp _Qp Qp Qp %Rp gRp Rp Rp -Sp oSp Sp Sp 5Tp wTp Tp Tp =Up Up Up Vp EVp Vp Vp Wp MWp Wp Wp Xp UXp Xp Xp Yp ]Yp Yp Yp #Zp eZp Zp Zp +[p m[p [p [p 3\p u\p \p \p ;]p }]p ]p ^p C^p ^p ^p _p K_p _p _p `p S`p `p `p ap [ap ap ap !bp cbp bp bp )cp kcp cp cp 1dp sdp dp dp 9ep {ep ep ep Afp fp fp gp Igp gp gp hp Qhp hp hp ip Yip ip ip jp ajp jp jp 'kp ikp kp kp /lp qlp lp lp 7mp ymp mp mp ?np np np op Gop op op pp Opp pp pp qp Wqp qp qp rp _rp rp rp %sp gsp sp sp -tp otp tp tp 5up wup up up =vp vp vp wp Ewp wp wp xp Mxp xp xp yp Uyp yp yp zp ]zp zp zp #{p e{p {p {p +|p m|p |p |p 3}p u}p }p }p ;~p }~p ~p p Cp p p p Kp p πp p Sp p ׁp p [p p ߂p !p cp p p )p kp p p 1p sp p p 9p {p p p Ap p Ňp p Ip p ͈p p Qp p Չp p Yp p ݊p p ap p p 'p ip p p /p qp p p 7p yp p p ?p p Ïp p Gp p ːp p Op p ӑp p Wp p ےp p _p p p %p gp p p -p op p p 5p wp p p =p p p p Ep p ɘp p Mp p љp p Up p ٚp p ]p p p #p ep p p +p mp p p 3p up p p ;p }p p p Cp p Ǡp p Kp p ϡp p Sp p עp p [p p ߣp !p cp p p )p kp p p 1p sp p p 9p {p p p Ap p Ũp p Ip p ͩp p Qp p ժp p Yp p ݫp p ap p p 'p ip p p /p qp p p 7p yp p p ?p p ðp p Gp p ˱p p Op p Ӳp p Wp p ۳p p _p p p %p gp p p -p op p p 5p wp p p =p p p p Ep p ɹp p Mp p Ѻp p Up p ٻp p ]p p p #p ep p p +p mp p p 3p up p p ;p }p p p Cp p p p Kp p p p Sp p p p [p p p !p cp p p )p kp p p 1p sp p p 9p {p p p Ap p p p Ip p p p Qp p p p Yp p p p ap p p 'p ip p p /p qp p p 7p yp p p ?p p p p Gp p p p Op p p p Wp p p p _p p p %p gp p p -p op p p 5p wp p p =p p p p Ep p p p Mp p p p Up p p p ]p p p #p ep p p +p mp p p 3p up p p ;p }p p p Cp p p p Kp p p p Sp p p p [p p p !p cp p p )p kp p p 1p sp p p 9p {p p p Ap p p p p p p p p p p p p % %!PS-AdobeFont-1.0: TeX-xipa10 001.001 % % Filtered by type1fix.pl 0.06 % %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see-copyright-of-original-TeX-font) def /FamilyName (TeX-xipa10) def /FullName (TeX-xipa10-Praat-Regular) def /ItalicAngle 0 def /Notice (converted-after-April-2001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-xipa10-Praat-Regular def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /grave put dup 1 /acute put dup 2 /circumflex put dup 3 /tilde put dup 4 /dieresis put dup 5 /hungarumlaut put dup 6 /ring put dup 7 /caron put dup 8 /breve put dup 9 /macron put dup 10 /dotaccent put dup 11 /cedilla put dup 12 /ogonek put dup 13 /quotesinglbase put dup 14 /guilsinglleft put dup 15 /guilsinglright put dup 16 /quotedblleft put dup 17 /quotedblright put dup 18 /quotedblbase put dup 19 /guillemotleft put dup 20 /guillemotright put dup 21 /endash put dup 22 /emdash put dup 23 /cwm put dup 24 /perthousand put dup 25 /dotlessi put dup 26 /dotlessj put dup 27 /ff put dup 28 /fi put dup 29 /fl put dup 30 /ffi put dup 31 /ffl put dup 32 /space put dup 33 /hungarumlaut put dup 34 /dotlessi put dup 35 /macron put dup 36 /grave put dup 37 /quotesinglbase put dup 38 /caron put dup 39 /quoteright put dup 40 /breve put dup 41 /tilde put dup 42 /ring put dup 43 /ff put dup 44 /comma put dup 45 /dieresisunder put dup 46 /period put dup 47 /P put dup 48 /tildeunder put dup 49 /ffi put dup 50 /ffl put dup 51 /fi put dup 52 /fl put dup 53 /quotedblright put dup 54 /guillemotright put dup 55 /endash put dup 56 /ringunder put dup 57 /quotedblleft put dup 58 /l put dup 59 /Idieresis put dup 60 /n put dup 61 /Lcaron put dup 62 /semicolon put dup 63 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Q@ Y@ @ R@ @@ Q??{Gz?ffffff?Q ? I@ Y@ |@ ? >@ ? I@ ?? C:\WINDOWS\DESKTOP\Pitch Log.txt Time 'time:6' seconds, pitch 'f0:2' Hertz C:\WINDOWS\DESKTOP\Formant Log.txt 't1:4''tab$''t2:4''tab$''f1:0''tab$''f2:0''tab$''f3:0' C:\WINDOWS\DESKTOP\Log script 3.praat C:\WINDOWS\DESKTOP\Log script 4.praat ? ? @ @ ? @ Y@ I@ @ @ Q??{Gz?ffffff?Q ? q= ףp? Q ? @ ?쿶lq lq lq lq lq lq Zwq nxq zxq xq T}q Z}q b}q j}q FunctionEditor.longestAnalysis FunctionEditor.timeStepStrategy FunctionEditor.fixedTimeStep FunctionEditor.numberOfTimeStepsPerView FunctionEditor.spectrogram.show FunctionEditor.spectrogram.timeSteps2 FunctionEditor.spectrogram.frequencySteps2 FunctionEditor.spectrogram.viewFrom2 FunctionEditor.spectrogram.viewTo2 FunctionEditor.spectrogram.method2 FunctionEditor.spectrogram.windowLength2 FunctionEditor.spectrogram.windowShape2 FunctionEditor.spectrogram.maximum2 FunctionEditor.spectrogram.autoscaling2 FunctionEditor.spectrogram.dynamicRange2 FunctionEditor.spectrogram.preemphasis2 FunctionEditor.spectrogram.dynamicCompression2 FunctionEditor.pitch.show FunctionEditor.pitch.floor FunctionEditor.pitch.ceiling FunctionEditor.pitch.unit FunctionEditor.pitch.viewFrom FunctionEditor.pitch.viewTo FunctionEditor.pitch.method FunctionEditor.pitch.veryAccurate FunctionEditor.pitch.maximumNumberOfCandidates FunctionEditor.pitch.silenceThreshold FunctionEditor.pitch.voicingThreshold FunctionEditor.pitch.octaveCost FunctionEditor.pitch.octaveJumpCost FunctionEditor.pitch.voicedUnvoicedCost FunctionEditor.intensity.show FunctionEditor.intensity.viewFrom FunctionEditor.intensity.viewTo FunctionEditor.intensity.averagingMethod FunctionEditor.intensity.subtractMeanPressure FunctionEditor.formant.show FunctionEditor.formant.maximumFormant FunctionEditor.formant.numberOfPoles FunctionEditor.formant.windowLength FunctionEditor.formant.dynamicRange FunctionEditor.formant.dotSize FunctionEditor.formant.method FunctionEditor.formant.preemphasisFrom FunctionEditor.pulses.show FunctionEditor.pulses.maximumPeriodFactor FunctionEditor.pulses.maximumAmplitudeFactor FunctionEditor.log1.toInfoWindow FunctionEditor.log1.toLogFile FunctionEditor.log1.fileName FunctionEditor.log1.format FunctionEditor.log2.toInfoWindow FunctionEditor.log2.toLogFile FunctionEditor.log2.fileName FunctionEditor.log2.format FunctionEditor.logScript3 FunctionEditor.logScript4 CURSOR SELECTION at CURSOR in SELECTION Window too long to show analyses. Zoom in to at most %s seconds or set the "longest analysis" to at least %s seconds. Make a selection first. Command ambiguous: a part of the selection is out of view. Either zoom or re-select. Show analyses Show spectrogram Show pitch Show intensity Show formants Show pulses 5.0 Longest analysis (s) Longest analysis Time step settings... Time step settings Time step strategy Automatic Fixed View-dependent If the time step strategy is "fixed": 0.01 Fixed time step (s) If the time step strategy is "view-dependent": 100 Number of time steps per view Fixed time step Intro 3.2. Configuring the spectrogram Spectrogram settings 0.0 left View range (Hz) 5000.0 right View range (Hz) 0.005 Window length (s) 50.0 Dynamic range (dB) note1 note2 left View range right View range Window length Dynamic range Warning: you have non-standard "advanced settings". (all of your "advanced settings" have their standard values) Warning: you have a non-standard "time step strategy". (your "time step strategy" has its standard value: automatic) Advanced spectrogram settings... Advanced spectrogram settings Time and frequency resolutions: 1000 Number of time steps 250 Number of frequency steps Spectrogram analysis settings: Method Fourier Window shape Spectrogram view settings: Autoscaling 100.0 Maximum (dB/Hz) 6.0 Pre-emphasis (dB/oct) Dynamic compression (0-1) Maximum Pre-emphasis Dynamic compression No spectrogram is visible. First choose "Show spectrogram" from the Spectrum menu. No spectrogram available (out of memory?). slice Hertz Click inside the spectrogram first. Hz) seconds and frequency = Pa2/Hz (at time = Intro 4.2. Configuring the pitch contour Pitch settings 75.0 left Pitch range (Hz) 500.0 right Pitch range (Hz) Unit Optimize for Intonation (AC method) Voice analysis (CC method) left Pitch range right Pitch range Warning: you have some non-standard "advanced settings". Advanced pitch settings... Advanced pitch settings Make view range different from analysis range: 0.0 (= auto) left View range (units) right View range (units) Analysis settings: Very accurate 15 Max. number of candidates 0.03 Silence threshold 0.45 Voicing threshold Octave cost 0.35 Octave-jump cost 0.14 Voiced / unvoiced cost Maximum number of candidates must be greater than 1. No pitch contour is visible. First choose "Show pitch" from the Pitch menu. No pitch contour available (out of memory?). Time_s F0_ %s %s (interpolated pitch at CURSOR) %s %s (mean pitch %s) %s %s (minimum pitch %s) %s %s (maximum pitch %s) Intro 6.2. Configuring the intensity contour Intensity settings left View range (dB) right View range (dB) Averaging method median mean energy mean sones mean dB Subtract mean pressure Note: the pitch floor is taken from the pitch settings. No intensity contour is visible. First choose "Show intensity" from the Intensity menu. No intensity contour available (out of memory?). Time_s Intensity_dB mean-energy mean-sones mean-dB %s dB (intensity at CURSOR) %s dB (%s intensity %s) Intro 5.2. Configuring the formant contours Formant settings 5500.0 Maximum formant (Hz) Number of formants 0.025 30.0 1.0 Dot size (mm) Maximum formant Dot size Advanced formant settings... Advanced formant settings Burg Pre-emphasis from (Hz) Pre-emphasis from No formant contour is visible. First choose "Show formants" from the Formant menu. No formant contour available (out of memory?). Time_s F1_Hz F2_Hz F3_Hz F4_Hz %s Hertz (nearest F%d to CURSOR) %s Hertz (mean F%d %s) %s Hertz (nearest B%d to CURSOR) %s Hertz (B%d in centre of %s) Get formant 5 Formant number Get bandwidth Advanced pulses settings... Advanced pulses settings 1.3 Maximum period factor 1.6 Maximum amplitude factor No pulses are visible. First choose "Show pulses" from the Pulses menu. No pulses available (out of memory?). Selection too small (or out of memory). -- Date: -- Voice report for WARNING: some of the following measurements may be imprecise. For more precision, go to "Pitch settings" and choose "Optimize for voice analysis". Time range of Time_s No pitch contour is visible. First choose "Show pitch" from the View menu. Empty selection. Selection is voiceless. (.5) (\muE) (\muS) (\mu) To see the analyses, zoom in to at most %s seconds, or raise the "longest analysis" setting in the View menu. %.5g %s %.4g %s (Cannot show pitch contour. Zoom out or change bottom of pitch range in pitch settings.) %.4g dB%s %.4g dB %.4g Hz %.5g Hz Log files Log settings Write log 1 to Log file only Info window only Log file and Info window Log file 1: C:\WINDOWS\DESKTOP\Pitch Log.txt Log file 1 Log 1 format: Time 'time:6' seconds, pitch 'f0:2' Hertz Log 1 format Write log 2 to Log file 2: C:\WINDOWS\DESKTOP\Formant Log.txt Log file 2 Log 2 format: 't1:4''tab$''t2:4''tab$''f1:0''tab$''f2:0''tab$''f3:0' Log 2 format Log script 3: C:\WINDOWS\DESKTOP\Log script 3.praat Log script 3 Log script 4: C:\WINDOWS\DESKTOP\Log script 4.praat Log script 4 time t1 t2 dur freq tab$ editor$ f0 No formant contour is visible. First choose "Show formant" from the View menu. intensity No intensity contour is visible. First choose "Show intensity" from the View menu. %.*f %.17g %s Analysis window: View Show analyses... -- sound analysis -- -- query log -- Query Log settings... Delete log file 1 Delete log file 2 Log 1 Log 2 Log script 3 (...) Log script 4 (...) Spectrum Spectrogram settings... Extract visible spectrogram View spectral slice -- query spectrogram -- Query: Get frequency at frequency cursor Get spectral power at cursor cross Pitch Pitch settings... Extract visible pitch contour -- query pitch -- Pitch listing Get pitch Get minimum pitch Get maximum pitch -- select pitch -- Select: Move cursor to minimum pitch Move cursor to maximum pitch Intensity Intensity settings... Extract visible intensity contour -- query intensity -- Intensity listing Get intensity Formant Formant settings... Extract visible formant contour -- query formants -- Formant listing Get first formant Get first bandwidth Get second formant Get second bandwidth Get third formant Get third bandwidth Get fourth formant Get fourth bandwidth Get formant... Get bandwidth... Pulses Extract visible pulses -- query pulses -- Voice report Pulse listing q q q q q @ q ̨i q 0 q 8 q < &q lq 6q T q i @ ̆q ?nCoefficients c samplingFrequency maxnCoefficients (empty) frame []: %s frame [%ld]: Trying to read "%s". 0 my nCoefficients Cepstrumc frame Cepstrumc_Frame my nx Cepstrumc info Name: %s Time domain: from %.8g to %.8g seconds. number of coefficients: %ld Number of frames: %ld Time step: %.8g seconds First frame at: %.8g seconds Cepstrumc_difference: Cepstrumc orders must be equal. Cepstrumc_difference: time window for regression coefficients too small. Cepstrumc_difference: #frames used for regression coefficients %ld Calculate distances: frame %ld from %ld ? @"T q xq H ܉q -DT! @ ?MFCC MFCC.c lifter > 0 @q Uq Xq q Ѝq H Ѝq ̨i Zq 0 _q 8 dq @ Ӎq D ٍq q q T Ѝq i H xq ?numberOfCoefficients c0 c fmin fmax maximumNumberOfCoefficients (empty) frame []: %s frame [%ld]: Trying to read "%s". my numberOfCoefficients CC frame CC_Frame my nx CC info Name: %s Time domain: from %.8g to %.8g seconds. Number of frames: %ld Time step: %.8g seconds First frame at: %.8g seconds number of coefficients: %ld minimum frequency %.8g maximum frequency %.8g Time (s) Coefficients CC.c startframe <= endframe ( @ @-DT! @ ? @ 8@ ? |= 4 Y@? T@ @Sound_to_BarkFilter: The combination of filter parameters is not valid. BarkFilter analysis BarkFilter analysis: frame %ld from %ld Sound_to_BarkFilter: analysis results of %ld frame(s) out of %ld will be suspect. MelFilters analysis Sound to MFCC: frame %ld out of %ld Sound_to_MelFilters: analysis results of %ld frame(s) out of %ld will be suspect. Sound_and_FilterBank.c bw > 0 Sound_and_Pitch_to_FormantFilters: the domain of the Sound is not included in the domain of the Pitch. Sound_and_Pitch_to_FormantFilters: pitch values undefined. Bandwith fixed to 100 Hz. Sound_and_Pitch_to_FormantFilters: frame %ld out of %ld ? MelFilter_and_MFCC.c numberOfCoefficients > 0 MFCC_to_MelFilter: the position of the first filter, the distance between the filters, and, the maximum do not result in a positive number of filters. MFCC_to_MelFilter: coefficients must be in interval [%d,%d]. TableOfReal_matrixColumnsIntoRows: Column indices out of range. TableOfReal_matrixColumnsIntoRows: Row index out of range. TableOfReal_matrixColumnsIntoRows: not enough rows available. TableOfReal_matrixColumnsIntoRows: not enough columns available. <@ 8@Q ?J +? 1@ @ @ $@ ?|= 4@Uk@ ?8T q i ` `q 9T q `q ` q @T q `q ` q DT q `q ` q Frequency (Hz) Frequency (Bark) Frequency (mel) Frequency (undefined) &s: filter numbers must be in range [%d, %d] &s: Frequencies must be positive. FilterBank BarkFilter FilterBank_drawFrequencyScales %s: Frequencies must be >= 0. BarkFilter_drawSekeyHansonFilterFunctions Amplitude (dB) Amplitude MelFilter MelFilter_drawFilterFunctions FormantFilter FormantFilter_drawFilterFunctions %s: Bandwidth must be greater than zero. Component too large. +? ?CCs_to_DTW: CC orders must be equal. CCs_to_DTW: Time window for regression coefficients is too small. CCs_to_DTW: %ld frames used for regression coefficients. CCs_to_DTW Calculate distances: frame %ld from %ld ?YRT q i ` (q @ ?Cepstrum Quefrency Amplitude ? @ @XT q xq H 0q LFCC @-DT!@ ?-DT! @ ? (@? @ffffff?Spectrum_unwrapPhases: dimension of Spectrum is not (power of 2 - 1). Phase unwrapping %ld phases from %ld unwrapped. Spectrum_unwrapPhases: %d spectral values calculated. (iphase = %d). Spectrum_drawPhases: Spectrum has not been unwrapped. Spectra_multiply: Dimensions of both spectra do not conform. eT q i q Proximity (fT ̞q q ,q Distance (q q q xi (q Bq q q xi Nq Sq Yq `q dq jq (q q q xi Nq Sq Yq `q dq nq wq q q q j q q q q q q q j q q q .q Dq ؞q Mq Dq ؞q ӯq ( q 0 q 8 nq < bq \q nq )q @ Iq D pq H q @q Yq L cq P kq T uq X }q \ q ` q d q h q l ưq p Ӱq t ްq x q | q q q q q q %q 1q :q Eq Nq aq vq q Dq ؞q q Dq ؞q q q ȱq wq ʳq q ֳq q q q q q q +q 3q q 9q q Aq q Kq q Vq q xi T q lj q q aq qq |q q q ? ? +eG?ET q lj q name Trying to read "%s". visibleText left right bottom top label key stimulus response goodness numberOfTrials stimuliAreSounds stimulusFileNameHead stimulusFileNameTail stimulusInitialSilenceDuration stimulusMedialSilenceDuration numberOfDifferentStimuli numberOfReplicationsPerStimulus breakAfterEvery startText runText pauseText endText maximumNumberOfReplays replay_left replay_right replay_bottom replay_top replay_label replay_key ok_left ok_right ok_bottom ok_top ok_label ok_key oops_left oops_right oops_bottom oops_top oops_label oops_key responsesAreSounds responseFileNameHead responseFileNameTail responseInitialSilenceDuration responseMedialSilenceDuration numberOfDifferentResponses numberOfGoodnessCategories (empty) result []: %s result [%ld]: stimulusCarrierBefore: stimulusCarrierAfter: stimulus []: %s stimulus [%ld]: randomize responseCarrierBefore: responseCarrierAfter: response []: %s response [%ld]: goodness []: %s goodness [%ld]: sound Sound ResultsMFC result TrialMFC my numberOfTrials ExperimentMFC stimulusCarrierBefore SoundMFC stimulusCarrierAfter StimulusMFC my numberOfDifferentStimuli Experiment_RANDOMIZE responseCarrierBefore responseCarrierAfter ResponseMFC my numberOfDifferentResponses GoodnessMFC my numberOfGoodnessCategories samplePeriod pausing trial stimuli responses goodnesses playBuffer CyclicNonRandom PermuteAll PermuteBalanced PermuteBalancedNoDoublets WithReplacement %s%s%s No sound in file "%s". The sound in file "%s" has a different sampling frequency than some other sound. (ExperimentMFC_extractResults:) Experiment not finished. No shared stimuli. (ResultsMFC_removeUnsharedStimuli:) Not performed. subject @ ?? ? мT /q 'j صq Cannot start experiment. %s %ld / %ld RunnerMFC.c experiment -> trial >= 1 && experiment -> trial <= experiment -> numberOfTrials experiment -> trial >= 2 && experiment -> trial <= experiment -> numberOfTrials experiment -> ok_right <= experiment -> ok_left drawingArea RunnerMFC < ?? < @ @-DT! @ ? ?0123456789 {.*+?[(|)^<>$ q fedcbaFEDCBA9876543210 abefnrtv()-[]<>{}.\|^$*+?& ()-[]<>{}.\|^$*+?& _ NULL argument, `CompileRE' internal error #1, `CompileRE' regexp > %lu bytes out of memory in `CompileRE' number of ()'s > %d missing right parenthesis ')' missing left parenthesis '(' junk on end min operand of {%lu%c,???} > 65535 max operand of {%lu,%lu%c} > 65535 {0} is an invalid range {0,0} is an invalid range {%lu,0} is an invalid range {,0} is an invalid range {m,n} specification missing right '}' {%lu,%lu} is an invalid range number of {m,n} constructs > %d {%lu,%lu} operand could be empty %c operand could be empty internal error #2, `piece' nested quantifiers, {m,n}%c nested quantifiers, %c%c invalid grouping syntax, "(?%c...)" internal error #3, `atom' %c follows nothing {m,n} follows nothing \%c is not allowed as range operand \%c is an invalid char class escape sequence invalid [] range \%c not allowed as range operand missing right ']' \%c is an invalid escape sequence internal error #4, `atom' ByYdDlLsSwW internal error #5 `shortcut_escape' internal error #6 `shortcut_escape' internal error #7 `shortcut_escape' internal error #8 `shortcut_escape' \00 is an invalid octal escape \%c0 is an invalid hexadecimal escape \%d is an illegal back reference NULL parameter to `ExecRE' corrupted program out of memory in `ExecRE' internal error #9 `init_ansi_classes' memory corruption, `match' corrupted pointers, `match' internal error #10 `greedy' NULL parm to `SubstituteRE' damaged regexp passed to `SubstituteRE' damaged match string in `SubstituteRE' Internal error processing regular expression (%s) N\s{O}C\s{ODA} P\s{ARSE} pat pa Y@ 4@ T@*G\s{ESTURE} *R\s{EPLACE} (n, m) *R\s{EPLACE} (t, p) an+pa anpa ampa at+ma atma apma @q Bq Dq Hq Lq Pq $@ Y@ i e \sw \ic \ep a %st%s *[rtr / hi] *[atr / lo] P\s{ARSE} (rtr) P\s{ARSE} (atr) *G\s{ESTURE} (contour) *[rtr / mid] *[rtr / lo] *[atr / mid] *[atr / hi] q q q q $q ,q 0q 4q ;q Bq Fq Jq Sq \q dq lq wq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q X , @ % @ q q q q q q q ? WSP FtNonfinal Iambic Parse FootBin WFL WFR Main-L Main-R AFL AFR Nonfinal Trochaic FtBimor FtBisyl Peripheral MainNonfinal HeadNonfinal *Clash *Lapse WeightByPosition *C\mu L L1 L2 H H1 H2 K K1 K2 J J1 J2 [ ] \-> / ( ) / cv cv: cvc | . OTGrammar_ex_metrics.c my output != NULL ư>q q j q q q q q q U q lj q n t r Trying to read "%s". AffineTransform my n AffineTransform.c n > 0 %d Strings_setString: index must be in range [1, %d]. Strings_extractPart: begin and end must be in interval [1, %d]. Strings_and_Permutation_permuteStrings: The number of strings and the number of elements in the Permutation must be equal. ?ư> @Configuration_AffineTransform.c nr > 0 && nc > 0 t NUMmaximizeCongruence: we cannot rotate a zero matrix. Configuration_and_AffineTransform_to_Configuration: dimensions do not agree. Eigen_and_TableOfReal_project_into %s: Column selection not correct. %s: The number of selected columns to project (%d) must equal the dimension of the eigenvectors (%d). %s: The number of selected columns in the result (%d) cannot exceed the number of eigenvectors (%d). TablesOfReal_to_Eigen: Number of columns must be equal. SSCP_and_Eigen_project: dimensions don't agree. Covariance_and_Eigen_project: dimensions don't agree. ? ?Eigen_and_Matrix_project_into Eigen_and_Matrix.c him != NULL %s: The number of rows in the 'from' Matrix must equal the dimension of the eigenvector. %s: The number of columns in the 'from' and the 'to' Matrix object must be equal. %s: The number of rows in the 'to' Matrix cannot exceed the number of eigenvectors. @ Lq q q %q Mq qq q q q q q q )q ?q Uq kq q q q q pq vq q @ @ Lq q q Lq -q q This is the tutorial about basic statistical techniques in Praat, which work with the @Table object. It assumes that you are familiar with the @Intro. (Under construction..................) \bu @@Logistic regression@ For more sophisticated techniques, see: \bu @@Principal component analysis@ \bu @@Multidimensional scaling@ \bu @@Discriminant analysis@ This page explains how you do logistic regression with Praat. You start by writing a table in a text file. The following example contains natural stimuli (female speaker) with measured F1 and duration values, and the responses of a certain listener who is presented each stimulus 10 times. F1 Dur /ae/ /E/ 764 87 2 8 674 104 3 7 574 126 0 10 566 93 1 9 618 118 1 9 1025 147 10 0 722 117 7 3 696 169 9 1 1024 124 10 0 752 92 6 4 In this table we see 10 different stimuli, each characterized by a certain combination of the independent variables %F1 (first formant in Hertz) and %Dur (duration in milliseconds). The first row of the table means that there was a stimulus with an F1 of 764 Hz and a duration of 87 ms, and that the listener responded to this stimulus 2 times with the response category /\ae/, and the remaining 8 times with the category /\ep/. A table as above can be typed into a text file. The columns can be separated with spaces and/or tab stops. The file can be read into Praat with ##Read Table from table file...#. The command "To logistic regression" will become available in the #Statistics menu. What does it do? Axes... 60 180 900 500 Marks bottom every... 1 30 yes yes no Marks left every... 1 50 yes yes no Text bottom... yes Duration (ms) Text left... yes F1 (Hz) mdur_ae = 135 mdur_ep = 95 sdur = 25 mf1_ae = 780 mf1_ep = 620 sf1 = 60 Draw ellipse... mdur_ae-sdur mdur_ae+sdur mf1_ae-sf1 mf1_ae+sf1 Text... mdur_ae Centre mf1_ae Half /\ae/ Draw ellipse... mdur_ep-sdur mdur_ep+sdur mf1_ep-sf1 mf1_ep+sf1 Text... mdur_ep Centre mf1_ep Half /\ep/ Draw inner box The logistic regression method will find values %\al, %%\be__F1_% and %%\be__dur_% that optimize %\al + %%\be__F1_% %F1__%k_ + %%\be__dur_% %Dur__%k_ = ln (%p__%k_(/\ep/)/%p__%k_(/\ae/)) where %k runs from 1 to 10, and %p__%k_(/\ae/) + %p__%k_(/\ep/) = 1. The optimization criterion is %%maximum likelihood%, i.e. those %\al, %%\be__F1_% and %%\be__dur_% will be chosen that lead to values for %p__%k_(/\ae/) and %p__%k_(/\ep/) that make the observations in the table most likely. Praat will create an object of type #LogisticRegression in the list. When you then click the #Info button, Praat will write the values of %\al (the %intercept), %%\be__F1_% and %%\be__dur_% into the Info window. The number of independent variables does not have to be 2; it can be 1 or more. The number of dependent categories is always 2, and they should always be put in the last two columns of the table. Statistics ppgb Logistic regression q &q &q j q /q 5q q ?q q Rq Rq j q Xq fq q ?q xq }q hj (q ;U &q lj (q <U Rq lj q ? ? $@ @string numberOfColumns (empty) cells []: %s cells [%ld]: label columnHeaders []: %s columnHeaders [%ld]: rows: size rows [%ld]: Trying to read "%s". TableRow cells TableCell my numberOfColumns Table columnHeaders TableColumnHeader rows Ordered Number of rows = %ld Number of columns = %ld (Table_init:) Cannot create cell-less table. Cannot remove the only row. No row %ld. (Table_removeRow:) Not performed. Cannot remove the only column. No column %ld. (Table_removeColumn:) Not performed. Cannot create row %ld. (Table_insertRow:) Not performed. Cannot create column %ld. (Table_insertColumn:) Not performed. Row number %ld out of range. Column number %ld out of range. Table.c icol >= 1 && icol <= my numberOfColumns No row matches criterion. (Table_selectRowsWhereColumn:) Not performed. w ? %s %s rb No columns. The number of elements (%ld) is not a multiple of the number of columns (%ld). (Table_readFromTableFile:) File %s not read. Empty file. Row %ld has wrong number of columns. No rows. (Table_readFromCharacterSeparatedTextFile:) File %s not read. ? @ ? Y@Table: Append column newcolumn Label Table: Append difference column left Columns right Columns diff No such column. Table: Append product column Table: Append quotient column Table: Append sum column Table: Extract rows where column Extract all rows where column... ...is... 0.0 ...the value %s_%ld_%ld Table: Formula... Table: Formula Column label abs (self) formula Table: Get column index %ld Table: Get column label 1 Column number Column number must not be greater than number of columns. %s Table: Get value Row number Row number out of range. Column number out of range. Table Table: Insert column Position Table: Insert row Table: Remove column Table: Remove row %.17g --undefined-- "%.39s" Report correlation (Kendall tau) 0.025 Significance level Correlation between column %s and column %s: Correlation = %s (Kendall's tau-b) Significance from zero = %s (one-tailed) Confidence interval (%f%%): Lower limit = %s (lowest tau that cannot be rejected with p = %f) Upper limit = %s (highest tau that cannot be rejected with p = %f) Report correlation (Pearson r) Correlation between column %s and column %s: Correlation = %s (Pearson's r) Significance from zero = %s (one-tailed) Confidence interval (%f%%): Lower limit = %s (lowest r that cannot be rejected with p = %f) Upper limit = %s (highest r that cannot be rejected with p = %f) Report difference (Student t) Difference between column %s and column %s: Difference = %s Student's t = %s Significance from zero = %s (one-tailed) Confidence interval (%f%%): Lower limit = %s (lowest difference that cannot be rejected with p = %f) Upper limit = %s (highest difference that cannot be rejected with p = %f) Scatter plot (marks) Horizontal column left Horizontal range 0.0 (= auto) right Horizontal range Vertical column left Vertical range right Vertical range 1.0 Mark size (mm) Garnish + Mark string (+xo.) Mark string Mark size Table: Search column Value Set column label Old label New label Table: Set numeric value 1.5 Numeric value Table: Set string value xx String value Table: Sort rows Secondary column (optional) Secondary column Table: Down to TableOfReal Column for row labels Write Table to table file txt Statistics Table help Write to table file... Draw - Scatter plot (mark)... Query - Get number of rows Get number of columns Get column label... Get column index... Search column... -- get value -- Get value... Statistics - Statistics tutorial Report correlation (Pearson r)... Report correlation (Kendall tau)... Report difference (Student t)... To linear regression To logistic regression Modify - Set string value... Set numeric value... Formula... Sort rows... -- structure -- Append row Append column... Append sum column... Append difference column... Append product column... Append quotient column... Remove row... Remove column... Insert row... Insert column... -- set -- Set column label (index)... Set column label (label)... Extract - Extract rows where column... Select rows where column... Down to Matrix Down to TableOfReal q q q q q q q q q q q q q q q q q q q q q q q q q #q &q (q *q 2q 5q 7q Aq Fq Kq Pq Uq Xq [q ^q aq eq iq nq sq uq wq |q q q q q q q q q q q q q q q q q q q q q q q q q q !q /q 4q 7q =q Eq Qq ]q tq q q q q q q q q q q q q q #q 1q :q Cq Oq Tq \q dq xq q q q q q q q q q q q q q q q q q q q q $q -q 9q Fq Tq aq nq wq q q q q q q q q q q q q q q q q q $q .q 8q Bq Lq Vq cq kq sq yq q q q q q q q q q q q q q @ ? ? +eG? if then else ( [ , or and not = <> <= < >= > + - * / div mod ^ _neg endif fi ) ] _number pi e undefined xmin xmax ymin ymax nx ny dx dy row col nrow ncol y x self _matriks stopwatch abs round floor ceiling sqrt sin cos tan arcsin arccos arctan exp sinh cosh tanh arcsinh arccosh arctanh sigmoid erf erfc gaussP gaussQ invGaussQ randomPoisson log2 ln log10 lnGamma hertzToBark barkToHertz phonToDifferenceLimens differenceLimensToPhon hertzToMel melToHertz hertzToSemitones semitonesToHertz erb hertzToErb erbToHertz arctan2 randomUniform randomInteger randomGauss chiSquareP chiSquareQ invChiSquareQ studentP studentQ invStudentQ beta besselI besselK soundPressureToPhon fisherP fisherQ invFisherQ binomialP binomialQ invBinomialP invBinomialQ min max imin imax length fileReadable date$ left$ right$ mid$ environment$ index rindex startsWith endsWith index_regex rindex_regex extractNumber extractWord$ extractLine$ selected selected$ numberOfSelected fixed$ percent$ . _true _false _iftrue _iffalse _gaNaar _label _self0 _selfmatriks1 _selfmatriks2 _selffunktie1 _selffunktie2 _matriks0 _matriks1 _matriks2 _funktie0 _funktie1 _funktie2 _rowIndex _columnIndex _square _string _str= _str<> _str<= _str< _str>= _str> _str+ _str- _numericVariable _stringVariable _numericColumn _stringColumn _selected2 _selected2$ _end %s: \>> %.*s Missing exponent Unknown variable, or function with missing arguments Function with missing arguments \<<%s\>> is ambiguous: a variable or an attribute of the current object. Change variable name. Unknown variable \<<%s\>> in formula (no "current object" here). Unknown token \<<%s\>> in formula (no variables or current objects here). Unknown function \<<%s\>> in formula Unknown variable \<<%s\>> in formula Unknown function or attribute \<<%s\>> in formula. Unknown symbol \<<%s\>> in formula (variables start with lower case; object names contain an underscore). No such object (note: variables start with lower case) No closing quote in string constant Unknown symbol Expected "%s", but found "%s" Formula.c thee != NULL Attribute "xmin" not defined for this object Attribute "xmax" not defined for this object Attribute "ymin" not defined for this object Attribute "ymax" not defined for this object Attribute "nx" not defined for this object Attribute "ny" not defined for this object Attribute "dx" not defined for this object Attribute "dy" not defined for this object Attribute "ncol" not defined for this object Attribute "nrow" not defined for this object Unknown attribute. After a name of a matrix there should be "(", "[", or "." Function returning a number expected Symbol misplaced Expressions like -3^4 are ambiguous; use (-3)^4 or -(3^4) or -(3)^4 Function returning a string expected Symbol misplaced... Expected numeric expression but found string expression %d %s %.17g %d %s %d %d %s %s %s %d %s "%s" %d %s %ld %s %d %s Out of memory during formula computation. No values for "x" for this object. No values for "y" for this object. n >= 1 --undefined-- The name "self" is restricted to formulas for objects. We are not in a loop, hence no implicit column index for the current %s object (self). Try using the [column] index explicitly. We are not in a loop over rows and columns, hence no implicit row and column indexing for the current %s object (self). Try using both [row, column] indexes explicitly. We are not in a loop over columns only, hence no implicit row index for the current %s object (self). Try using the [row] index explicitly. %s objects (like self) accept no [] indexing. We are not in a loop, hence no implicit row index for the current %s object (self). Try using both [row, column] indexes instead. %s objects (like self) accept no [column] indexes. %s objects like "self" accept no [row, column] indexing. The current %s object (self) accepts no implicit y values. Try using both (x, y) arguments instead. %s objects like "self" accept no (x) values. %s objects like "self" accept no (x, y) values. We are not in a loop, hence no implicit column index for this %s object. Try using the [column] index explicitly. We are not in a loop over rows and columns, hence no implicit row and column indexing for this %s object. Try using both [row, column] indexes explicitly. We are not in a loop over columns only, hence no implicit row index for this %s object. Try using the [row] index explicitly. %s objects accept no [] indexing. We are not in a loop, hence no implicit row index for this %s object. Try using both [row, column] indexes instead. %s objects accept no [column] indexes. %s objects accept no [row, column] indexing. No current object (we are not in a Formula command), hence no implicit x value for this %s object. Try using the (x) argument explicitly. The current %s object gives no implicit x values, hence no implicit x value for this %s object. Try using the (x) argument explicitly. No current object (we are not in a Formula command), hence no implicit x or y values for this %s object. Try using both (x, y) arguments explicitly. The current %s object gives no implicit x values, hence no implicit x value for this %s object. Try using both (x, y) arguments explicitly. The current %s object gives no implicit y values, hence no implicit y value for this %s object. Try using the (y) argument explicitly. %s objects accept no () values. No current object (we are not in a Formula command), hence no implicit y value for this %s object. Try using both (x, y) arguments instead. The current %s object gives no implicit y values, hence no implicit y value for this %s object. Try using both (x, y) arguments instead. %s objects accept no (x) values. %s objects accept no (x, y) values. No row labels for this object. No row "%s" for this object. No column labels for this object. No column "%s" for this object. Symbol "%s" without action. w == 1 && sw == 0 %s w == 0 && sw == 1 theExpressionType == EXPRESSION_TYPE_UNKNOWN [r [r j r r 2r _r i :r _r i Br gr b Dr gr b V [r lj Xr ?numberOfCoefficients numberOfObservations yLabels xLabels y x Trying to read "%s". CCA Strings Eigen CCA info Name: %s Number of coefficients: %d ny: %d nx: %d TableOfReal_to_CCA %s: Dimension of first part not correct. %s: The dimension of the dependent part (%d) must be less than or equal to the dimension of the independent part (%d). %s: The number of observations must be larger then %d %s: One of the parts of the table contains only zeros. CCA.c thy x -> dimension == thy xLabels -> numberOfStrings && thy y -> dimension == thy yLabels -> numberOfStrings CCA_and_TablesOfReal_scores %s: the number of columns in the table (%d) does not agree with the dimensions of the CCA object (ny + nx = %d + %d). %s: number of factors must be in interval [1, %d]. y_ x_ CCA_and_TableOfReal_predict %s: There are not enough correlations present for prediction. %s: the number of columns to analyze must be equal to %d. CCA_and_Correlation_dvFactorLoadings %s: the number of columns in the Correlation object must equal the sum of the dimensions in the CCA object dv iv ?Cannot seek in file %s. LongSounds_writeToStereoAudioFile16 %s: LongSounds must be mono. %s: Sample rates must be equal. PpgB MelderFile_truncate %s: Can't open file "%s". %s: Can't set the position at size %d for file "%s". LongSounds_appendToFile %s: No Sound or LongSound objects to append. r+b %s: Not a sound file %s: Sample rates do not match. %s: Cannot mix stereo and mono. %s: Cannot write header. %s: File "%s" restored to original size. Hint: %s. r r r r r r r r r r r r r r r r r r r r r r r r r r !r %r )r -r /r 3r r :r " ` P 6 Nt :( 0 d v N< l . $P X ` . f r 26 ^ 8 bx : L J 8t } q$ L~ DD 00j v > " j i x o d 2 h d & _ ] v` ^ d X i d. 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" Z X XR , * @ ( T ( N ,x ` T r" l X" T ,. % x` L " L( ` , ,` ` : ` X ^R( & T ( & & R ' , ^:` ` T r ! ( ) ^ ( x " R * r( " @( Z ~Z % ,RZ + F & % # &` ,r` ` X@ R T & ^ , LT R( . r & , # : ` . " : & , . , " 6 ~" X L " ` # B $ ` T % XZ Z ! Z , ' Z # X ! r " , 4 r &Z : ,R / Lx &T , ! ! # , ( # ,l $ ! & & & ^ , ` $ XZ x , " $ ` Xr( p ^. ) RL X Rx( Z ( ,` ` T l lT X` # ` T ,R 4 x ` , R" % r , h $ ,l % ( " & T @R 2 LFT ( ' ,( ,l` T Z : " & " ! ^ 0 " &( ~ &( ,` , X RT & ^ 3 T 0 # ( " Jl * T : XN & ` # ,Z ( 2 R , * # T $ & " - 4( " 4( " X $ 0 & JT , ~ # " ( R $ ,( ,` r :T LT $ ,R * 8x L ,. " ,4( ( T X Z ^ . T " " L , , & : Z " ` ,T - r" ' ~ &r , " " : ` " 4 &L< . , t 2 Z &" + ! ` ` ,` & v" ' T r r r r r r r r r r r r jr Hr r Kr Nr Pr Sr Vr Yr -r \r ^r r jr -r Nr ^r !r `r r dr \r fr r %r r r :r O F : \ XF 1( % :e H q nH 4 H , b l :T? / ` DO | W;| 2} ~ o } R0 y !B yN | > w BNbn X j Mmx fk 25 m Um Ds *-rw m g6 l l &qO 3 v $ u s u L v w [ jjz V x aB r X z YB 0] ? Y ? #1p 4 fx ~ 0 ; E" FW 'V ~ g U .G {6 K i e ] a U lN[ 6 tW fp -X 3u W i@ \Q > F P 9 " e9 6E oQ es@ EI 1J> -u ^Bv 3/ , " C^ 8# / Yg 3 Q + + I w / / O C ~ ! *5s X| }p ) o h f B . GJ ' T f zv # qW QJ > :6 SU~ &j z& l VB v m Si1 E ( A[ <# A5 * !y Q r $ 9B %W ` z * !% 9 ' ^ JN u` ( %t _$ Y /2o (% L R B M5 Y !_ \ ^ M , Q ; 2 }R DT | 4 J }n # "X h 6 f P Va 5s N A(r <iL J 7|# KeU q LQ _J 8m 5 4Fg >w (or o"v Fx :S AD RZ @| }2c @K}O 8<\ :aC 1 *z ,~D 0| .J 8# Y' r +f R -;, <mu1\KK. B )E% 3e@ BK3 FF _3# "4e ~;n hb k5 TK Qb 6`9i Ct} z kk R 4+ 6 F/ w| s D^ T[ x j\rVcsv ]i eS ^D a f8SR?k @a-a (*) )Mf Db /J #9 1 A#A 3h ab= Wi 6s D} ) j :z `] cfZX ACa ); /` ) 9 +ik mF G> I E dt yD P# _ VY( UZ * F K b L` T 0 "t [$ /PI + (I" ;F *14 9o Type Sex Speaker Vowel IPA F0 F1 F2 F3 m w c iy ih eh ae aa ao uh uw ah er i \ic \ep \ae \as \ct \hs u \vt \er\hr f %d L1 L2 L3 oe oo a eu ie uu ee e o \o/ y \yc Ąr ( Ąr j xr r r r Ȅr r r r r r r r ( r j xr r r r r r r r r r r r +V Ąr lj ( ,r 1V r lj ( r tolerance numberOfRows numberOfColumns u v d q r d1 d2 Trying to read "%s". SVD my numberOfRows my numberOfColumns GSVD Number of rows = %ld Number of columns = %ld SVD_synthesize: indices must be in range [1, %d]. Number of columns = %ld GSVD_create_d %s: Error info = %d bits Cannot run experiments from the command line. listening experiments %ld ResultsMFC: Get response 1 Trial Trial %ld does not exist (maximum %ld). %s ResultsMFC: Get stimulus %s_shared allResults Sort Get enthropy Run Extract results Query - Get number of trials Get stimulus... Get response... Modify Remove unshared stimuli Convert To Categories (stimuli) To Categories (responses) Collect Collect to Table r dr r r װr r r <r jr r r ݱr r .r fr r Ȳr r "r Ir lr r r r +r Sr r r lr .r r װr r r <r jr r r ݱr r Mr Zr lr r r ûr r r 6r Xr ur r r r r żr ټr r r Lr r r ؽr r r )r Rr qr r r ξr r r +r Jr br zr r r /r r r /r >r Nr ]r Er r 'r \r r r [r r >r r r r 6r r Yr r Jr r ;r Pr r r <r rr Kr xr r r $r Xr qr r r r r r Cr ټr {r r r r r Ir ar r r r r r r .r fr r Ȳr Gr r Mr Zr r r r 1r Vr r r r /r r r Ir r r r r r 2r ir r r r r r 3r ^r tr r r r r Xr zr Mr Zr lr r Er Tr hr r r r r r r r r r "r ir or r r r r 3r r r r r r r `r Mr Zr lr Fr r r r r hr r r r r 9r fr r r r r Gr tr r r r (r Ur r r r r 6r cr r r r r Dr qr r r r ;r ټr r r Lr r r ؽr r r nr r r r r r r 5r Tr tr r r r r r s s s "r Ir lr =s r ؽr s ,s Js s $s s ,s s =s r s s 4s s s s s =s r s s s P s s s r r =s Xr ur r r r r r r s s s s "s r r Gs Ts s =s Xr ur r r r r r Rr qr r r ξr r s s \s ys s s s s s r r s "s ?s ]s s ys s s s Bs `s s s s s r Gs r s "s ?s s s Ws Ts Mr Zr s s s s s 5s r r Gs Lr r r ؽr Is r os s s r r s r s s )s Es as }s s s s s s % s A s ] s y s s s r +r Jr br zr r s s ) s Mr s s s s s s s żr r 7 s Gs s s r ؽr Is r os s s r r s r s s !s 2!s M!s h!s !s r s !s s s !s s żr r !s Gs s $"s r ؽr Is r os s s r r s r s r"s "s "s "s "s "s r #s x$s One of the @@types of objects@ in P\s{RAAT}, for running a Multiple Forced Choice listening experiment. @@ExperimentMFC 1. When to use Praat @@ExperimentMFC 2. The first example @@ExperimentMFC 2.1. The experiment file @@ExperimentMFC 2.2. The stimuli @@ExperimentMFC 2.3. The carrier phrase @@ExperimentMFC 2.4. Breaks @@ExperimentMFC 2.5. Randomization strategies @@ExperimentMFC 2.6. Instructions @@ExperimentMFC 2.7. Response categories @@ExperimentMFC 2.8. Goodness judgments @@ExperimentMFC 2.9. How an experiment proceeds @@ExperimentMFC 3. More examples @@ExperimentMFC 3.1. A simple discrimination experiment @@ExperimentMFC 3.2. An AXB discrimination experiment @@ExperimentMFC 3.3. A 4I-oddity experiment @@ExperimentMFC 3.4. Variable inter-stimulus intervals @@ExperimentMFC 4. Special buttons @@ExperimentMFC 4.1. The replay button @@ExperimentMFC 4.2. The OK button @@ExperimentMFC 4.3. The oops button @@ExperimentMFC 5. Stimulus-dependent texts @@ExperimentMFC 5.1. The stimulus-dependent run text @@ExperimentMFC 5.2. Stimulus-dependent response buttons @@ExperimentMFC 6. Responses are sounds @@ExperimentMFC 7. Running multiple experiments With Praat, you can do simple experiments on identification and discrimination. `Simple' means that for identification, the subject hears a sound and has to click on one of a set of labelled rectangles (optionally, you can have the subject give a goodness-of-fit judgment). For discrimination, you can have simple same-different choices, or more intricate things like AXB, 4I-oddity, and so on. The advantage of using Praat for this is that it is free, it works on Windows, Unix, and Macintosh, and the whole experiment (experiment file plus sound files) is portable across computers (you can run it from a CD, for instance). Because of the limited possibilities, it is also quite easy to set up the experiment. Just read the description below. If you require more from your experiment design, you use a dedicated program like Presentation or E-prime instead of Praat. With these programs, you can measure reaction times as well, or you can let the stimulus depend on the subject's previous responses. If you do not need those extra capabilities, you can use the simpler method of Praat. My estimation is that that is fine for 90 percent of the perception experiments that phoneticians perform. The following pages give an example of an experiment definition, and explain the main features of an identification task. An experiment is defined in a simple text file, which we call an %%experiment file%. The following is an example of such an experiment file. The first two lines have to be typed exactly as in this example, the rest depends on your stimuli, on your response categories, and on the way the experiment is to be presented to the listener. The order of the elements in this file cannot be changed, and nothing can be skipped. "ooTextFile" "ExperimentMFC 4" stimuliAreSounds? <yes> stimulusFileNameHead = "Sounds/" stimulusFileNameTail = ".wav" stimulusCarrierBefore = "weSayTheWord" stimulusCarrierAfter = "again" stimulusInitialSilenceDuration = 0.5 seconds stimulusMedialSilenceDuration = 0 numberOfDifferentStimuli = 4 "heed" "" "hid" "" "hood" "" "hud" "" numberOfReplicationsPerStimulus = 3 breakAfterEvery = 0 randomize = <PermuteBalancedNoDoublets> startText = "Click to start." runText = "Choose the vowel that you heard." pauseText = "You can have a short break if you like. Click to proceed." endText = "The experiment has finished." maximumNumberOfReplays = 0 replayButton = 0 0 0 0 "" "" okButton = 0 0 0 0 "" "" oopsButton = 0 0 0 0 "" "" responsesAreSounds? <no> "" "" "" "" 0 0 numberOfDifferentResponses = 5 0.2 0.3 0.7 0.8 "h I d" "" "i" 0.3 0.4 0.5 0.6 "h E d" "" "e" 0.4 0.5 0.3 0.4 "h A d" "" "a" 0.5 0.6 0.5 0.6 "h O d" "" "o" 0.6 0.7 0.7 0.8 "h U d" "" "u" numberOfGoodnessCategories = 5 0.25 0.35 0.10 0.20 "1 (poor)" 0.35 0.45 0.10 0.20 "2" 0.45 0.55 0.10 0.20 "3" 0.55 0.65 0.10 0.20 "4" 0.65 0.75 0.10 0.20 "5 (good)" This experiment will play 4 different stimuli to the listener, each 3 times. Thus, the listener is confronted with 12 trials. You can see that the @@ExperimentMFC 2.1. The experiment file|example experiment@ contains four different stimuli: %heed, %hid, %hood, and %hud. These are the %names of the four stimuli. Because in the example experiment stimuli are sounds, each of the four stimuli should be in a sound file. The names of these sound files must be identical to the names of the stimuli, bracketed with %stimulusFileNamehead and %stimulusFileNameTail. Hence, the stimuli are expected in the following four files: Sounds/heed.wav Sounds/hid.wav Sounds/hood.wav Sounds/hud.wav You need not use WAV files. You can also use AIFF files, in which case %stimulusFileNameTail would probably be ".aiff", or any other type of sound file that Praat supports. But all sound files must have the same sampling frequency. In this example, the experiment will look for the sound files in the directory #Sounds, which has to be in the same directory as your experiment file. In other words, "Sounds/heed.wav" is a %%relative file path%. Instead of a relative path, you can also supply a %%full file path%. Such a path depends on your computer and on your operating system. For instance, if you have a Windows computer and the stimuli are in the directory ##D:\bsCorpus\bsAutumn\bsSpeaker23#, you can write fileNameHead = "D:\bsCorpus\bsAutumn\bsSpeaker23\bs" If you have a Macintosh (OS X) or Unix computer and the stimuli are in ##/Users/mietta/Sounds/Dutch#, you write fileNameHead = "/Users/mietta/Sounds/Dutch/" If you have an older Macintosh and the stimuli are in ##My disk:My experiment:Stimuli#, you write fileNameHead = "My disk:My experiment:Stimuli:" But relative file paths will usually be preferred: they are more %portable. The advantage of using relative file paths is that you can move your whole experiment (experiment file plus sounds) from one computer to another without changing the experiment file, as long as you put the experiment file in the same directory as where you put the directory #Sounds. Or you can put the whole experiment on a CD and run the experiment directly from the CD. Since Praat supports the forward slash "/" as a directory separator on all computers, you can run the exact same experiment on Macintosh, Windows and Unix computers, independent of the type of computer where you have created your experiment. The stimuli can be embedded in a %%carrier phrase%. In the @@ExperimentMFC 2.1. The experiment file|example experiment@, we see that the stimulus will be inserted between the sounds in the files ##weSayTheWord.wav# and ##again.wav#, both of which are expected to be in the directory #Sounds. If you do not want a carrier phrase, you do stimulusCarrierBefore = "" stimulusCarrierAfter = "" If you want only an introductory phrase before the stimulus, and nothing after the stimulus, you do something like stimulusCarrierBefore = "listenTo" and of course you supply the file ##listenTo.wav# in the directory #Sounds. If you want to have a short silence before every stimulus (and before the carrier phrase), you supply a non-zero %stimulusInitialSilenceDuration, as in the example. Since the carrier phrase is concatenated with the stimulus before it is played, it should have the same sampling frequency as the stimulus files. A new stimulus will arrive as soon as the listener makes her choice. To allow her some breathing time, you can insert a break after every so many trials. In the example, %breakAfterEvery is 0, because there are only 12 trials. A typical experiment has perhaps 180 trials, and you may want to insert a break after every 40 trials. In that case, you do breakAfterEvery = 40 The 3 times 4 stimuli will have to be played in a certain order. For the least random order, you say randomize = <CyclicNonRandom> In this case, the stimuli will be played in the order in which they were specified in the file, 3 times: heed hid hood hud heed hid hood hud heed hid hood hud The most likely case in which you would want to use this randomization strategy, is if you have, say, 120 different stimuli and you want to play them only once (%numberOfReplicationsPerStimulus = 1) in a fixed order. The other extreme, the most random order, is randomize = <WithReplacement> In this case, a stimulus will be chosen at random 12 times without memory, for instance hid hood hood heed hid hood hud hud hid hood heed hid The order will probably be different for each listener. In this example, %hood and %hid occur four times each, %heed and %hud only twice each. This strategy is too random for most experiments. Usually, you will want to have the same number of replications of each stimulus. The most random way to do this is randomize = <PermuteAll> In this case, all stimuli will be played exactly 3 times, for instance heed hood hud hud hid heed heed hud hood hid hid hood Quite often, you will want a less random order, namely one in which the 12 trials are divided into 3 blocks of 4 stimuli. Within each block, all 4 different stimuli occur in a random order: randomize = <PermuteBalanced> In this case, each stimulus occurs exactly once within each block: heed hood hud hid hood hud hid heed heed hud hood hid This strategy ensures a certain spreading of the stimuli over the sequence of 12 trials. As we see here, it is still possible that the same stimulus (%heed) occurs twice in a row, namely as the last stimulus of the second block and the first stimulus of the third. If you want to prevent that situation, you use This will ensure that the same stimulus is never applied twice in a row: heed hood hud hid hood hud hid heed hud heed hood hid This randomization strategy is used in our example, and advised for most listening experiments in which you want to minimize effects of stimulus order. The randomization procedure does not interfere in any way with the breaks. The order is determined before any breaks are inserted. Before the experiment begins, the listener will see the %startText in the centre of the screen. During each trial, she will see the %runText at the top of the screen. During breaks, she will see the %pauseText in the centre of the screen. After all the trials have been performed, she will see the %endText. Every trial comes with the same set of response categories. The @@ExperimentMFC 2.1. The experiment file|example experiment@ has five of them. For each response category, you supply the area of the screen where a rectangle will be drawn. The whole screen measures from 0.0 (left) to 1.0 (right) and from 0.0 (bottom) to 1.0 (top). Thus, "0.2 0.3 0.7 0.8" means that a rectangle will be drawn somewhere in the top left quadrant of the screen. You also supply the text that will be drawn in this rectangle, for instance the text "h I d". The second text that you supply for every response is a response key on the keyboard. In the above example this is "", i.e. the subject cannot press a key as a response. If you want the user to be able to press the "m" key instead of clicking in the "h I d" rectangle, the line in the experiment file would be: 0.2 0.3 0.7 0.8 "h I d" "m" "i" The third text that you supply for each rectangle is the response category as it will be reported by Praat to you when the user clicks it, e.g. the text "i". If you want Praat to ignore mouse clicks on this rectangle, specify an empty response category, i.e. "". The border of the rectangles will be maroon, the background of the screen will be light grey. The colour of clickable rectangles will be yellow, that of non-clickable rectangles (those with empty category specifications) light grey. If %numberOfGoodnessCategories is not 0, some more rectangles will be drawn, as in the @@ExperimentMFC 2.1. The experiment file|example experiment@. You specify again the locations of these rectangles (in the example, they touch each other), and the texts on them. Praat will record the number of the button when the listener clicks on it. Thus, if she clicks on the button labelled "1 (poor)", Praat will record a goodness judgment of 1, because this is the first button in the list. If she clicks on "5 (good)", Praat will record a goodness judgment of 5. A text file with an ExperimentMFC object can be read into Praat with @@Read from file...@ (it is not a script but a data file, so do not try to read it with ##Open Praat script...#). You can then choose #Run. After the experiment finishes, you can close the experiment window and choose ##Extract results#. The resulting ResultsMFC object contains for each trial the stimulus name (e.g. "hood"), the response category (e.g. "u"), and the goodness judgment (e.g. 4). You will want to save this ResultsMFC object to a text file with @@Write to text file...@. You may want to call these text files by the names of the subjects, e.g. ##ts.ResultsMFC# and ##mj.ResultsMFC#. Once you have collected the results of all your subjects, you can read all the results files into Praat with @@Read from file...@, then select all the resulting ResultsMFC objects (which will have automatically been named #ts, #mj, and so on), then choose ##Collect to table#. This will result in a table whose first column contains the names of the subjects, while the second column contains the stimulus names and the third column the responses (if there are goodness judgments, these will go into a fourth column). The table can be saved as a table file (with ##Write to table file...#), which can be read by programs like Excel and SPSS. You can do many more kinds of experiments than simple identification experiments. The @@ExperimentMFC 2.1. The experiment file|example experiment@ was an %identification experiment: the subject had identify a single sound as one element of a set of categories. Phoneticians will often do %discrimination experiments, which are experiments in which a stimulus consists of multiple sub-stimuli played in sequence, and the subject has to judge the similarity between these sub-stimuli. The simplest discrimination task has only two sub-stimuli, and the subject has to say whether these are the %same or %different. Suppose you have vowel-like sounds along an F1 continuum with seven steps, say 300, 320, 340, 360, 380, 400, and 420 Hertz, and you are interested in knowing how well the listeners can distinguish these. As your stimuli, you create pairs of these sounds, separated by 0.8 seconds of silence. It is important to include stimuli in which the sounds are identical, e.g. stimuli in which both sounds have an F1 of 340 Hz (see the literature on signal detection theory). Since sounds that are very different acoustically will always be heard as different, you do not include pairs in which the distance is larger than 60 Hz. The experiment file will look like this: stimuli are sounds? <yes> "stimuli/" ".wav" carrier phrase "" "" initial silence duration 0.5 seconds medial silence duration 0.8 seconds ! inter-stimulus interval 37 different stimuli "300,300" "" "300,320" "" "300,340" "" "300,360" "" "320,300" "" "320,320" "" "320,340" "" "320,360" "" "320,380" "" "340,300" "" "340,320" "" "340,340" "" "340,360" "" "340,380" "" "340,400" "" "360,300" "" "360,320" "" "360,340" "" "360,360" "" "360,380" "" "360,400" "" "360,420" "" "380,320" "" "380,340" "" "380,360" "" "380,380" "" "380,400" "" "380,420" "" "400,340" "" "400,360" "" "400,380" "" "400,400" "" "400,420" "" "420,360" "" "420,380" "" "420,400" "" "420,420" 10 replications per stimulus break after every 50 stimuli <PermuteBalancedNoDoublets> "Click to start." "Say whether these sounds were the same or different." "You can have a short break if you like. Click to proceed." "The experiment has finished. Call the experimenter." 0 replays replay button 0 0 0 0 "" "" ok button 0 0 0 0 "" "" oops button 0 0 0 0 "" "" responses are sounds? <no> "" "" "" "" 0 0 2 response categories 0.1 0.4 0.35 0.65 "same" "" "same" 0.6 0.9 0.35 0.65 "different" "" "different" 0 goodness categories In this example, the subject will have to click 370 times. After every 50 times, she will have the opportunity to sip her tea. A 0.5-seconds silence is played before every stimulus, so that the listener will not hear the stimulus immediately after her mouse click. The experimenter does not have to create the stimulus pairs as sound files. You can specify multiple sound files by separating them with commas. Thus, "320,300" means that Praat will play the files ##320.wav# and ##300.wav#. These two substimili will be separated here by a silence of 0.8 seconds, called the %%inter-stimulus interval% (or %stimulusMedialSilenceDuration). Note that the text in this file is rather different from the previous example. It does not matter whether you write "numberOfDifferentStimuli", or "different stimuli", or anything else; Praat ignores these texts as long as they do not contain numbers, quoted strings, or things between <>. In the AXB task, the subject will hear three stimuli in sequence, and has to say whether the second (X) is more similar to the first (A) or to the second (B). An experiment file could look like follows: carrier "" "" initial silence 0.5 inter-stimulus interval 0.3 100 stimuli "300,300,320" "" "300,320,340" "" "300,340,340" "" "300,340,360" "" ... (and 96 more triplets of substimuli) 4 replications break every 50 "Say whether the second sound is more similar to the first or to the third." "The experiment has finished." 3 response categories 0.1 0.3 0.4 0.6 "first" "" "A" 0.4 0.6 0.4 0.6 "second" "" "" 0.7 0.9 0.4 0.6 "third" "" "B" In this example, the subject has to click 400 times. She sees three buttons, labelled %first, %second, and %third, but the second button (the one with the empty response category) is not clickable: it has a light grey rather than a yellow interior and cannot be chosen by the subject. In your ResultsMFC object, you will only see %A and %B responses. In the four-items-oddity task, the subject will hear four stimuli in sequence, and has to say whether the second or the third is the odd one out. The other three substimuli are identical. An experiment file could look as follows: stimulusFileNameHead = "stimuli/" stimulusMedialSilenceDuration = 0.3 seconds numberOfDifferentStimuli = 60 "300,300,320,300" "" "300,320,300,300" "" "300,300,340,300" "" "300,340,300,300" "" "300,300,360,300" "" "300,360,300,300" "" "320,320,300,320" "" "320,300,320,320" "" "320,320,340,320" "" "320,340,320,320" "" "320,320,360,320" "" "320,360,320,320" "" "320,320,380,320" "" "320,380,320,320" "" "340,340,300,340" "" "340,300,340,340" "" "340,340,320,340" "" "340,320,340,340" "" "340,340,360,340" "" "340,360,340,340" "" "340,340,380,340" "" "340,380,340,340" "" "340,340,400,340" "" "340,400,340,340" "" "360,360,300,360" "" "360,300,360,360" "" "360,360,320,360" "" "360,320,360,360" "" "360,360,340,360" "" "360,340,360,360" "" "360,360,380,360" "" "360,380,360,360" "" "360,360,400,360" "" "360,400,360,360" "" "360,360,420,360" "" "360,420,360,360" "" "380,380,320,380" "" "380,320,380,380" "" "380,380,340,380" "" "380,340,380,380" "" "380,380,360,380" "" "380,360,380,380" "" "380,380,400,380" "" "380,400,380,380" "" "380,380,420,380" "" "380,420,380,380" "" "400,400,340,400" "" "400,340,400,400" "" "400,400,360,400" "" "400,360,400,400" "" "400,400,380,400" "" "400,380,400,400" "" "400,400,420,400" "" "400,420,400,400" "" "420,420,360,420" "" "420,360,420,420" "" "420,420,380,420" "" "420,380,420,420" "" "420,420,400,420" "" "420,400,420,420" "" numberOfReplicationsPerStimulus = 5 runText = "Say whether the second or the third sound is different from the rest." responsesAreSounds? <no> responseFileNameHead = "" responseFileNameTail = "" responseCarrierBefore = "" responseCarrierAfter = "" responseInitialSilenceDuration = 0 responseMedialSilenceDuration = 0 numberOfResponseCategories = 4 0.04 0.24 0.4 0.6 "first" "" "" 0.28 0.48 0.4 0.6 "second" "" "2" 0.52 0.72 0.4 0.6 "third" "" "3" 0.76 0.96 0.4 0.6 "fourth" "" "" numberOfGoodnessCategories = 0 In this example, the subject has to click 300 times. She sees four buttons, but the first and fourth buttons cannot be chosen. In your ResultsMFC object, you will only see the responses %2 and %3. Praat only supports a fixed inter-stimulus interval, but sometimes you may want to test discrimination as a function of the inter-stimulus interval itself. You can achieve this by supplying an %interStimulusInterval of 0 and using sound files with various silences: "300,silence0.5,320" "300,silence1.5,320" "300,silence4.5,320" In this example, you have to supply the sound files ##silence0.5.wav# and so on. You can create them with the help of @@Create Sound...@ (supply a %formula of 0). You can include up to three special buttons on the screen that the participant sees. It is probably inadvisable to use all three at the same time. The @@ExperimentMFC 2.1. The experiment file|example experiment@ contained the following lines: This means that that experiment did not have a replay button. To add a replay button along the lower edge of the screen, you do something likw maximumNumberOfReplays = 1000 replayButton = 0.3 0.7 0.01 0.07 "Click here to play the last sound again" "" If you supply a right edge (here 0.7) that is greater than the left edge (here 0.3), Praat will know that you want to show a replay button. When the participant clicks this button, Praat will play the current stimulus again. In this example, the button will be visible until the partipant has clicked it 1000 times. To assign a keyboard shortcut to the replay button, do something like replayButton = 0.1 0.9 0.01 0.07 "Click here or press the space bar to play the last sound again" " " This means that that experiment did not have an OK button. To add an OK button in the lower right corner of the screen, you do something likw okButton = 0.8 0.95 0.05 0.15 "OK" "" If you supply a right edge (here 0.95) that is greater than the left edge (here 0.8), Praat will know that you want to show an OK button. The behaviour of the experiment changes appreciably if you include an OK button. If you do not include an OK button, Praat will present the next stimulus as soon as the participant has clicked a response category (and a goodness category, if there are such). If you do include an OK button, it will become visible to the participant as soon as she has chosen a response category (and a goodness catgory, if there are such). The participant can then click the OK button, but she can also choose to click the response (and goodness buttons) a bit more first. The OK button seems to be useful only if there is also a replay button, or if the response categories are sounds (see @@ExperimentMFC 6. Responses are sounds@). To assign a keyboard shortcut (here, the space bar) to the OK button, do something like okButton = 0.8 0.95 0.05 0.15 "OK" " " This means that that experiment did not have an oops button. To add an oops button in the lower left corner of the screen, you do something likw okButton = 0.05 0.2 0.05 0.15 "oops" "" If you supply a right edge (here 0.2) that is greater than the left edge (here 0.05), Praat will know that you want to show an oops button. If you include an oops button, it will become visible to the participant for every stimulus except the first, and it will also be visible on the pause (break) screens and on the final screen. If the participant clicks the oops button, Praat will forget everything the participant did with the current stimulus and the previous stimulus. The experiment will continue with playing the previous stimulus again and waiting for the participant's choice. In the @@ExperimentMFC 2.1. The experiment file|example experiment@, the text at the top of the screen stayed the same throughout the experiment, and so did the texts on the response buttons. There are ways to have these texts depend onthe stimulus at hand. For every stimulus, the same `run text' was written at the top of the screen. But suppose you want to make that text dependent on the stimulus. You would do: "heed" "Choose the vowel you heard." "hid" "Click the vowel you heard." "hood" "Select the vowel you heard." "hud" "What's thevowel you heard?" runText = "" In this case, each stimulus comes with its own text. The %runText will only show up for stimuli for which you do not supply a separate text. This feature is useful mainly in cases where the responses are sounds but the stimulus is not (see @@ExperimentMFC 6. Responses are sounds@) or if you want to cause some lexical priming. For every stimulus, the buttons contained the same visible texts, such as "h I d" and "h A d". But suppose you have an experiment about the perception of voicing in plosives. The first stimulus starts with an ambiguous /b/ or /p/, and you want the participant to choose between "bath" and "path". The next stimulus starts with an ambiguous /d/ or /t/, and you want the participant to choose between "dart" and "tart". You would go about like this: numberOfDifferentStimuli = 6 "bpath1" "|bath|path" "bpath2" "|bath|path" "bpath3" "|bath|path" "dtart1" "|dart|tart" "dtart2" "|dart|tart" "dtart3" "|dart|tart" numberOfDifferentResponses = 2 0.2 0.4 0.7 0.8 "" "" "left" 0.6 0.8 0.7 0.8 "" "" "right" In this case, the two response buttons show either "path" and "path", or "dart" and "tart". In the ResultsMFC (see @@ExperimentMFC 2.9. How an experiment proceeds@), the stimuli will be recorded as "bpath1|bath|path" and the like, not just as "bpath1". Praat does this in order to be able to cope with balanced designs such as "bpath1" "|path|bath" In other words, the button ordering is considered part of the stimulus. This trick can be combined with a stimulus-dependent run text: numberOfDifferentStimuli = 32 "bpath1" "Throw a...|bath|path" "bpath1" "Walk a...|bath|path" "bpath2" "Walk a...|bath|path" "dtart1" "Throw a...|dart|tart" "dtart1" "Carry a...|dart|tart" In the @@ExperimentMFC 2.1. The experiment file|example experiment@, the stimuli were sounds, and the responses were categories wose labels appeared on buttons. Sometimes you want it the other way around. An example is the %%/i/ prototype% task: the top of the screen just says "Please choose the best %ee", and no stimulus sound is played. Instead, the participant can click repeatedly on an array of 40 buttons, each of which contains a different [i]-like sound. That is, if the participant clicks on a response button, an [i]-like sound is played, and every response button has its own sound. Such a task can be regarded as reversing the task of the example experiment, in which the stimulus was a sound and the reponse was a phonological category. In the /i/ prototype task, the stimulus is a phonological category, and the response is a sound. This is what the experiment file could look like: stimuliAreSounds? <no> "" "" "" "" 0 0 numberOfDifferentStimuli = 2 "i" "Choose the best \% \% ee\% ." "I" "Choose the best \% \% i\% ." numberOfReplicationsPerStimulus = 1 breakAfterEvery = 1 okButton = 0.8 0.95 0.45 0.55 "OK" "" responsesAreSounds? <yes> responseFileNameHead = "Sounds/" responseFileNameTail = ".wav" responseInitialSilenceDuration = 0.3 numberOfDifferentResponses = 16 0.2 0.3 0.7 0.8 "" "" "i11" 0.3 0.4 0.7 0.8 "" "" "i12" 0.4 0.5 0.7 0.8 "" "" "i13" 0.5 0.6 0.7 0.8 "" "" "i14" 0.2 0.3 0.6 0.7 "" "" "i21" 0.3 0.4 0.6 0.7 "" "" "i22" 0.4 0.5 0.6 0.7 "" "" "i23" 0.5 0.6 0.6 0.7 "" "" "i24" 0.2 0.3 0.5 0.6 "" "" "i31" 0.3 0.4 0.5 0.6 "" "" "i32" 0.4 0.5 0.5 0.6 "" "" "i33" 0.5 0.6 0.5 0.6 "" "" "i34" 0.2 0.3 0.4 0.5 "" "" "i41" 0.3 0.4 0.4 0.5 "" "" "i42" 0.4 0.5 0.4 0.5 "" "" "i43" 0.5 0.6 0.4 0.5 "" "" "i44" The participant will see 16 squares on the screen. First she will have to find the best /i/, then the best /\ic/. The sound files ##Sounds/i11.wav# and so on must exist and have the same sampling frequency. A silence of 0.3 seconds is played just before each response sound. In all the earlier examples, either the set of stimulus sounds or the set of response sounds stayed the same throughout the experiment. If you want more than one set of stimuli, or more than one set of responses, you can run several experiments after each other, simply by selecting more than one experiment, then clicking #Run. You can put all these ExperimentMFC objects in one text file. The following example contains two experiments. The second line has to contain the text "Collection", followed by the number of experiments: "Collection" 2 "ExperimentMFC 4" "i" numberOfDifferentStimuli = 1 startText = "You are going to choose the best \% \% ee\% . Click to start." pauseText = "" endText = "Thank you for choosing the best \% \% ee\% . Click to proceed." numberOfDifferentResponses = 6 0.2 0.3 0.7 0.8 "" "" "i1" 0.3 0.4 0.7 0.8 "" "" "i2" 0.4 0.5 0.7 0.8 "" "" "i3" 0.5 0.6 0.7 0.8 "" "" "i4" 0.6 0.7 0.7 0.8 "" "" "i5" 0.7 0.8 0.7 0.8 "" "" "i6" "ExperimentMFC 4" "u" "u" "Choose the best \% \% oo\% ." startText = "You are going to choose the best \% \% oo\% . Click to start." endText = "All the experiments have finished. You can call the experimenter." 0.2 0.3 0.7 0.8 "" "" "u1" 0.3 0.4 0.7 0.8 "" "" "u2" 0.4 0.5 0.7 0.8 "" "" "u3" 0.5 0.6 0.7 0.8 "" "" "u4" 0.6 0.7 0.7 0.8 "" "" "u5" 0.7 0.8 0.7 0.8 "" "" "u6" In this example, the participant first has to choose the best /i/ from among six [i]-like sounds, which are in the sound files ##i1.wav# through ##i6.wav#. After that, she has to choose the best /u/ from among six [u]-like sounds, which are in the sound files ##u1.wav# through ##u6.wav#. The percent signs in \% \% ee\% mean that %ee will be italicized. If you read this file with ##Read from file...#, you will see two ExperimentMFC objects, named #i and #u. They both stand selected. You then click #Run, and after the participant finishes, you select both ExperimentMFC objects again (probably they still stand selected), and click ##Extract results#. You will then get two #ResultMFC objects. ExperimentMFC ppgb ExperimentMFC 1. When to use Praat ExperimentMFC 2. The first example ExperimentMFC 2.1. The experiment file ExperimentMFC 2.2. The stimuli ExperimentMFC 2.3. The carrier phrase ExperimentMFC 2.4. Breaks ExperimentMFC 2.5. Randomization strategies ExperimentMFC 2.6. Instructions ExperimentMFC 2.7. Response categories ExperimentMFC 2.8. Goodness judgments ExperimentMFC 2.9. How an experiment proceeds ExperimentMFC 3. More examples ExperimentMFC 3.1. A simple discrimination experiment ExperimentMFC 3.2. An AXB discrimination experiment ExperimentMFC 3.3. A 4I-oddity experiment ExperimentMFC 3.4. Variable inter-stimulus intervals ExperimentMFC 4. Special buttons ExperimentMFC 4.1. The replay button ExperimentMFC 4.2. The OK button ExperimentMFC 4.3. The oops button ExperimentMFC 5. Stimulus-dependent texts ExperimentMFC 5.1. The stimulus-dependent run text ExperimentMFC 5.2. Stimulus-dependent response buttons ExperimentMFC 6. Responses are sounds ExperimentMFC 7. Running multiple experiments COMSPEC System command cannot find system version. cmd.exe command.com /c TablesOfReal_to_GSVD: Both tables must have the same number of columns. @ ? @ Y@ @ N C T DGEMM %s: parameter %d not correct! DGER DGEMV E S B P R M U L O WARNING. The value EMIN may be incorrect:- EMIN = %8i If, after inspection, the value EMIN looks acceptableplease comment out the IF block as marked within thecode of routine DLAMC2, otherwise supply EMINexplicitly. DSYMV DSYR2 DSYR2K DTRMM DTRMV DTRSM ? ? Y@ $@ {Gz? @ffffff? ?? ? @@ @ ? ? ܿ @ ? Zd;O?jt??)\(? @? ? ? ? ? ? ? ? ? @ ? ? A A ? ? ? ? ? ? ? ? L U DBDSQR %s: parameter %d not correct! Epsilon Safe minimum F V R B DGEBD2 Left Right N P S NUMlapack_dgebak NUMlapack_dgebal DGEBRD Transpose No transpose NUMlapack_dgehrd EN NUMlapack_dhseqr DORGHR SV NUMlapack_dgeev M G E NUMlapack_dgehd2 Columnwise Forward DGELQ2 DGELQF Rowwise DGELSS DGEQRF LT DORMQR QLT DORMBR DORGBR DORMLQ T Q DGEQPF LEFT DGEQR2 DGERQ2 DGESV DGESVD A O DORGQR DORGLQ DGETF2 DGETRI Non-unit Upper Unit Lower DGETRF C DGETRS DGGSVD 1 Precision Safe Minimum DGGSVP Full I H Z DLASCL DLASQ1 D DLASQ2 DLASR DLASRT EPS DORG2L DORG2R DORGL2 DORGQL Backward DORGTR DORM2R DORML2 DORMR2 DPOTF2 DSTEQR DSTERF DSYTRD DSYEV DSYTD2 DTGSJA NUMlapack_dtrevc DTRTI2 DTRTRI GE TRF QRF RQF LQF QLF HRD BRD TRI PO SY TRD GST HE OR QR RQ LQ QL HR TR BR UN GB PB LA UUM ST EBZ ? ? AGz? @ @ @LongSound: Extract part 0.0 left Time range (s) 1.0 right Time range (s) Preserve times right Time range left Time range Sound: Get index from time... LongSound: Get sample index from time 0.5 Time (s) Time seconds Hertz Sound: Get time from index... LongSound: Get time from sample index 100 Sample index %ld samples LongSound Open long sound file LongSound: Play part 10.0 LongSound: Write part to audio file Audio file: Audio file Type LongSound: To TextGrid... Mary John bell Tier names bell Point tiers Cannot view a LongSound from batch. Write to AIFC file aifc Write to AIFF file aiff Write to NeXT/Sun file au Write to NIST file nist Write to WAV file wav Write left channel to AIFC file Write left channel to AIFF file Write left channel to NeXT/Sun file Write left channel to NIST file Write left channel to WAV file Write right channel to AIFC file Write right channel to AIFF file Write right channel to NeXT/Sun file Write right channel to NIST file Write right channel to WAV file LongSound preferences This setting determines the maximum number of seconds for viewing the waveform and playing a sound in the LongSound window. The LongSound window can become very slow if you set it too high. 60 Maximum viewable part (seconds) Note: this setting works for the next long sound file that you open, not for currently existing LongSound objects. Maximum viewable part Sound: Add The following number will be added to the amplitudes of all samples of the sound. 0.1 Number To concatenate sounds, their sampling frequencies must be equal. You could resample one or more of the sounds before concatenating. chain labels praat_Sound_init.c sound1 && sound2 && i1 && i2 %s_%s Cross-correlate -0.1 From lag (s) To lag (s) Normalize cc_%s_%s To lag From lag Create Sound... Create Sound sineWithNoise Name Starting time (s) Finishing time (s) 22050 Sampling frequency (Hz) Formula: 1/2 * sin(2*pi*377*x) + randomGauss(0,0.1) formula Starting time Finishing time Sampling frequency A Sound cannot have a duration of zero. A Sound cannot have a duration less than zero. Please set the finishing time to something greater than 0 seconds. Please lower the starting time or raise the finishing time. A Sound cannot have a negative sampling frequency. Please set the sampling frequency to something greater than zero, e.g. 44100 Hz. A Sound cannot have zero samples. Please raise the finishing time. A Sound cannot have %s samples; the maximum is %s samples (or less, depending on your computer's memory). Please lower the finishing time or the sampling frequency. Please raise the starting time, lower the finishing time, or lower the sampling frequency. memory There is not enough memory to create a Sound that contains %s samples. You could lower the finishing time or the sampling frequency and try again. You could raise the starting time or lower the finishing time or the sampling frequency, and try again. Please correct the formula. Create Sound from tone complex... Create Sound from tone complex toneComplex Phase Sine Cosine Frequency step (Hz) 0 (= frequency step) First frequency (Hz) 0 (= Nyquist) Ceiling (Hz) 0 (= maximum) Number of components Ceiling First frequency Frequency step Sound: De-emphasize (in-line)... Sound: De-emphasize (in-line) 50.0 From frequency (Hz) From frequency Sound: Deepen band modulation... Deepen band modulation 20 Enhancement (dB) 300 8000 To frequency (Hz) 3 Slow modulation (Hz) 30 Fast modulation (Hz) Band smoothing (Hz) Enhancement %s_%.0f Band smoothing Fast modulation Slow modulation To frequency Sound: Draw 0.0 (= all) left Vertical range 0.0 (= auto) right Vertical range Garnish curve Drawing method bars poles speckles slice Cannot edit a Sound from batch. Sound: Extract part 0 Window Relative width %s_part Sound: Filter (de-emphasis)... Sound: Filter (de-emphasis) %s_deemp Formula... Sound: Filter (formula)... Frequency-domain filtering with a formula (uses Sound-to-Spectrum and Spectrum-to-Sound): x is frequency in Hertz if x<500 or x>1000 then 0 else self fi; rectangular band filter %s_filt Sound: Filter (one formant)... Sound: Filter (one formant) 1000 Frequency (Hz) Bandwidth (Hz) Bandwidth Frequency Sound: Filter with one formant (in-line)... Sound: Filter with one formant (in-line) Sound: Filter (pass Hann band)... Sound: Filter (pass Hann band) 500 To frequency (s) Smoothing (Hz) %s_band Smoothing Sound: Filter (pre-emphasis)... Sound: Filter (pre-emphasis) %s_preemp Sound: Filter (stop Hann band)... Sound: Filter (stop Hann band) Sound: Formula... Sound: Formula ! `x' is the time in seconds, `col' is the sample number. label1 x = x1 ! time associated with first sample label2 for col from 1 to ncol label3 self [col] = ... label4 self x = x + dx label5 endfor label6 Sound: Get absolute extremum... Sound: Get absolute extremum Interpolation None Parabolic Cubic Sinc70 Sinc700 Pascal Sound: Get energy... Sound: Get energy Pa2 sec Joule/m2 Get sample number from time... Get sample number from time dB Sound: Get maximum... Sound: Get maximum Sound: Get mean... Sound: Get mean Sound: Get minimum... Sound: Get minimum Sound: Get nearest zero crossing... Sound: Get nearest zero crossing Sound: Get power... Sound: Get power Pa2 Watt/m2 Sound: Get root-mean-square... Sound: Get root-mean-square Sound: Get standard deviation... Sound: Get standard deviation Get time from sample number... Get time from sample number Sample number Sound: Get time of maximum... Sound: Get time of maximum Sound: Get time of minimum... Sound: Get time of minimum Sound: Get value at sample number... Sound: Get value at sample number Sound: Get value at time... Sound: Get value at time Nearest Linear Sound Sound: Lengthen (PSOLA)... Sound: Lengthen (PSOLA) 75 Minimum pitch (Hz) 600 Maximum pitch (Hz) 1.5 Factor Minimum pitch Maximum pitch Maximum pitch should be greater than minimum pitch. %s %s_%.2f Sound: Multiply Multiplication factor Sound: Multiply by window Window shape Sound: Override sampling frequency 16000.0 New sampling frequency (Hz) New sampling frequency Sound: Pre-emphasize (in-line)... Sound: Pre-emphasize (in-line) Read two Sounds from stereo file %.200s_left %.200s_right left right Read Sound from raw Alaw file Cannot record a Sound from batch. Record Sound Input source Microphone Line Digital Gain (0-1) Balance (0-1) 11025 44100 Duration (seconds) Duration Balance Gain Sound: Resample... Sound: Resample 10000 50 Precision (samples) %s %ld Precision Sound: Scale peak 0.99 New maximum amplitude Sound: Scale intensity 70.0 New average intensity (dB) New average intensity Sound: Set value at sample number... Sound: Set value at sample number New value The sample number should not exceed the number of samples, which is %ld. Sound: Set part to zero Cut at exactly these times at nearest zero crossing Manipulation Sound: To Manipulation 0.01 Time step (s) Maximum pitch must be greater than minimum pitch. Time step Sound: To Cochleagram Frequency resolution (Bark) 0.03 Window length (s) Forward-masking time (s) Forward-masking time Window length Frequency resolution Sound: To Cochleagram (De Boer, Meddis & Hewitt) Has synapse Meddis synapse properties 5.05 replenishment rate (/sec) 2500 loss rate (/sec) 6580 return rate (/sec) 66.31 reprocessing rate (/sec) reprocessing rate return rate loss rate replenishment rate Sound: To Formant (burg)... Sound: To Formant (Burg method) 5 Max. number of formants 5500 (= adult female) Maximum formant (Hz) 0.025 Pre-emphasis from (Hz) Pre-emphasis from Maximum formant Sound: To Formant (keep all)... Sound: To Formant (keep all) Sound: To Formant (sl)... Sound: To Formant (split Levinson (Willems)) Number of formants Sound: To Harmonicity (ac)... Sound: To Harmonicity (ac) Silence threshold 4.5 Periods per window Number of periods per window must be >= 3. Sound: To Harmonicity (cc)... Sound: To Harmonicity (cc) Sound: To Harmonicity (gne) Minimum frequency (Hz) 4500 Maximum frequency (Hz) 80 Step (Hz) Step Maximum frequency Minimum frequency Sound: To Intensity... Sound: To Intensity Subtract mean Sound: To long-term average spectrum Sound: To Ltas (pitch-corrected)... Sound: To Ltas (pitch-corrected) 5000 0.0001 Shortest period (s) 0.02 Longest period (s) 1.3 Maximum period factor Longest period Shortest period Sound: To Pitch... Sound: To Pitch 75.0 Pitch floor (Hz) 600.0 Pitch ceiling (Hz) Pitch ceiling Pitch floor Sound: To Pitch (ac)... Sound: To Pitch (ac) Finding the candidates 15 Max. number of candidates Very accurate Finding a path 0.45 Voicing threshold Octave cost 0.35 Octave-jump cost 0.14 Voiced / unvoiced cost Maximum number of candidates must be greater than 1. Sound: To Pitch (cc)... Sound: To Pitch (cc) Sound: To PointProcess (extrema) Include maxima Include minima Sound: To PointProcess (periodic, cc)... Sound: To PointProcess (periodic, cc) Sound: To PointProcess (periodic, peaks)... Sound: To PointProcess (periodic, peaks) Get zeroes Include raisers Include fallers Sound: To Spectrogram... Sound: To Spectrogram 0.005 0.002 Sound: To Spectrum... Sound: To Spectrum Fast Sound: To TextGrid... Sound: To TextGrid All tier names Which of these are point tiers? SoundRecorder Sound input preferences Buffer size (MB) Buffer size Buffer size cannot exceed 1000 megabytes. Sound output preferences The following determines how sounds are played. Between parentheses, you find what you can do simultaneously. Decrease asynchronicity if sound plays with discontinuities. Maximum asynchronicity Synchronous (nothing) Calling back (view running cursor) Interruptable (Escape key stops playing) Asynchronous (anything) Silence before and after (s) Silence before and after Write to raw 8-bit unsigned sound file 8uns Write to raw 8-bit signed sound file 8sig Write to raw sound file Raw binary file: Raw binary file Encoding Linear 8-bit signed Linear 8-bit unsigned Linear 16-bit big-endian Linear 16-bit little-endian Write to Kay sound file kay Write to Sesam file sdf Write to stereo AIFC file s1 && s2 Write to stereo AIFF file Write to stereo NeXT/Sun file Write to stereo NIST file Write to stereo WAV file Intro 7. Annotation Filtering File %.200s is empty FORM AIF RIFF WAVE CDDA .snd NIST_1A .sdf .SDF SIG FORMDS16 Record mono Sound... New Objects Record stereo Sound... Record Sound (fixed time)... -- read sound -- Read Open long sound file... Read two Sounds from stereo file... Read from special sound file Read Sound from raw Alaw file... Stop playing sound Goodies -- sound prefs -- Preferences Sound input prefs... Sound output prefs... LongSound prefs... LongSound help View Play part... Query - Sampling Get number of samples Get sampling period Get sample duration Get sample period Get sampling frequency Get sample rate -- get time discretization -- Get time from index... Get index from time... Annotate - Annotation tutorial -- to text grid -- To TextGrid... Convert to Sound Extract part... Write to WAV file... Write to AIFF file... Write to AIFC file... Write to Next/Sun file... Write to NIST file... Write left channel to WAV file... Write left channel to AIFF file... Write left channel to AIFC file... Write left channel to Next/Sun file... Write left channel to NIST file... Write right channel to WAV file... Write right channel to AIFF file... Write right channel to AIFC file... Write right channel to Next/Sun file... Write right channel to NIST file... Write part to audio file... Write to Sun audio file... Write to Kay sound file... Write to Sesam file... Write to raw 8-bit signed file... Write to raw 8-bit unsigned file... Write to stereo WAV file... Write to stereo AIFF file... Write to stereo AIFC file... Write to stereo Next/Sun file... Write to stereo NIST file... Sound help Edit Play Draw... Time sampling -- get content -- Get value at time... Get value at sample number... Get value at index... -- get shape -- Get minimum... Get time of minimum... Get maximum... Get time of maximum... Get absolute extremum... Get nearest zero crossing... -- get statistics -- Get mean... Get root-mean-square... Get standard deviation... -- get energy -- Get energy... Get power... -- get energy in air -- Get energy in air Get power in air Get intensity (dB) Modify - Reverse -- add & mul -- Add... Multiply... Multiply by window... Scale peak... Scale... Scale intensity... -- set -- Set value at sample number... Set value at index... Set part to zero... -- modify hack -- Override sampling frequency... Override sample rate... -- in-line filters -- In-line filters Filter with one formant (in-line)... Pre-emphasize (in-line)... De-emphasize (in-line)... Annotate - -- to single tier -- To TextTier To IntervalTier Analyse Periodicity - To Pitch... To Pitch (ac)... To Pitch (cc)... To PointProcess (periodic, cc)... To PointProcess (periodic, peaks)... -- hnr -- To Harmonicity (cc)... To Harmonicity (ac)... To Harmonicity (gne)... Spectrum - To Spectrum... To Spectrum (fft) To Spectrum To Spectrum (dft) To Ltas... To Ltas (pitch-corrected)... -- spectrotemporal -- To Spectrogram... To Cochleagram... To Cochleagram (edb)... Formants & LPC - To Formant (burg)... To Formant (hack) To Formant (keep all)... To Formant (sl)... Points - To PointProcess (extrema)... To PointProcess (zeroes)... To Intensity... Manipulate To Manipulation... Synthesize Convert - Resample... -- enhance -- Lengthen (PSOLA)... Deepen band modulation... -- cast -- Down to Matrix Filter - Filtering tutorial -- frequency-domain filter -- Filter (pass Hann band)... Filter (stop Hann band)... Filter (formula)... -- time-domain filter -- Filter (one formant)... Filter (pre-emphasis)... Filter (de-emphasis)... Combine sounds - Convolve Concatenate Concatenate recoverably To ParamCurve Cross-correlate... Write to NeXT/Sun file... ms ns ns +os os os ps ps ps qs Srs Oss -ts ets ts us us vs vs Bws ws xs jys zs {s k|s +}s }s ~s s xs s s s 7s s >s s s s s Diana Archangeli & Douglas Pulleyblank (1994): %%Grounded Phonology%. Cambridge, Mass.: MIT Press. Paul Boersma (1993): "Accurate short-term analysis of the fundamental frequency and the harmonics-to-noise ratio of a sampled sound." %%Proceedings of the Institute of Phonetic Sciences% #17: 97\--110. University of Amsterdam. Can be downloaded as a PDF file from http://fon.hum.uva.nl/paul/ Paul Boersma (1997a): "The elements of Functional Phonology." Ms. University of Amsterdam. Available as Rutgers Optimality Archive #173, http://ruccs.rutgers.edu/roa.html Superseded by chapters 1 and 7 through 13 of @@Boersma (1998)@. Paul Boersma (1997b): "How we learn variation, optionality, and probability." %%Proceedings of the Institute of Phonetic Sciences% #21: 43\--58. University of Amsterdam. Equals chapter 15 of @@Boersma (1998)@. A less correct version (demoting and promoting a single pair of constraints, instead of them all) is available as Rutgers Optimality Archive #221, http://ruccs.rutgers.edu/roa.html Paul Boersma (1998): %%Functional Phonology% [%%LOT International Series% ##11#]. The Hague: Holland Academic Graphics. Pages i-ix, 1-493. [Doctoral thesis, University of Amsterdam] This book can be downloaded as a PDF file from ##http://www.fon.hum.uva.nl/paul/#, where you can also find many Praat scripts for the simulations and pictures in this book. A paperback version is also available from the author (paul.boersma\@ uva.nl). Paul Boersma (2000): "Learning a grammar in Functional Phonology." In Joost Dekkers, Frank van der Leeuw, & Jeroen van de Weijer (eds.): %%Phonology, Syntax, and Acquisition in Optimality Theory%. Oxford University Press. An extended version is chapter 14 of @@Boersma (1998)@. Paul Boersma & Bruce Hayes (2001): "Empirical tests of the Gradual Learning Algorithm." %%Linguistic Inquiry% #32: 45\--86. Paul Boersma & Gordana Kovacic (to appear): "Spectral characteristics of three styles of Croatian folk singing." To appear in %%Journal of the Acoustical Society of America%. %%Modern spectrum analysis%, IEEE Press. The Burg algorithm for linear prediction coefficients is described on pages 252-255. Dimitar D. Deliyski: "Acoustic model and evaluation of pathological voice production." %%Proceedings Eurospeech '93%, Vol. 3, 1969\--1972. Paola Escudero & Paul Boersma (2004): "Bridging the gap between L2 speech perception and phonological theory." %%Studies in Second Language Acquisition% #26: 551\--585. Gunnar Fant (1960): %%Acoustic Theory of Speech Production.% Mouton, The Hague. James L. Flanagan & L.L. Landgraf (1968): "Self-oscillating source for vocal-tract synthesizers", %%IEEE Transactions on Audio and Electroacoustics% ##AU-16#: 57-64. Reprinted in: James L. Flanagan & Lawrence R. Rabiner (eds.) (1973): %%Speech Synthesis%, Dowden, Hutchinson & Ross, Stroudsburg. The authors show that if we model each vocal cord as a single mass-spring system, the vocal cords will vibrate passively as a result of the interaction with a glottal airflow. Kenzo Ishizaka & James L. Flanagan (1972): "Synthesis of voiced sounds from a two-mass model of the vocal cords", %%Bell System Technical Journal% #51: 1233-1268. Reprinted in: James L. Flanagan & Lawrence R.Rabiner (eds.) (1973): %%Speech Synthesis%, Dowden, Hutchinson & Ross, Stroudsburg. The authors show that if we model each vocal cord as two coupled mass-spring systems, the passive vibration that results from the interaction with a glottal airflow will show more realistic behaviour than with the one-mass model of @@Flanagan & Landgraf (1968)@, at least for a male speaker. W. Jesteadt, G.C. Wier, & D.M. Green (1977): "Intensity discrimination as a function of frequency and sensation level." %%Journal of the Acoustical Society of America% #61: 169\--177. D.H. Klatt & L.C. Klatt (1990): "Analysis, synthesis and perception of voice quality variations among male and female talkers." %%Journal of the Acoustical Society of America% #87: 820\--856. Peter Ladefoged (2001). %%Vowels and consonants%: %%an introduction to the sounds of languages%. Oxford: Blackwell. A very readable introduction to phonetics, mainly acoustic and articulatory. Has lots of spectrograms of the sounds of the world's languages. Comes with a CD that has all those sounds and includes training material for transcription (from another book). For a more encyclopaedic treatment of the sounds of the world's languages, see @@Ladefoged & Maddieson (1996)@ instead. Peter Ladefoged & Ian Maddieson (1996). %%The sounds of the world's languages%. Oxford: Blackwell. An extensive reference source for the articulation and acoustics of `all' vowels and consonants that occur in the world's languages. If you don't find the answer in this book, you will find the answer in the articles referred to in this book. The book uses lots of spectrograms, palatograms, and other techniques. The book is not an introductory text. For that, see @@Ladefoged (2001)@ instead. R. Patterson & F. Wightman (1976): "Residue pitch as a function of component spacing." %%Journal of the Acoustical Society of America% #59: 1450\--1459. Reinier Plomp (1967): "Frequencies dominant in the perception of pitch of complex sounds." %%Journal of the Acoustical Society of America% #42: 191\--198. A. Rosenberg (1971): "Effect of glottal pulse shape on the quality of natural vowels." %%Journal of the Acoustical Society of America% #49: 583\--590. Bruce Tesar & Paul Smolensky (1998): "Learnability in Optimality Theory." %%Linguistic Inquiry% #29: 229\--268. The first version of the constraint-demotion algorithm appeared in: Bruce Tesar & Paul Smolensky (1993): "The learnability of Optimality Theory: an algorithm and some basic complexity results", ms. Department of Computer Science & Institute of Cognitive Science, University of Colorado at Boulder. Available as Rutgers Optimality Archive #2, http://ruccs.rutgers.edu/roa.html The Error-Driven Constraint Demotion algorithm can be found in: Bruce Tesar & Paul Smolensky (1996): "Learnability in Optimality Theory (long version)". Technical Report ##96-3#, Department of Cognitive Science, Johns Hopkins University, Baltimore. Available as Rutgers Optimality Archive #156, http://ruccs.rutgers.edu/roa.html Lei Willems (1986): "Robust formant analysis." %%IPO report% #529: 1\--25. Eindhoven: Institute for Perception Research. Archangeli & Pulleyblank (1994) ppgb Boersma (1993) Boersma (1997a) Boersma (1997b) Boersma (1998) Boersma (2000) Boersma & Hayes (2001) Boersma & Kovacic (to appear) Childers (1978) Deliyski (1993) Escudero & Boersma (2004) Fant (1960) Flanagan & Landgraf (1968) Ishizaka & Flanagan (1972) Jesteadt, Wier & Green (1977) Klatt & Klatt (1990) Ladefoged (2001) Ladefoged & Maddieson (1996) Patterson & Wightman (1976) Plomp (1967) Rosenberg (1971) Tesar & Smolensky (1998) Willems (1986) ? s s s s ňs eAPraatTests _ CheckRandom1009_2009 TimeRandomFraction TimeSort %.20g %.6g nanoseconds xs Js s s s s s 's Us s s ]s s ؗs s ؙs s s s s s s hs s s ~s s s s סs qs ~s Ys gs ts s Os ͦs ݦs s s s s qs s es us s s ys Ss Bs \s {s s s Us s Rs s s s {s s 3s Vs s 7s s s !s ]s s ѿs s s This tutorial describes how you can do voice analysis with P\s{RAAT}. To understand this tutorial, you have to be familiar with the @Intro, which describes the more general features of the @SoundEditor window. Most of P\s{RAAT}'s voice analysis methods start from the glottal pulses that are visible in the @SoundEditor window as blue vertical lines through the waveform. If you do not see these lines, choose @@Show pulses@ from the #Pulses menu. If your sound is long, you may have to zoom in in order to see the separate pulses. You may notice that for some sounds, the time location of the pulses can vary when you zoom or scroll. This is because only the visible part of the sound is used for the analysis. The measurement results will also vary slightly when you zoom or scroll. The Pulse menu contains the command @@Voice report@, which will show in the Info window the results of many voice measurements for the visible part of the selection (or for the visible part of the whole sound, if there is a cursor instead of a selection or if the selection is not visible). In general, you will want to be careful about the pitch range. The standard range is 75\--600 Hertz, but take a range of e.g. 50\--200 Hertz for pathological male voices if that is the typical range. The `advanced' pitch settings like %%silence threshold% and %%octave jump cost% can stay at their standard values. @@Voice 1. Voice breaks@ @@Voice 2. Jitter@ @@Voice 3. Shimmer@ @@Voice 4. Additive noise@ (HNR, harmonicity) @@Voice 5. Comparison with other programs@ @@Voice 6. Automating voice analysis with a script@ Normal voices can easily maintain phonation for some time when saying [a]. Some pathological voices have trouble with it. This can be measured in P\s{RAAT} in two ways. Fraction of locally unvoiced pitch frames This is the fraction of pitch frames that are analysed as unvoiced (MDVP calls it DUV). If the pitch floor is 75 Hz, your Sound editor window will contain pitch measurements that are 0.01 seconds apart, so that if you select one second, there will be 100 pitch frames. If 86 of these are locally voiced, the Fraction will be 14 percent. The usual pitch analysis contains a %%path finder% that searches for a smooth path through the local pitch candidates. This path finder is temporarily switched off to determine the fraction of locally unvoiced frames. A frame is regarded as %locally unvoiced if it has a voicing strength below the %%voicing threshold% (whose standard value is 0.45), or a local peak below the %%silence threshold% (whose standard value is 0.03). In the voice report, the fraction of unvoiced frames will be reported as follows: Fraction of locally unvoiced frames: 14.000\% (14/100) The numbers between parentheses are the number of unvoiced frames and the total number of frames, respectively (in MDVP, these are called NUV and SEG, respectively). The normative value for the fraction of unvoiced frames is 0, i.e., normal healthy voices should have no trouble maintaining voicing during a sustained vowel. Every non-zero value can be considered a sign of pathology (like a common cold). Naturally, you will not select the leading and trailing silences when measuring this parameter. Number of voice breaks The number of distances between consecutive pulses that are longer than 1.25 divided by the pitch floor. Thus, if the pitch floor is 75 Hz, all inter-pulse intervals longer than 16.6667 milliseconds are regarded as voice breaks. Degree of voice breaks This is the total duration of the breaks between the voiced parts of the signal, divided by the total duration of the analysed part of the signal (MDVP calls it DVB). Since silences at the beginning and the end of the signal are not considered breaks, you will probably not want to select these silences when measuring this parameter. In the voice report, the degree of voice breaks will be reported like this: Degree of voice breaks: 29.529\% (1.163061 s / 3.938685 s) The numbers between parentheses are the total duration of the voice breaks and the duration of the analysed part of the signal, respectively. You can measure jitter in the Sound editor window, after choosing @@Show pulses@ from the #Pulses menu. You will see blue lines that can be thought of as representing the glottal closures. Use the Pulse menu to get the jitter in the selected part. You typically perform jitter measurements only on long sustained vowels. The voice report gives five kinds of jitter measurements. Jitter (local) This is the average absolute difference between consecutive periods, divided by the average period. MDVP calls this parameter %Jitt, and gives 1.040\% as a threshold for pathology. Jitter (local, absolute) This is the average absolute difference between consecutive periods. MDVP calls this parameter %Jita, and gives 83.200 \mus as a threshold for pathology. Jitter (rap) This is the Relative Average Perturbation, the average absolute difference between a period and the average of it and its two neighbours, divided by the average period. MDVP gives 0.680\% as a threshold for pathology. Jitter (ppq5) This is the five-point Period Perturbation Quotient, the average absolute difference between a period and the average of it and its four closest neighbours, divided by the average period. MDVP calls this parameter %PPQ, and gives 0.840\% as a threshold for pathology. Jitter (ddp) This is the average absolute difference between consecutive differences between consecutive periods, divided by the average period. This is P\s{RAAT}'s original ##Get jitter#. The value is three times RAP. You can measure shimmer in the Sound editor window, after choosing @@Show pulses@ from the #Pulses menu. You will see blue lines that can be thought of as representing the glottal closures. Use the Pulse menu to get the shimmer in the selected part. You typically perform shimmer measurements only on long sustained vowels. The voice report gives six kinds of shimmer measurements. Shimmer (local) This is the average absolute difference between the amplitudes of consecutive periods, divided by the average amplitude. MDVP calls this parameter %Shim, and gives 3.810\% as a threshold for pathology. Shimmer (local, dB) This is the average absolute base-10 logarithm of the difference between the amplitudes of consecutive periods, multiplied by 20. MDVP calls this parameter %ShdB, and gives 0.350 dB as a threshold for pathology. Shimmer (apq3) This is the three-point Amplitude Perturbation Quotient, the average absolute difference between the amplitude of a period and the average of the amplitudes of its neighbours, divided by the average amplitude. Shimmer (apq5) This is the five-point Amplitude Perturbation Quotient, the average absolute difference between the amplitude of a period and the average of the amplitudes of it and its four closest neighbours, divided by the average amplitude. Shimmer (apq11) This is the 11-point Amplitude Perturbation Quotient, the average absolute difference between the amplitude of a period and the average of the amplitudes of it and its ten closest neighbours, divided by the average amplitude. MDVP calls this parameter %APQ, and gives 3.070\% as a threshold for pathology. Shimmer (ddp) This is the average absolute difference between consecutive differences between the amplitudes of consecutive periods. This is P\s{RAAT}'s original ##Get shimmer#. The value is three times APQ3. For a signal that can be assumed periodic (i.e., a sustained vowel), the signal-to-noise ratio equals the harmonics-to-noise ratio, which you get can get by selecting a Sound and choosing one of the "To Harmonicity..." commands from the Periodicity menu (for the algorithm, see @@Sound: To Harmonicity (ac)...@ or @@Sound: To Harmonicity (cc)...@). These are the world's most sensitive HNR measurements (up to 90 dB). For more information, see the @Harmonicity manual page. Voicing, jitter, and shimmer measurements made by P\s{RAAT} cannot always be compared directly with those made by other programs such as MDVP. The causes are the voicing decision strategy and the accuracy of period and peak determination. Voicing decision strategy Different programs use very different methods for deciding whether an irregular part of the signal is voiced or not. A comparison of @@Boersma (1993)@ for P\s{RAAT} and @@Deliyski (1993)@ for MDVP leads to the following considerations. Both P\s{RAAT} and MDVP use an autocorrelation method for pitch analysis, but MDVP quantizes the amplitudes into the values -1, 0, and +1 before computing the autocorrelation, whereas P\s{RAAT} uses the original amplitude. Also, P\s{RAAT} corrects the autocorrelation function by dividing it by the autocorrelation function of the window, unlike any other program. Lastly, P\s{RAAT} uses sinc interpolation to compute an accurate estimate of the height of the autocorrelation peaks, unlike any other program. All three of these differences (and there are more) influence the measurement of the height of the autocorrelation peak at 1/F0. This height is generally taken as a criterion for voicing: if it is more than the %%voicing threshold% (which you can change with @@Pitch settings...@, the frame is considered voiced, otherwise voiceless. In P\s{RAAT}, the standard voicing threshold is 0.45, in MDVP it is 0.29, which suggests that MDVP tends to regard more frames as voiced than P\s{RAAT}. But the difference between these two numbers may partly be explained by MDVP's failure to correct the autocorrelation function and by MDVP's failure to do an accurate sinc interpolation: both of these failures cause the measured height of the peak at 1/F0 (in MDVP) to be lower than the real height, as explained by @@Boersma (1993)@. Peak determination In a Praat script you usually do not want to raise a Sound window. Instead, you probably want to work with objects in the Objects window only. This page tells you how to do that for voice analysis. 1. Creating the pulses in the Objects window The pulses you see as blue lines are a @PointProcess object. You can see this if you choose ##Extract visible pulses# from the #Pulses menu in the Sound window: a PointProcess object will appear in the list. You can also create a PointProcess in the Objects window directly. To do this, select a Sound and choose @@Sound: To PointProcess (periodic, cc)...@ from the #Periodicity menu. You can also do this in two steps. First you create a Pitch with @@Sound: To Pitch...@ or @@Sound: To Pitch (ac)...@ or @@Sound: To Pitch (cc)...@. Then you select the resulting Pitch %together with the original Sound and choose @@Sound & Pitch: To PointProcess (cc)@. Since the direct method of @@Sound: To PointProcess (periodic, cc)...@ actually uses the AC method for computing the Pitch (which is optimal for intonation analysis), you may prefer the two-step version if your goal is to do voice analysis. In that case, you use @@Sound: To Pitch (cc)...@ as the first step, and @@Sound & Pitch: To PointProcess (cc)@ as the second step. What you should %not do if you want to perform voice analysis is to create the PointProcess by selecting a Pitch only and then choosing @@Pitch: To PointProcess@. In that way, the resulting pulses would not be aligned to the periods in the Sound. 2. Measuring jitter from a script Once you have a PointProcess that represents the periods in the Sound, you can select it and choose some ##Get jitter# commands from the #Query menu. 3. Measuring shimmer from a script Once you have a PointProcess that represents the periods in the Sound, you can select it together with the Sound, then choose some ##Get shimmer# commands from the #Query menu. 4. Getting the whole voice report from a script If you select the Sound, the Pitch, and the PointProcess together (all three), there will be a button that says ##Voice report...#. If you press it, the voice report will be written to the Info window. This is identical to the voice report in the Sound window, although you will have to specify the time range by manually typing it. In a script, you can get the jitter and shimmer from the voice report by doing something like: voiceReport\$ = Voice report... 0 0 75 500 1.3 1.6 0.03 0.45 jitter = extractNumber (voiceReport\$ , "Jitter (local): ") shimmer = extractNumber (voiceReport\$ , "Shimmer (local): ") echo Jitter = 'jitter:3\% ', shimmer = 'shimmer:3\% ' 5. Disadvantage of automating voice analysis In all the commands mentioned above, you have to guess the time range, and you would usually supply "0.0" and "0.0", in which case you will get the average jitter and shimmer for the whole sound. This may include parts of the sound that you are often not interested in, such as false starts. You do not have these problems when asking for a voice report in the sound window, because there you would make an explicit time selection by hand after judging what part of the sound is relevant. A command in the #Pulses menu that will write to the Info window an extensive report about many voice parameters. See the @Voice tutorial. Voice ppgb Voice 1. Voice breaks Voice 2. Jitter Voice 3. Shimmer Voice 4. Additive noise Voice 5. Comparison with other programs Voice 6. Automating voice analysis with a script Voice report $Z `s 0i 4s 4@ $@h㈵>?-DT! @ ?? @ @ &@ ? @ư>AmplitudeTier Sound pressure (Pa) Time (s) <Z s d s AmplitudeTier AmplitudeTier help Help AmplitudeTierEditor Sound pressure (Pa) Sound pressure %4g %4g Pa Set amplitude range... -1.0 +1.0 Minimum amplitude (Pa) Maximum amplitude (Pa) Minimum amplitude Maximum amplitude ? MbP? ?LPC_to_VocalTract: Vocal tract length could not be calculated. 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F?? o? ƾ#?ɒ? 0s?'T ?CΑ?r*#?Y0X5?fu+?/ i?Dh6b?:("* ?tPDTU?p=D?Bˎ?x:kW?RK?w? ?l?Fq??y^?/1Q}?C ?fl WŊ?mnl?ڼ? ?[Mp?tҠ ?1҈?-҆?$@<?h ?o?ҫM2g?_\$? ?恺-? a?2\U#?" N?8*?dq?8?'UD?)b!Ӭʄ?:`.? < ?q?AAp?UUUUUU ? @ @ -DT! @ @@AAp?UUUUUU? $@YY? |? < @ &@ "@ox? @%C<)g =ό'QdK)?ox @aa?gsl_sf__psi.c domain error gsl_sf_psi_int_e(n, &result) gsl_sf_psi_e(x, &result) gsl_sf_psi_1piy_e(x, &result) gsl_sf_psi_1_int_e(n, &result) gsl_sf_psi_n_e(n, x, &result) ? <gsl_sf__pow_int.c overflow gsl_sf_pow_int_e(x, n, &result) UUUUUU?llVgjV? 4w+jV>&D(bIJm=\y NW.e U=hWo7gY<\+:ٗ2; r[m̤-;)&aL9bRޙ\:tee\J;9aG"^ $@ &@ ? ?=, p _7'{O^2@ (@ <-DT! @-DT!? @ <? `e@ .@iW @}<ٰj_? X@ @Z@ @ >@ @ a@ @ 5@ A@ 9B.@gsl_sf__poch.c error domain error overflow gsl_sf_lnpoch_e(a, x, &result) gsl_sf_poch_e(a, x, &result) gsl_sf_pochrel_e(a, x, &result) KtT@UVo'Hҿ'x?of`D.)? tp%GT>,fx$Ux[סi>F ;D9n >.Y; {`R=G;)ၽY4S=^@"(%hjxF<`֍zɼz<'Ӂ osEV5A<xs ? Å! 6WG?` <N[?,: * N(>oǾ"Ju >&1Gnh * :>NGĚ L`ٍ=GïMG67=\BnRp[(,~$=,f}k?P<ơGdՙ{F^n<@s ? < ? ? < r(d? q q? $I$I?UUUUUUſ? пUUUUUU? @ @Z`@H?gsl_sf__log.c domain error gsl_sf_log_e(x, &result) gsl_sf_log_abs_e(x, &result) gsl_sf_log_1plusx_e(x, &result) gsl_sf_log_1plusx_mx_e(x, &result) $@ ? <-DT!@ < ;f?Z`@H? h@ @ 0?\y@Υ?UUUUUU?UUUUUUտ ' @ ? @ox?iAǡd %ܡ^xO~| Nxy >P`ݿuj b'?M. R?, ~@dl$@ *D6V Ǿ?q]n EWSAҠ?^m2?: @"@kSev> 2k;;/cu9m_~ȿ]ȈY?:MT@w툗 @I)@̎*oz*Z wu8P?r@R0+ @p3IwllV*gg쿰bs?NB?|U4@k }WIѿPlc?{@|c3v ]!UUUUUUM*?eR"n@ @SbQ?ײ[դٿ .A? @? 4@gsl_sf__gamma_inc.c error domain error gsl_sf_gamma_inc_P_e(a, x, &result) gsl_sf_gamma_inc_Q_e(a, x, &result) ? ? @ @ 8@ ^@x @ @ @ &A KA _7 A a A 2A (;L4B uwsB uwB 7B s6C h0{C ZAC Ƶ;(D lYaRwND Τ5D {zhRlD !a?@)E ~tE 凗E gi=-F Q[F - n'F 3 VF 3 VIG ! Asb!G " 3xG # ]>H $ H % H & _Tt7I ' daI ( p]I ) Dh,6J * HH J + h9/J , Lp8;K - 3K . KA K / $sPDL 0 ,xL 1 ;DL 2 %{RM 3 G# uM 4 c:M)N 5 Z3cN 6 ;N 7 (I_ O 8 @5&yO 9 a[fO : #L4P ; l]öP < 'WP = ~ϸPQ > 2C3Q ? 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P? ö)$@Ԏشa@]/Qf)@U(+O2NNQ>?P5> ? @ ?dg? <iW @ @ < <S? ץO?(K _RBBu`p?zg|0xo?X)Uߵms?:qiȰ}gij @ λE%?t%52.V cE?VAWTʽc f?z'pS1}?FLqѡ?Ȱ}gij?F8cP\ƚ?g Gjȿl+@?SbQh㈵>-C 6*?MbP?{Gzt?{Gz? @ @ ^@ 8@ @ @ SˆBAAz?}<ٰj_#+ K?88CJ?llfUUUUUU? `e@Γ ?=2D<a?d.In^g׆?q*@71Z?PF9?[? @ $@ .@' @ @{Gz?m0_-DT! @"[ ? HP?-6tY?w,Veq?8!;[T7m ?M %@Qh@jf@%Y?h@X0?%Q[ȓ?\k.<ƙs?y.@&,?N+]?GL""+ @ e dg?UUUUUU? ? (@ @ 0CΕ$?a ` ?Ҽz+9B&@9B.?HP?%(t=ٸM@l-j'?BpOT?C/D"' > 9ŋ¾gC>8\lfW絞:>/ P=zTZCތ=Z& b6=ϙψ }% d< 7n}Dyi<^gkcʠ|9< x.(s ? gsl_sf__gamma.c error overflow domain error underflow gsl_sf_fact_e(n, &result) gsl_sf_lnfact_e(n, &result) gsl_sf_doublefact_e(n, &result) gsl_sf_lndoublefact_e(n, &result) gsl_sf_lngamma_e(x, &result) gsl_sf_gamma_e(x, &result) gsl_sf_gammastar_e(x, &result) gsl_sf_gammainv_e(x, &result) gsl_sf_taylorcoeff_e(n, x, &result) gsl_sf_choose_e(n, m, &result) gsl_sf_lnchoose_e(n, m, &result) ? _ < @ <9B.@Ҽz+# A Uk@9B.v@Ҽz+#v_333333 A..@$ub#Mb`Mb`? @? ? ? UUUUUU?UUUUUU?An=e>O+oB9B@ $gsl_sf__exp.c error overflow underflow domain error gsl_sf_exp_e(x, &result) gsl_sf_exp_mult_e(x, y, &result) gsl_sf_expm1_e(x, &result) gsl_sf_exprel_e(x, &result) gsl_sf_exprel_2_e(x, &result) gsl_sf_exprel_n_e(n, x, &result) wSd@ؙ @Li> @%Ł@*dg?bBP ? @aM7#@M1@m":(@w"@"@ ? @ ?mBP ? < @ @ ? $@ .@ <02?kﴑ[?Ț J??S}iWj{QU?af O?@,r\}2v?ܑT?ܚPCy?(ܖ]lG*t P? @' @ ;f? c?PH:@ۿ ?^?ɔ}/gr?"*UO A~ftj/>0Lo,գ- ?PN>}Xi'> \93F?MK=. ,C=ٚAa˳ȼ <YӤ<AF<U%1t ? ,x0?;?>m¿l A?uУS+ To?XQA^2?uX_,>zcfӾ_[hh>' qSrNp>9BMG{y6*>zw/= '` 9']=X]TWv'Q=~:,sJdCI=W,_ G<t ? ˍ ?vn?C2 N;:*?HW etH> /5<N>TbhYX/!p/A>%jɋj='x1ĽFf%=6b>qO$^F=OC ڥgu< żM<pt ? ? <_ gsl_sf__elementary.c underflow overflow gsl_sf_multiply_e(x, y, &result) ? < @ < @ gsl_sf__beta_inc.c error domain error underflow gsl_sf_beta_inc_e(a, b, x, &result) ?;f?kﴑ[? ? < < I@gsl_sf__beta.c domain error gsl_sf_lnbeta_e(x, y, &result) gsl_sf_beta_e(x, y, &result) @ ? @ < @ _ .@ @ @Z@ @ s@ @},oB ?@ @UUUUUU? @ T@@ @ WA O28A %@88? @},A Tt A jB P#@? $W'B P |B O?D PV B M @UUApt?R Q?y,e(qU F!u O?PR;?mVn7T? \}g?+Tx?P\?DKn? 8@ @ H@ ?-DT! @ [n<+= UUUUUU?V瞯< SA ?V瞯< @UUUUUUMbP? < I@ ? @ ? < ? ?9B@-DT! @ ? @ox < < @An=e> `> @ ? ? @@ ? < @ ? ? mF=DgEZ4V >*?UUUUUUſ ? <( ? @z ֎8u7>gjV A Am? ? .@`TwMtv<R\#'Ť=Q Gf>lUمAA`?$I$I $@iW @ <-DT!?An=e>:n=ey@ P> 0? @ @ ? $@ < < ?An=e> @ ? $@iW @ < < @ ?(\?An=e> ~@ ~@9B&@gsl_sf__bessel_In.c domain error overflow gsl_sf_bessel_In_scaled_e(n, x, &result) gsl_sf_bessel_In_e(n, x, &result) '&`?Ij֡? 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UUUUUU? ? ?9B&@ ?UUUUUU @ @ffffff? < ? ܿ @ @? ? ? seconds to From seconds) (duration: Pitch: Hz Median pitch: Mean pitch: Standard deviation: Minimum pitch: Maximum pitch: Pulses: Number of pulses: Number of periods: Mean period: Standard deviation of period: Voicing: Fraction of locally unvoiced frames: ) / ( Number of voice breaks: Degree of voice breaks: seconds / Jitter: Jitter (local): Jitter (local, absolute): Jitter (rap): Jitter (ppq5): Jitter (ddp): Shimmer: Shimmer (local): dB Shimmer (local, dB): Shimmer (apq3): Shimmer (apq5): Shimmer (apq11): Shimmer (dda): Harmonicity of the voiced parts only: Mean autocorrelation: Mean noise-to-harmonics ratio: Mean harmonics-to-noise ratio: edit GuiText.c MEMBER (me, Text) @@ i@ 0t 1t 1t 2t 63t [3t h3t 3t 3t 3t 4t 4t 4t 4t 5t A5t 5t ^6t 3t v6t 6t 7t 7t ]8t 8t 9t =9t j9t :t :t <t >t ?t 1t @t At Bt Bt Ct #Dt Dt Et Et Ft WFt Ft Gt Gt Ht Ht DIt It It ^Jt Jt Kt Lt "Lt {Lt Lt Mt lNt Ot BPt lQt zQt Rt St St Tt Tt Tt Tt Tt Tt Tt Tt Tt Tt Tt Tt Tt _Vt uVt Wt Wt Yt yZt [t \t ]t ]t 2_t _t _t _t K`t a`t `t `t 3t at 63t dbt wbt K`t bt 3t bt ct dt et gt jt >lt nt ot ot Xqt rt st 4st xst st Utt tt 2ut Qut 3vt jvt wt {t |t }t }t ~t t t ŀt t @ @<[ @ @ =[ bt t Mt ht t t t !t t Ԅt t t Ht t Յt t @t t /t Jt t t ԉt t t "t t t t t t (t ft эt t "t t t t (t t t t 8t \t t t Ȓt t Kt et t t Ót ߓt t t Ct lt t .t t =t Ut ut t t Ϙt t "t [t xt t nt t ӛt t t t Ut t ĝt Ct +t 5t \t t It ɢt t -t Wt t ףt t t t ,t t *t et t t Pt t t t t 5t t t t t nt ݪt t >t t t curve Aliasing (Du. %vouwvervorming) is the phenomenon of the ambiguity of a sampled signal. Example With a sampling frequency of 10 kHz, a sine wave with a frequency of 3 kHz receives the same representation as a sine wave with a frequency of 7 kHz, 13 kHz, or 17 kHz, and so on. If the sampled signal is meant to represent a continuous spectral range starting at 0 Hz (which is the most common case for speech recordings), all these tones are likely to be interpreted as 3 kHz tones after sampling. To remedy this unwanted situation, the signal is usually low-pass filtered with a cut-off frequency just below 5 kHz, prior to sampling. One of the ways to control @Editors. How to click 1. Position the mouse above the object that you want to click. 2. Press and release the (left) mouse button. See also @@Shift-click@. Usage in the Praat program Clicking on an object is used for selecting this object while deselecting all previously selected objects; clicking is also used for moving a cursor hair. Dragging is one of the ways to control @Editors. How to drag 1. Position the mouse above the object that you want to drag. 2. Press the (left) mouse button. 3. Keeping the mouse button pressed, move the mouse across the window. A shadow of the object will follow. 4. Release the mouse button when it is above the location where you want your object to be moved (the %drop %site). If the drop site makes any sense, the object will move there. See also @@Shift-drag@. Dragging is used for manipulating the time and value of one or more marks, targets, or boundaries: An algorithm for fast computation of the Fourier transform of a sampled signal. It involves increasing the number of samples %N to the next-highest power of two, and the computation time scales as %N log %N. In Praat, the Fast Fourier Transform is used: 1. For the Fourier transform of an entire sound: @@Sound: To Spectrum...@ with #yes for the #Fast setting, and @@Spectrum: To Sound@. 2. For the Fourier transform of consecutive frames in a sound. See @@Sound: To Spectrogram...@. 3. For the fast computation of correlations, e.g. in @@Sound: To Pitch (ac)...@. An abbreviation for @@Fast Fourier Transform@. - the end of the @@time domain@ (see there). Frequency is how often something happens in a certain time, for instance the number of times the P\s{RAAT} home page www.praat.org is visited every day. In P\s{RAAT}, frequency is the number of vibration cycles per second. Although one can sometimes see the abbreviation %cps, P\s{RAAT} always uses Hz (short for %Hertz), which means the same. Unfortunately, there are two very distinct kinds of vibrations in speech analysis. For pitch, frequency is the number of glottal cycles per second, and for spectral analysis, frequency is the number of sine wave cycles per second. Quite some bit of the training of an acoustic phonetician goes into the understanding of the difference between the ideas behind F0 and F1, and many years can be spent on understanding the influence they have on each other in production, acoustics, perception, or measurement... In order to prevent confusion, P\s{RAAT} always requires frequency to be expressed in Hz. So if you want to supply a sampling frequency of 20 kiloHertz (20 kHz), you fill in 20000 or 2e4 or 20e3. If you want to switch off pre-emphasis in some spectral analysis, you supply 1 GigaHertz (GHz) for its "from-frequency", by typing 1e9. In P\s{RAAT} editor windows, frequency usually runs from bottom to top, since time already has to run from left to right. This goes for spectrograms, pitch contours, and formant contours. In spectral slices, frequency runs from left to right, since these have no time axis. The %%Nyquist frequency% is the bandwidth of a sampled signal, and is equal to half the sampling frequency of that signal. If the sampled signal should represent a continuous spectral range starting at 0 Hz (which is the most common case for speech recordings), the Nyquist frequency is the highest frequency that the sampled signal can unambiguously represent. If a speech signal is sampled at 22050 Hz, the highest frequency that we can expect to be present in the sampled signal is 11025 Hz. This means that to heed this expectation, we should run the continuous signal through a low-pass filter with a cut-off frequency below 11025 Hz; otherwise, we would experience the phenomenon of @aliasing. Of course, with a sampling frequency of 22050 Hz we could also represent a signal band-limited between, say, 40000 Hz and 51025 Hz, but this seems less useful in speech research. The things that contain the data in the P\s{RAAT} program. The objects are visible in the @@List of Objects@ in the @@Object window@. Most objects are contained in memory: they are %not files! Therefore, you may want to save them with one of the commands from the @@Write menu@ before you @Quit. Exceptions are the LongSound objects in the Praat program and the file-based dictionaries in the ALS program. You can create an object by choosing a command from the @@New menu@ or from the @@Read menu@. When you select one or more objects, you can perform on them the actions that are shown in the @@dynamic menu@, on the ##fixed buttons# below the list of objects, or in the @@Write menu@. You can choose hidden actions with the help of the @ButtonEditor. The average power in a sound during a certain time range and in a certain frequency range, expressed in Pa^2/s. Mathematical definition The %%complex spectrum% of a sound %x(%t) in the time range (%t__1_, %t__2_) is %X(%f) \=3 \in__%%t%1_^^%%t%2^ %x(%t) e^^-2%\pi%ift^ %dt for any frequency %f in the two-sided frequency domain (-%F, +%F). If %x(%t) is expressed in units of Pascal, %X(%f) is expressed in units of Pa/Hz. From the complex spectrum we can compute the %%one-sided power spectral density% in Pa^2/Hz as PSD(%f) \=3 2|%X(%f)|^2 / (%t__2_ - %t__1_) where the factor 2 is due to adding the contributions from positive and negative frequencies. The PSD divides up the total power of the sound. To see this, we integrate it over its entire one-sided frequency domain (0, %F): \in__0_^^%F^ PSD(%f) %df = \in__0_^^%F^ 2|%X(%f)|^2/(%t__2_-%t__1_) %df = = 1/(%t__2_-%t__1_) \in__-%F_^^+%F^ |%X(%f)|^2 %df = 1/(%t__2_-%t__1_) \in__%%t%1_^^%%t%2^ |%x(%t)|^2 %dt where the last step uses %%Parceval's theorem%. The result is precisely the average power of the sound in the time range (%t__1_, %t__2_). The logarithmic power spectral density It is often useful to express the power spectral density in dB relative to %%P__ref_% = 2\.c10^^-5^ Pa: PSD__dB_(%f) = 10 log__10_ { PSD(%f) / %%P__ref_%^2 } Since the argument of the logarithm is in units of Hz^^-1^, this spectral measure can loosely be said to be in units of `dB/Hz'. P\s{RAAT} shows this spectral measure in pictures of a @Spectrum; it is also the units in which an @Ltas and a @Spectrogram are expressed. Pitch-Synchronous Overlap and Add, a method for manipulating the pitch and duration of an acoustic speech signal. PSOLA synthesis When a @Sound is created from a @Manipulation object, the following steps are performed: 1. From the @PitchTier, new points are generated along the entire time domain, with the method of @@PitchTier: To PointProcess@. 2. The period information in the pulses is used to remove from the new %pulses all points that lie within voiceless intervals (i.e., places where the distance between adjacent points in the original %pulses is greater than 20 ms. 3. The voiceless parts are copied from the source Sound to the target Sound, re-using some parts if the local duration is greater than 1. 4. For each %target point, we look up the nearest source point. A piece of the source Sound, centred around the source point, is copied to the target Sound at a location determined by the target point, using a bell-shaped window whose left-hand half-length is the minimum of the left-hand periods adjacent to the source and target points (and analogously for the right-hand half-length). An algorithm to compute the specified quantile of a sorted array of real numbers. The %n\% %quantile of a continuous real-valued distribution is the value below which %n\% of the values is expected to lie. If we are given an array of real numbers that we want to interpret as having been drawn from a distribution, we can %estimate the quantiles of the underlying distribution. 1. The median The %median is a special case of a quantile: it is the 50\% quantile. It is usually estimated as follows: from an odd number of values, take the middle value; form an even number, take the average of the two midmost values. For instance, if our values are 15, 20, and 32, the median is 20; if our values are 15, 20, 32, and 60, the median is 26. This estimate is direction-independent: if we multiply all values by -1 (i.e., they become -60, -32, -20, and -15), the median is also multiplied by -1 (it becomes -26). 2. Percentiles? The %%n%th %percentile of a set of values is usually defined as the highest attested value for which at most %n\% of all attested values are less or equal. For instance, if our values are 15, 20, 32, and 60, the 30th percentile is 15. Here is an extensive list: Percentile number Value 0 - 10 - 20 - 30 15 40 15 50 20 60 20 70 20 80 32 90 32 100 60 However, this procedure does not yield an estimate of the quantiles of the underlying distribution. For instance, the estimate is direction-dependent: if we multiply all values by -1, the 50th percentile becomes -32 instead of -20, and the 70th percentile becomes -32 instead of the expected -15, which is minus the 30th percentile of the original data set. 3. Unbiased quantiles To get a better estimate of the quantiles of the underlying distribution, the interpolation that we used to determine the median, is generalized to %any quantile. We assume that the attested values 15, 20, 32, and 60 each take up one quarter of the "quantile space". These four values are in the middles of those quarters, so they are at the 0.125, 0.375, 0.625, and 0.875 quantiles. Quantiles in between 0.125 and 0.875 are evaluated by linear interpolation: the 0.25, 0.50, and 0.75 quantiles are 17.5, 26, and 46, respectively. Note that the 0.50 quantile is the median. The 0.40 quantile, for example, is estimated as 20 + (32 - 20)\.c(0.40 - 0.375)/(0.625 - 0.375) = 21.2. Quantiles between 0 and 0.125 or between 0.875 and 1 are evaluated by linear extrapolation from the lowest or highest pair of values: the 0\% quantile is estimated as 15 - 1/2 (20 - 15) = 12.5, and the 100\% quantile is estimated as 60 + 1/2 (60 - 32) = 74. The 0.10 quantile is estimated as 12.5 + (15 - 12.5)\.c(0.10 - 0.0)/(0.125 - 0.0) = 14.5. Note that the estimated values for the very low or high quantiles can lie outside the range of attested values. In fact, the computed 0\% and 100\% quantiles are thought to be estimates of the minimum and maximum values of the distribution. For uniform distributions, these estimates are reasonable; for a normal distribution, of course, the 0\% and 100\% quantiles are meaningless. The sampling frequency (or %%sample rate%) is the number of samples per second in a @Sound. For example: if the sampling frequency is 44100 Hertz, a recording with a duration of 60 seconds will contain 2,646,000 samples. Usual values for the sampling frequency are 44100 Hz (CD quality) and 22050 Hz (just enough for speech, since speech does not contain relevant frequencies above 11025 Hz; see @aliasing). To get the sampling frequency of a selected #Sound, click #Info or choose @@Get sampling frequency@. The sampling period is the time difference between two consecutive samples in a @Sound. It is the inverse of the @@sampling frequency@. For example: if the sampling frequency is 44100 Hz, the sampling period is 1/44100 = 2.2675736961451248e-05 seconds: the samples are spaced approximately 23 microseconds apart. To get the sampling period of a selected #Sound, click #Info or choose @@Get sampling period@. Shift-dragging is one of the ways to control @Editors. How to Shift-drag 1. Position the mouse above any of the objects that you want to drag (the objects were probably selected first). 2. Press a Shift key. 3. Press the (left) mouse button. 4. Keeping the mouse button pressed, move the mouse across the window. A shadow of the objects will follow. 5. Release the mouse button when it is above the location where you want your objects to be moved. If this %%drop site% makes any sense, the objects will move there. While plain @@drag@ging is used for moving objects that were selected first by clicking, ##Shift-dragging# is used for manipulating the times and values of more marks, targets, or boundaries simultaneously: How to Shift-click 1. Position the mouse above the object that you want to Shift-click. 3. Press and release the (left) mouse button. Whereas plain @@click@ing is used for selecting only one object while deselecting all previously selected objects, ##Shift-click# is used for selecting a mark, target, or boundary, %without deselecting the previously selected objects: Your computer's sound-recording software returns integer values between -32768 and 32767. Praat divides them by 32768 before putting them into a Sound object, so that the values in the Sound objects are always between -1 and +1. The Praat program considers these numbers to be air pressures in units of Pascal. These values in Pascal are probably not the actual true air pressures that went into the microphone. To determine what the actual air pressures were, you have to record an extra sound with a known air pressure, with the same recording gain as the rest of your recordings. It is best if this extra sound is something like a white noise, so that its @@sound pressure level@ can be determined reliably. A sine wave of 400 Hz, for instance, is less suitable, since its sound pressure level at your microphone can depend very strongly on the precise position and direction of the loudspeaker and on the position of other objects (like you, the experimenter) in the room (differences of 10 dB are no exception). For example, suppose that you record some speech on a CD recorder or with Praat's SoundRecorder. Immediately before or after this recording, you also record a white noise produced by a noise generator. With a dB meter (Linear or C setting), located at the same position as the microphone of the recording, you measure that the Sound Pressure Level of this noise is 76.5 dB. When you later open the recorded noise in Praat's sound window, Praat tells you that its average intensity (switch on ##Show intensity#) is 68.6 dB. You then know that you have to add 7.9 dB to intensities measured in Praat to get at the true sound pressure level. Thus, if your speech contains a long [a:] whose average intensity is measured in the Sound window as 71.1 dB, its true sound pressure level must be 79.0 dB. In this example, you can make Praat's sound window show the true sound pressures in Pascal and true sound pressure levels in dB, if you multiply the sound with a factor of 10^^(7.9/20)^, which you can do by selecting the Sound and choosing ##Multiply...# from the #Modify menu, then supplying $$10\^ (7.9/20)$ as the multiplication factor. Air pressures are measured in Pascal (Pa), which are Newtons per square metre (N/m^2). The ambient air pressure is about 100,000 Pa, and the lungs modify this in phonation only by a small amount, namely 200 to 1000 Pa (= 2 to 10 cm H__2_O). Outside your body, the air pressures caused by your speech are much smaller again, namely 0.01 to 1 Pa at 1 metre from your lips. These are comparable to the values that you see for a typical speech recording in Praat's sound window, although these numbers in Praat can be interpreted as true air pressures only if you perform a @@sound pressure calibration@ (including the multiplication). A normative human ear can detect a root-mean-squared air pressure as small as 0.00002 Pa, for a sine wave with a frequency of 1000 Hz. The %%sound pressure level% can be expressed in dB relative to this normative threshold: SPL = 10 log__10_ { 1/(%t__2_-%t__1_) \in__t1_^^t2^ %x^2(%t) %dt / (2\.c10^^-5^ Pa)^2 } where %x(%t) is the sound pressure in Pa as a function of time, and %t__1_ and %t__2_ are the times between which the energy (squared air pressure) is averaged. For a calibrated sound, Praat's sound window will show you the SPL as a function of time, if you switch on ##Show intensity# and set its ##averaging method# to #energy (with ##Intensity settings...#). A representation (of a sound signal, for instance) as some sort of intensity as a function of @time and @frequency. In P\s{RAAT}, we have the @Spectrogram, which is acoustic energy density as a function of time in seconds and frequency in Hz, and the @Cochleagram, which is basilar membrane excitation as a function of time in seconds and frequency in Bark. For tutorial information, see @@Intro 3.1. Viewing a spectrogram@. - the beginning of the @@time domain@ (see there). A stereo sound is a sound consisting of a left and a right channel. Reading a stereo sound from disk If you read a @Sound into Praat from disk with @@Read from file...@, and that sound file is a stereo file, Praat will combine the two channels into one and warn you that it has done that. If you want to read both channels into Praat separately, you use @@Read two sounds from stereo file...@. If you want to see and listen to both channels into Praat together, you use @@Open long sound file...@, then #View. Writing a stereo sound to disk If you have two @Sound objects that you want to regard as the two channels of a stereo sound, you can select them both together and chose @@Write to stereo WAV file...@ (or any of the other file types) from the @@Write menu@. In normal life, time is how late the watch says it is. In P\s{RAAT}, this definition is largely irrelevant. Sound files rarely tell us the absolute time of recording. So when you read a sound file into P\s{RAAT} and click #Edit, you will see that the Sound starts at a time of 0 seconds, and if its duration is 3.5 seconds, you will see that the Sound finishes at a time of 3.5 seconds. Besides sounds, many other types of objects in P\s{RAAT} have a time scale as well: spectrograms, pitch contours, formant contours, point processes, and so on. None of these are required to have a time domain that starts at 0 seconds. In the Sound editor window, for example, you can select the part that runs from 1.4. to 1.7 seconds, and "extract" it to the Objects window while "preserving the times". The resulting Sound object will have a starting time of 1.4 seconds and a finishing time of 1.7 seconds, as you can see when you click #Edit. Spectrograms and pitch contours that you create from this sound will also have a time domain from 1.4 to 1.7 seconds. This time domain is preserved if you save these objects to a text file or to a binary file and read them into P\s{RAAT} again later. Only if you save the Sound object to an audio file (WAV, AIFF), the time information is not preserved in that file; if you read such an audio file into P\s{RAAT} again, the time domain of the new Sound object will run from 0 to 0.3 seconds. In order to prevent confusion, P\s{RAAT} always requires times to be expressed in seconds. So if you want to supply a window length of 5 milliseconds (5 ms), you fill in 0.005 or 5e-3. For 83.2 microseconds (83.2 \mus), you say 0.0000832, or better 83.2e-6 or 8.32e-5. On a clock, time runs around in circles. In P\s{RAAT}'s editor windows, time runs from left to right. You can often see only a part of the time scale in the window. To see another part, you %scroll backward or forward. This manual page assumes that you have read the @Intro. Many objects in Praat are %%functions of time%. Examples are: @Sound, @Pitch, @Spectrogram, @Formant, @Intensity, @TextGrid, @PitchTier, @DurationTier, @Harmonicity, @PointProcess. In Praat, these functions have a contiguous ##time domain#, i.e. a single time stretch with a @@starting time@ and a @@finishing time@. The @@total duration@ of such a function is the difference between the starting time and the finishing time. There are up to five ways to see the time domain of an object. The time domain in editor windows If you select an object that is a function of time and click #Edit, an editor window will appear on the screen. The rectangle at the bottom will show the starting time, the finishing time, and the total duration. The time domain in the picture window If you select an object that is a function of time and choose one of the #Draw commands, the settings window invites you to supply a time range. If you keep this time range at its standard setting (from 0.0 to 0.0 seconds), Praat will draw the object for the whole time domain and print the starting time and the finishing time below the horizontal axis (if #Garnish is on): The time domain in the Info window If you select an object that is a function of time and click #Info, the Info window will tell you the starting time, the finishing time, and the total duration (among other properties of the object). Time domain query commands If you select an object that is a function of time, the following three commands will become available in the #Query menu: ##Get starting time ##Get finishing time ##Get total duration If you choose one of these commands, the Info window will tell you the result, expressed in seconds. These commands are most useful in a Praat script. Example: select Pitch hello startingTime = Get starting time finishingTime = Get finishing time centreTime = (startingTime + finishingTime) / 2 echo This Pitch runs from 'startingTime' to 'finishingTime' seconds, printline and the centre of its time domain is at 'centreTime' seconds. Details for hackers If you select an object that is a function of time and you click @Inspect, you can see how the time domain information is stored in the object: the starting time is the object's #xmin attribute and the finishing time is its #xmax attribute. The total duration is not stored in the object, since it can easily be computed as #xmax minus #xmin. The ways to select a part of the time domain in some @editors in Praat, namely those that contain a function of time. The ##time selection# is used for selecting the time interval that will be played, copied, cut, modified, or questioned: 1. How to make a selection The easiest way is to @drag the mouse across the part that you want to select. This is analogous to how selection works in a text processor. 2. How to extend or shrink a selection The easiest way is to click with the Shift key pressed. The nearest edge of the selection will move to the time position where you clicked. This is analogous to how extending a selection works in a text processor. For instance, if the currently selected time interval runs from 2 to 5 seconds, and you shift-click at a time position of 4 seconds, the end of the selection will move from 5 to 4 seconds, thus shrinking the selection. You can also shift-drag, i.e. hold the Shift key and the mouse button down while moving the mouse. 3. Other tricks To select a specific time stretch or collapse the selection to its start or end, use the Select menu. - the extent of the @@time domain@ (see there). An algorithm for finding a maximum or a minimum in a sampled signal. Overview The signal is described with the sequence %y__%i_, %i = 1...%n, where %n is the number of samples. Each sample %i is associated with an %x value (typically, time) given by %x__%i_ = %x__1_ + (%i - 1) %dx, where %dx is the sample period. The maximum is looked for in two kinds of locations: 1. At the left and right edge, i.e. at %i = 1 and at %i = %n. 2. At or %near all local maxima, i.e. at or %near those %i that satisfy %y__%i-1_ < %y__%i_ \<_ %y__%i+1_. The greatest of the following values, therefore, will be the maximum: 1. %y__1_. 2. The local maxima, which are at or %near %y__%i_, where %y__%i-1_ < %y__%i_ \<_ %y__%i+1_. 3. %y__%n_. We will now see what %near means. The precision of the result depends on the %%interpolation method% of this algorithm. 1. Lowest precision: round to sample If the interpolation method is None, the local maxima are %at the samples %m that satisfy %y__%m-1_ < %y__%m_ \<_ %y__%m+1_. Thus, their %x values are at %x__%m_ = %x__1_ + (%m - 1) %dx, and their %y values are %y__%m_. This kind of precision is appropriate for an unordered sequence of values %y__%i_: the result is simply the greatest available value. 2. Middle precision: parabolic interpolation If the interpolation method is Parabolic, the algorithm uses one point on each side of every local maximum %y__%m_ to estimate the location and value of the local maximum. Because a Taylor expansion shows that any smooth curve can be approximated as a parabola in the vicinity of any local maximum, the location %x__%max_ and value %y__%max_ can be found with the following procedure: %dy \=3 1/2 (%y__%m+1_ - %y__%m-1_) %d^2%y \=3 2 %y__%m_ - %y__%m-1_ - %y__%m+1_ %m\'p \=3 %m + %dy/%d^2%y %x__%max_ = %x__1_ + (%m\'p - 1) %dx %y__%max_ = %y__%m_ + 1/2 %dy^2 / %d^2%y This kind of precision is appropriate if %y is considered a smooth function of %x, as in: @@Formant: Get minimum... @@Formant: Get time of minimum... @@Formant: Get maximum... @@Formant: Get time of maximum... @@Intensity: Get minimum... @@Intensity: Get time of minimum... @@Intensity: Get maximum... @@Intensity: Get time of maximum... 3. Higher precision: cubic interpolation If the interpolation method is Cubic, the interpolation is performed over four points (see @@vector value interpolation@). The results are similar to those of the parabolic interpolation method, but you can use it (or sinc interpolation) if you want the result of a command like ##Get maximum...# to be equal to the result of a sequence of commands like ##Get time of maximum...# and ##Get value at time...#. 4. Highest precision: sinc interpolation If the interpolation method is Sinc70 or Sinc700, the algorithm assumes that the signal is a sum of sinc functions, so that a number of points (namely, 70 or 700) on each side of the initial guess %m must be taken into account (see @@vector value interpolation@). The algorithm finds the maximum of this continuous function by Brent's method (see @@Press et al. (1992)@). This method is appropriate for signals that result from sampling a continuous signal after it has been low-pass filtered at the @@Nyquist frequency@. See: @@Sound: Get minimum... @@Sound: Get time of minimum... @@Sound: Get maximum... @@Sound: Get time of maximum... @@Sound: Get absolute extremum... An algorithm for estimating the value of a sampled signal at a specified location. The signal is described with the sequence %y__%i_, %i = 1...%n, where %n is the number of samples. Each sample %i is associated with an %x location (typically, time) given by %x__%i_ = %x__1_ + (%i - 1) %dx, where %dx is the sample period, so that the real-valued sample number associated with a given time %x is %s = (%x - %x__1_) / %dx + 1 If the resulting %s is an integer number, the %y value must be %y__%s_. Otherwise, the estimated %y value %y(%s) must be interpolated from nearby values of %y. The precision of the result depends on the %%interpolation method% of this algorithm. If the interpolation method is Nearest, we take the value of the nearest point: %near \=3 round (%s) %y(%s) \~~ %y__%near_ 2. Middle precision: linear interpolation If you know or assume that the function that underlies your points is continuous, the "rounding" interpolation would be poor, because the rounded value would abruptly change at the centres between the sample points. For a linear interpolation, therefore, we use the attested values on both sides (%left and %right) of %s: %s__%l_ \=3 floor (%s) ; %s__%r_ \=3 %s__%l_ + 1 %y(%s) \~~ %y__%l_ + (%s - %s__%l_) \.c (%y__%r_ - %y__%l_) where #floor (%x) computes the greatest integer not greater than %x. This interpolation is continuous. If you know or assume that the function that underlies your points is %smooth, i.e. its derivative is defined for every %x, linear interpolation would probably be poor, because the derivative of the interpolated function would abruptly change at every sample point. The next higher interpolation (Cubic), therefore, is differentiable at sample points. To enforce this, we define the derivatives %y\'p__%l_ and %y\'p__%r_ at the left and right sample points on the basis of %their immediate neighbours (i.e., the algorithm needs four sample points), perhaps by a parabolic interpolation through these three points. A parabolic interpolation has the advantage that the extrema will be computed correctly if the underlying function can be approximated by a parabola near its extremes (see @@vector peak interpolation@). Because the derivative of a parabolic function is a linear function of %x, the derivatives at the left and right sample points are simply estimated as %y\'p__%l_ \~~ (%y__%r_ - %y__%l-1_) / 2 ; %y\'p__%r_ \~~ (%y__%r+1_ - %y__%l_) / 2 Now that we know %y__%l_, %y__%r_, %y\'p__%l_, and %y\'p__%r_, we can fit these values with a third-degree (%cubic) polynomial: %As__%l_^3 + %Bs__%l_^2 + %Cs__%l_ + %D = %y__%l_ %As__%r_^3 + %Bs__%r_^2 + %Cs__%r_ + %D = %y__%r_ 3%As__%l_^2 + 2%Bs__%l_ + %C = %y\'p__%l_ 3%As__%r_^2 + 2%Bs__%r_ + %C = %y\'p__%r_ If we shift the %x axis to the left sample point, we can reduce the four equations to %D = %y__%l_ %A + %B + %C + %D = %y__%r_ %C = %y\'p__%l_ 3%A + 2%B + %C = %y\'p__%r_ so that the interpolated value %y(%s) at any point %s between %s__%l_ and %s__%r_ is estimated as (%y\'p__%r_ + %y\'p__%l_ - 2%y__%r_ + 2%y__%l_) %\fi__%l_^3 + (3%y__%r_ - 3%y__%l_ - 2%y\'p__%l_ - %y\'p__%r_) %\fi__%l_^2 + %y\'p__%l_ %\fi__%l_ + %y__%l_ where %\fi__%l_ \=3 %s - %s__%l_. Some rearrangement gives %y(%s) \~~ %y__%l_ %\fi__%r_ + %y__%r_ %\fi__%l_ + - %\fi__%l_ %\fi__%r_ [1/2 (%y\'p__%r_ - %y\'p__%l_) + (%\fi__%l_ - 1/2) (%y\'p__%l_ + %y\'p__%r_ - 2(%y__%r_ - %y__%l_))] where %\fi__%r_ \=3 1 - %\fi__%l_. From this formula we see: 1. The first two terms define the linear interpolation. 2. If the underlying function is linear, so that %y\'p__%l_ equals %y\'p__%r_ and both equal %y__%r_ - %y__%l_, the higher-degree terms are zero. 3. If %y\'p__%l_ + %y\'p__%r_ equals 2(%y__%r_ - %y__%l_), the third-degree term is zero, so that the interpolated function is parabolic. 4. At the left and right points, one of the %\fi is 0 and the other is 1, so that at these boundary points, %y is computed with exact precision. If the interpolation method is Sinc70 or Sinc700, the algorithm assumes that the signal is a sum of sinc functions, so that a number of points (the %%interpolation depth%: 70 or 700) on each side of %s must be taken into account. Because the interpolation depth must be finite, the sum of sinc functions is multiplied by a Hanning window: %s__%l_ \=3 floor (%s); %s__%r_ \=3 %s__%l_ + 1 %\fi__%l_ \=3 %s - %s__%l_; %\fi__%r_ \=3 1 - %\fi__%l_ %y(%s) \~~ \su__%i=1...%N_ %y__%r-%i_ sinc (%\pi(%\fi__%l_+%i-1)) (1/2 + 1/2 cos (%\pi(%\fi__%l_+%i-1)/(%\fi__%l_+%N))) + + \su__%i=1...%N_ %y__%l+%i_ sinc (%\pi(%\fi__%r_+%i-1)) (1/2 + 1/2 cos (%\pi(%\fi__%r_+%i-1)/(%\fi__%r_+%N))) where the sinc function is defined as sinc (0) \=3 1; sinc (%x) \=3 sin %x / %x for %x \=/ 0 If %s is less than the interpolation depth or greater than %n + 1 minus the interpolation depth, the depth is reduced accordingly. @@Sound: Get value at time... aliasing ppgb Click Drag Fast Fourier Transform FFT finishing time frequency Nyquist frequency objects power spectral density PSOLA quantile algorithm sampling frequency sampling period Shift-drag Shift-click sound pressure calibration sound pressure level spectro-temporal representation starting time stereo time time domain time selection total duration vector peak interpolation vector value interpolation t ۵t t "t t t -t At t t t t t øt t t mt ιt 6t >t Nt t vt t t -t t mt Իt 6t Vt gt t t 't 1t t t Ƚt t Ht jt t vt t t -t t mt t t t -t qt t t 6t t /t t vt Vt }t -t t t t 6t Vt 0t t ft 't t Qt dt t t t t t vt t }t -t t t t -t t t t -t Zt A command that becomes available in the #Query menu if you select a @Sound object. The Info window will tell you the @@sampling period@ in seconds. Usage You will not often choose this command with the mouse, since the sampling period is included in the information that you get by clicking the #Info button. This command is probably more useful in a Praat script: select Sound hello samplingPeriod = Get sampling period Details for hackers With @Inspect, you can see how the sampling period is stored in a #Sound object: it is the #dx attribute. The Info window will tell you the @@sampling frequency@ in Hertz. You will not often choose this command with the mouse, since the sampling frequency is included in the information that you get by clicking the #Info button. This command is probably more useful in a Praat script: samplingFrequency = Get sampling frequency Algorithm The sampling frequency is defined as 1 / (\De%t), where \De%t is the @@sampling period@. See @@Get sampling period@. A command that becomes available in the #Query menu if you select a @Sound or @LongSound object. The Info window will tell you the time (in seconds) associated with the sample number that you specify. Setting %%Sample number the sample number whose time is sought. the result is %t__1_ + (%sample_number - 1) \.c \De%t where %t__1_ is the time associated with the first sample, and \De%t is the sampling period. If you select a Sound or LongSound and click @Inspect, you can see how the relation between sample numbers and times is stored in the object: %t__1_ is the #x1 attribute, and \De%t is the #dx attribute. The Info window will tell you the sample number belonging to the time that you specify. The result is presented as a real number. %%Time (seconds) the time for which you want to know the sample number. Example If the sound has a sampling frequency of 10 kHz, the sample number associated with a time of 0.1 seconds will usually be 1000.5. Scripting You can use this command to put the nearest sample number into a script variable: select Sound hallo sampleNumber = Get sample number from time... 0.1 nearestSample = round (sampleNumber) In this case, the value will not be written into the Info window. To round down or up, use leftSample = floor (sampleNumber) rightSample = ceiling (sampleNumber) 1 + (%time \-- %t__1_) / \De%t The Info window will tell you the total number of time samples in this object. If the sampling frequency is 44100 Hertz, a recording with a duration of 60 seconds will contain 2,646,000 samples. If you select a Sound or LongSound and click @Inspect, you can see how the number of samples is stored in the object: it is the #nx attribute. A command that becomes available in the #Query menu if you select a sound-analysis object that is a function of time and that is evenly sampled in time (@Pitch, @Formant, @Intensity, @Harmonicity). The Info window will tell you the time associated with the frame number that you specify. %%Frame number the frame number whose time is sought. %t__1_ + (%frame_number - 1) \.c \De%t where %t__1_ is the time associated with the centre of the first frame, and \De%t is the time step. If you select one of the above objects and click @Inspect, you can see how the relation between frame numbers and times is stored in the object: %t__1_ is the #x1 attribute, and \De%t is the #dx attribute. The Info window will tell you the frame number belonging to the time that you specify. The result is presented as a real number. the time for which you want to know the frame number. If the Pitch object has a time step of 10 ms, and the first frame is centred around 18 ms, the frame number associated with a time of 0.1 seconds is 9.2. You can use this command to put the nearest frame centre into a script variable: select Pitch hallo frame = Get frame from time... 0.1 nearestFrame = round (frame) leftFrame = floor (frame) rightFrame = ceiling (frame) The Info window will tell you the time difference between consecutive frames, e.g. the time difference between consecutive formant circles in the sound editor window. If you select one of the above objects and click @Inspect, you can see how the time step is stored in the object: it is the #dx attribute. The Info window will tell you the total number of time frames in the object. If you select one of the above objects and click @Inspect, you can see how the number of frames is stored in the object: it is the #nx attribute. Get sampling period ppgb Get sampling frequency Get time from sample number... Get sample number from time... Get number of samples Get time from frame number... Get frame number from time... 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'? ? @@ @@ @@ @@ K^v ^v 1_v G_v }_v _v _v _v _v _v #`v '`v V`v ]`v `v `v av Gav Rav av av 4bv >bv bv bv bv bv ?cv Ucv av ncv {cv av ncv cv cv cv dv !dv /dv Sdv av ncv dv dv ev 4ev ev fv av ncv gv Ygv bgv tgv ev fv av ncv hv Ahv ncv hv av ncv hv Ygv bgv tgv ev fv av ncv hv Ygv ev 8iv dv iv ,jv `jv jv kv av ncv Ekv dv ev 4ev ev fv av ncv kv av ncv kv dv ev kv dv lv lv 4mv mv mv av ncv Knv dv nv nv ev nv av ncv kov pv cv pv Dpv hqv dv qv qv tv tv uv uv wv wv Jyv Yyv {v }v *}v l}v }v ~v 3~v E~v `~v ~v ~v ~v Xv v v v v ?v @v vv 3~v v v v v ?v uv v 3~v v v v v ?v `v v 3~v v v v v ?v av v 3~v v v v v ?v _v v 3~v v v v v Zv ߆v %v pv v v v v #v ފv v Yv v Zv bv v /v qv v v v v Tv Sv \v fv v v v v v Mv Mv G_v bv hv v v v v #`v v לv ۜv v v ޝv v v v (v ,v Fv Jv v $v Mv v ͟v dv 1v Tv wv v ʠv v v v v v v @v Hv dv v v ^v pv zv v v Ȩv v v 2v Xv fv v v ͩv ٩v v v $v =v rv @ @@cN[ dv v "v v ʫv Iv mv v v @ @@N[ v v <v =v rv @ @@'O[ dv v v v 2v Iv v v v @ @@PO[ ðv <v v v Nv v ۱v v $v Av dv γv ֳv yv v v ƴv v Ȩv v v Nv v uv v $v v v yv v v v v v 2v Ȩv v v Nv :v v yv v v yv v v 2v Ȩv v Nv 'v v yv ܽv v ^v v v 2v Ȩv v Nv v v yv v v $v v v 2v v v 'v dv v v Jv v v Bv \v $v v @v 3v \v Fv dv }v v <v Intensity filter %H (%f) Frequency %f %f__1_-%w %f__1_ %f__1_+%w %f__2_-%w %f__2_ %f__2_+%w 0 dB -6 dB Frequency %f (Hz) curve One of the @@types of objects@ in P\s{RAAT}. #Ltas is short for Long-Term Average Spectrum. An object of class Ltas represents the power spectral density as a function of frequency, expressed in dB/Hz relative to 2\.c10^^-5^ Pa. Inside an Ltas object With @Inspect, you will see the following attributes: %x__%min_ the bottom of the frequency domain, in Hertz. Usually 0. %x__%max_ the top of the frequency domain, in Hertz. %n__%x_ the number of frequency bins (\>_ 1). %dx the frequency step, or %%bin width%, in Hertz. %x__1_ the frequency associated with the first bin, in Hertz. Usually equals %dx / 2, because the first bin tends to start at 0 Hertz. %z__1%i_, %i = 1 ... %n__%x_ the power spectrum, expressed in dB. A @query to the selected @Ltas object. Return bin the band number belonging to the specified frequency, expressed as a real number. Example If the Ltas has a bin width of 1000 Hz, and the lowest frequency is 0 Hz, the bin number associated with a frequency of 1800 Hz is 2.3. Scripting You can use this command to put the nearest bin centre into a script variable: select Ltas hallo bin = Get bin number from frequency... 1800 nearestBin = round (bin) In this case, the value will not be written into the Info window. To round down or up, use leftBin = floor (bin) rightBin = ceiling (bin) Return value the with of a bin, expressed in Hertz. the frequency (in Hz) associated with a specified bin number. %%Bin number the bin number whose frequency is sought. Algorithm the result is %f__1_ + (%binNumber - 1) \.c \De%f where %f__1_ is the frequency associated with the centre of the first bin, and \De%f is the bin width. the frequency (in Hertz) associated with the maximum energy density. Arguments %%From frequency% (s), %%To frequency% (s) the selected frequency domain. Values outside this domain are ignored. If %%To frequency% is not greater than %%From frequency%, the entire frequency domain of the Ltas object is considered. %%Interpolation the interpolation method (None, Parabolic, Cubic, Sinc) of the @@vector peak interpolation@. The standard is None because of the usual large binning. If the Ltas was computed with @@Spectrum: To Ltas (1-to-1)@, a Parabolic or Cubic interpolation would be more appropriate. the frequency (in Hertz) associated with the minimum energy density. Settings %%Time range% (s) the time range (%t__1_, %t__2_). Values outside this range are ignored. If %t__1_ is not less than %t__2_, the entire frequency domain of the Ltas is considered. the highest frequency, expressed in Hertz. A @query to the selected @Ltas object for its lowest frequency. the lowest frequency, expressed in Hertz. It is usually 0 Hz. the maximum value (in dB) within a specified frequency range. the mean value (in dB) within a specified frequency range. the frequency range. Values outside this range are ignored. If %%To frequency% is not greater than %%From frequency%, the entire frequency domain of the Ltas is considered. The mean value between the frequencies %f__1_ and %f__2_ is defined as 1/(%f__2_ - %f__1_) \in__%%f%1_^^%%f%2^ %df %x(%f) where %x(%f) is the LTAS as a function of frequency, expressed in dB. For our discrete Ltas object, this mean is approximated by 1/%n \su__%i=%m..%m+%n-1_ %x__%i_ where %n is the number of band centres between %f__1_ and %f__2_. the minimum value (in dB) within a specified frequency range. the total number of frequency bins. the standard deviation (in dB) of the LTAS within a specified frequency domain. the frequency window. Values outside this domain are ignored. If %%To frequency% is not greater than %%From frequency%, the entire frequency domain of the Ltas is considered. The standard deviation between the frequencies %f__1_ and %f__2_ is defined as 1/(%f__2_ - %f__1_) \in__%%f%1_^^%%f%2^ %df (%x(%f) - %\mu)^2 where %x(%f) is the LTAS as a function of frequency, and %\mu its mean. For our discrete Ltas object, the standard deviation is approximated by 1/(%n-1) \su__%i=%m..%m+%n-1_ (%x__%i_ - %\mu)^2 where %n is the number of band centres between %f__1_ and %f__2_. Note the "minus 1". the value (in dB) at a specified frequency. If %frequency is outside the bands of the Ltas, the result is 0. %Frequency (s) the time at which the value is to be evaluated. the interpolation method, see @@vector value interpolation@. The standard is None because binning is usually large. the LTAS value (in dB) in a specified bin. If the bin number is less than 1 or greater than the number of bin, the result is 0; otherwise, it is %z [1] [%%bin number%]. Setting the bin whose value is to be looked up. A command that creates a @Spectrogram from every selected @Sound object. It performs a %%short-term spectral analysis%, which means that for a number of time points in the Sound, Praat computes an approximation of the spectrum at that time. Each such spectrum is called an %%analysis frame%. For tutorial information, see @@Intro 3. Spectral analysis@. %%Window length the duration of the analysis window. If this is 0.005 seconds, Praat uses for each frame the part of the sound that lies between 0.0025 seconds before and 0.0025 seconds after the centre of that frame (for Gaussian windows, Praat actually uses a bit more than that). The window length determines the %bandwidth of the spectral analysis, i.e. the width of the horizontal line in the spectrogram of a pure sine wave. For a Gaussian window, the -3 dB bandwidth is 2*sqrt(6*ln(2))/(\pi*%%Window length%), or 1.2982804 / %%Window length%. To get a `broad-band' spectrogram (bandwidth 260 Hz), set %%Window length% to 5 milliseconds; to get a `narrow-band' spectrogram (bandwidth 43 Hz), set it to 30 milliseconds. The other window shapes give slightly different values. %%Maximum frequency the maximum frequency subject to analysis, e.g. 5000 Hertz. If it is higher than the Nyquist frequency of the Sound (which is half its sampling frequency), some values in the result will be zero (and will be drawn in white by @@Spectrogram: Paint...@). %%Time step the distance between the centres of subsequent frames, e.g. 0.002 seconds. This determines the number of frames of the resulting Spectrogram. For instance, if the Sound is 1 second long, and the time step is 2 milliseconds, the Spectrogram will consist of almost 500 frames (not %exactly 500, because no reliable spectrum can be measured near the beginning and end of the sound). See below for cases in which the time step of the resulting Spectrogram is different from what you supply here. %%Frequency step the frequency resolution, e.g. 20 Hertz. This determines the number of frequency bands (%bins) of the resulting Spectrogram. For instance, if the %%Maximum frequency% is 5000 Hz, and the frequency step is 20 Hz, the Spectrogram will consist of 250 frequency bands. See below for cases in which the frequency step of the resulting Spectrogram is different from what you supply here. %%Window shape determines the shape of the analysis window. You can choose from: Gaussian, Square (none, rectangular), Hamming (raised sine-squared), Bartlett (triangular), Welch (parabolic), and Hanning (sine-squared). The Gaussian window is superior, as it gives no sidelobes in your spectrogram; it analyzes a factor of 2 slower than the other window shapes, because the analysis is actually performed on twice as many samples per frame. For purposes of computation speed, Praat may decide to change the time step and the frequency step. This is because the time step never needs to be smaller than 1/(8\Vr\pi) of the window length, and the frequency step never needs to be smaller than (\Vr\pi)/8 of the inverse of the window length. For instance, if the window length is 29 ms, the actual time step will be never be less than 29/(8\Vr\pi) = 2.045 ms. And if the window length is 5 ms, the actual frequency step will never be less than (\Vr\pi)/8/0.005 = 44.32 Hz. Tests of the bandwidth You can check the bandwidth formula with the following procedure: ! create a 1000-Hz sine wave, windowed by a 0.2-seconds Gaussian window. Create Sound... gauss 0 1 22050 sin(2*pi*1000*x) * exp(-3*((x-0.5)/0.1)\^ 2) ! compute its spectrum and look at its bandwidth To Spectrum (fft) Draw... 980 1020 20 80 yes Marks bottom every... 1 2 yes yes yes Marks left every... 1 2 yes yes yes ! now you should see a peak at 1000 Hz with a 3 dB bandwidth of 7 Hz (20 dB: 17 Hz) ! more precise: compute the position and width of the peak, and write them to the console Formula... if x<980 or x>1020 then 0 else self fi To Formant (peaks)... 20 Write to console ! now you should be able to read that a peak was found at 999.99982 Hz ! with a bandwidth of 6.497 Hz; the theory above predicted 6.491 Hz ! The same, windowed by a 0.1-seconds Hamming window. Create Sound... Hamming 0 1 22050 if x<0.4 or x>0.6 then 0 else sin(2*pi*1000*x)*(0.54+0.46*cos(pi*(x-0.5)/0.1)) fi Formula... if x<970 or x>1030 then 0 else self fi ! peak at 999.99817 Hz, 3 dB bw 6.518 Hz, 20 dB bw 15 Hz, zero bw 20 Hz, sidelobe -42 dB ! The same, windowed by a 0.1-seconds rectangular window. Create Sound... rectangular 0 1 22050 if x<0.4 or x>0.6 then 0 else sin(2*pi*1000*x) fi ! peak at 999.99506 Hz, 3 dB bw 4.440 Hz, 20 dB bw 27 Hz, zero bw 10 Hz, sidelobe -14 dB ! The same, windowed by a 0.1-seconds Hanning window. Create Sound... Hanning 0 1 22050 if x<0.4 or x>0.6 then 0 else sin(2*pi*1000*x)*(0.5+0.5*cos(pi*(x-0.5)/0.1)) fi ! peak at 999.99945 Hz, 3 dB bw 7.212 Hz, 20 dB bw 16 Hz, zero bw 20 Hz, sidelobe -31 dB ! The same, windowed by a 0.1-seconds triangular window. Create Sound... triangular 0 1 22050 if x<0.4 or x>0.6 then 0 else sin(2*pi*1000*x)*(1-abs((x-0.5)/0.1)) fi ! peak at 999.99933 Hz, 3 dB bw 6.384 Hz, 20 dB bw 15 Hz, zero bw 20 Hz, sidelobe -26 dB ! The same, windowed by a 0.1-seconds parabolic window. Create Sound... parabolic 0 1 22050 if x<0.4 or x>0.6 then 0 else sin(2*pi*1000*x)*(1-((x-0.5)/0.1)^2) fi ! peak at 999.99921 Hz, 3 dB bw 5.786 Hz, 20 dB bw 12 Hz, zero bw 15 Hz, sidelobe -21 dB A command available in the #Spectrum menu if you select one or more @Sound objects. It tries to compute an @Ltas of the spectral envelope of the voiced parts, correcting away the influence of F0 in a way that does not sacrifice frequency selectivity. The resulting Ltas is meant to reflect only the resonances (formants) in the vocal tract and the envelope of the glottal source spectrum. The analysis method is described in @@Boersma & Kovacic (to appear)@. A command that appears in the #Spectrum menu if you select one or more @Sound objects. It turns the selected Sound into a @Spectrum by an over-all spectral analysis, a %%Fourier transform%. %Fast determines whether zeroes are appended to the sound such that the number of samples is a power of two. This can appreciably speed up the Fourier transform. Mathematical procedure For the Fourier transform, the P\s{RAAT}-defined @@time domain@ of the @Sound is ignored. Instead, its time domain is considered to run from %t=0 to %t=%T, where %t=0 is supposed to be aligned with the first sample, and %T is the total duration of the samples, i.e. %%N%\De%t, where %N is the number of samples and \De%t is the @@sampling period@. Thus, the last sample lies at %t=%T-\De%t. For a sound %x(%t), defined for all times %t in the domain (0, %T), the complex spectrum %X(%f) for any frequency %f is the forward Fourier transform of %x(%t), with a negative exponent: %X(%f) = \in__0_^^%T^ %x(%t) %e^^-2%%\piift%^ %dt If the Sound is expressed in Pascal (Pa), the Spectrum is expressed in Pa\.cs, or Pa/Hz. Since a @Spectrum object can only contain a finite number of frequency samples, it is only computed for frequencies that are multiples of \De%f = 1/%T. The number of those frequencies is determined by the number of samples %N of the sound. If %N is odd, there will be %N frequency samples. For instance, if the sound has 20,457 samples, the spectrum will be computed at the frequencies -10,228\De%f, -10,227\De%f, ..., -\De%f, 0, +\De%f, ..., +10,227\De%f, +10,228\De%f. If we suppose that a frequency sample represents a frequency bin with a width of \De%f, we see that the frequency samples span adjacent frequency ranges, e.g. the first sample runs from -10,228.5\De%f to -10,227.5\De%f, the second from -10,227.5\De%f to -10,226.5\De%f. Together, the frequency samples span the frequency domain of the spectrum, which runs from -%F to +%F, where %F = 10,228.5\De%f. We can see that this frequency equals one half of the @@sampling frequency@ of the original sound: %F = 10,228.5\De%f = 10,228.5/%T = 10,228.5/(20,457\De%t) = 0.5/\De%t. This is the so-called @@Nyquist frequency@. If %N is even, there will be %N+1 frequency samples. For instance, if the sound has 32,768 samples, the spectrum will be computed at the frequencies -16,384\De%f, -16,383\De%f, ..., -\De%f, 0, +\De%f, ..., +16,383\De%f, +16,384\De%f. Again, the frequency samples span adjacent frequency ranges, but the first and last samples are only half as wide as the rest, i.e. the first sample runs from -16,384\De%f to -16,383.5\De%f, the second from -16,383.5\De%f to -16,382.5\De%f, and the last from +16,383.5\De%f to +16,384\De%f. Together, the frequency samples again span the frequency domain of the spectrum, which runs from -%F to +%F, where %F = 16,384\De%f = 0.5/\De%t, the Nyquist frequency. Storage In a @Spectrum object, P\s{RAAT} stores the real and imaginary parts of the complex spectrum separately. The real part is equal to the cosine transform: re %X(%f) = \in__0_^^%T^ %x(%t) cos (2%%\pift%) %dt The imaginary part is equal to the reverse of the sine transform: im %X(%f) = - \in__0_^^%T^ %x(%t) sin (2%%\pift%) %dt The complex spectrum can be reconstructed from the real and imaginary part as follows: %X(%f) = re %X(%f) + %i im %X(%f) Since the cosine is a symmetric function of %t and the sine is an antisymmetric function of %t, the complex spectrum for a negative frequency is the complex conjugate of the complex spectrum for the corresponding positive frequency: %X(-%f) = re %X(-%f) + %i im %X(-%f) = re %X(%f) - %i im %X(%f) = %X^*(%f) For purposes of storage, therefore, the negative frequencies are superfluous. For this reason, the Spectrum object stores re %X(%f) and im %X(%f) only for frequencies %f = 0, \De%f, 2\De%f... In the case of a sound with 20,457 samples, the Spectrum object contains the real part of %X(0) (its imaginary part is always zero), and the real and imaginary parts of %X(%f) for frequencies from \De%f to 10,228\De%f, which makes in total 1+2\.c10,228 = 20,457 real values. In the case of a sound with 32,768 samples, the Spectrum object contains the real parts of %X(0) and %X(16,384\De%f) (their imaginary parts are always zero), and the real and imaginary parts of %X(%f) for frequencies from \De%f to 16,383\De%f, which makes in total 2+2\.c16,383 = 32,768 real values. Since the negative frequencies have been removed, the frequency domain now runs from 0 to %F. This means that the first frequency bin is now only 0.5\De%f wide (i.e. as wide as the last bin for even-%N spectra), which has consequences for computations of energies. Behaviour If you perform @@Spectrum: To Sound@ on the resulting Spectrum object, a Sound is created that is equal to the original Sound (or to the original Sound with appended zeroes). Properties The frequency integral over the squared Spectrum equals the time integral over the squared Sound: \in__-%F_^^+%F^ |%X(%f)|^2 %df = \in__0_^%T |%x(%t)|^2 %dt This is called %%Parceval's theorem%. One of the @@types of objects@ in P\s{RAAT}. For tutorial information, see @@Intro 3. Spectral analysis@. A Spectrogram object represents an acoustic time-frequency representation of a sound: the power spectral density %P (%f, %t), expressed in Pa^2/Hz. It is sampled into a number of points centred around equally spaced times %t__%i_ and frequencies %f__%j_. Inside a Spectrogram %xmin starting time, in seconds. %xmax end time, in seconds. %nx the number of times (\>_ 1). time step, in seconds. %x1 the time associated with the first column, in seconds. This will usually be in the range [%xmin, %xmax]. The time associated with the last column (i.e., %x1 + (%nx \-- 1) %dx)) will also usually be in that range. %ymin lowest frequency, in Hertz. Normally 0. %ymax highest frequency, in Hertz. %ny the number of frequencies (\>_ 1). %dy frequency step, in Hertz. %y1 the frequency associated with the first row, in Hertz. Usually %dy / 2. The frequency associated with the last row (i.e., %y1 + (%ny \-- 1) %dy)) will often be %ymax - %dy / 2. %z__%ij_, %i = 1 ... %ny, %j = 1 ... %nx the power spectral density, in Pa^2/Hz. A command for changing the data in all selected @Spectrogram objects. See the @Formulas tutorial for examples and explanations. A command to draw the selected @Spectrogram object(s) into the @@Picture window@ in shades of grey. %%From time%, %%To time% (seconds) the time domain along the %x axis. %%From frequency%, %%To frequency% (Hertz) the frequency domain along the %y axis. %%Dynamic range% (dB) The global maximum of the spectrogram (after preemphasis) will always be drawn in black; all values that are more than %%Dynamic range% dB below this maximum (after dynamic compression) will be drawn in white. Values in-between have appropriate shades of grey. %%Preemphasis% (dB/octave) determines the steepness of a high-pass filter, i.e., how much the power of higher frequencies will be raised before drawing, as compared to lower frequencies. Since the spectral slope of human vowels is approximately -6 dB per octave, the standard value for this parameter is +6 dB per octave, so that the spectrum is flattened and the higher formants look as strong as the lower ones. %%Dynamic compression determines how much stronger weak time frames should be made before drawing. Normally, this parameter is between 0 and 1. If it is 0, there is no dynamic compression. If it is 1, all time frames (vertical bands) will be drawn equally strong, i.e., all of them will contain frequencies that are drawn in black. If this parameter is 0.4 and the global maximum is at 80 dB, then a frame with a maximum at 20 dB (which will normally be drawn all white if the dynamic range is 50 dB), will be raised by 0.4 * (80 - 20) = 24 dB, so that its maximum will be seen at 44 dB (thus making this frame visible). A command to create a @Spectrum object from every selected @Spectrogram object. Purpose to extract the information contained in a Spectrogram at a certain time. The Spectrum will be constructed from one frame of the Spectrogram, namely the frame whose centre is closed to the %time argument. One of the @@types of objects@ in P\s{RAAT}. A Spectrum object represents the complex spectrum as a function of frequency. If the spectrum was created from a sound (which is expressed in units of Pascal), the complex values are expressed in units Pa/Hz (Pascal per Hertz). For detailed information, see @@Sound: To Spectrum...@. Spectrum commands Creation: \bu @@Sound: To Spectrum... Queries: \bu @@Spectrum: Get centre of gravity... \bu @@Spectrum: Get standard deviation... \bu @@Spectrum: Get skewness... \bu @@Spectrum: Get kurtosis... \bu @@Spectrum: Get central moment... Modification: \bu @@Spectrum: Filter (pass Hann band)... \bu @@Spectrum: Filter (stop Hann band)... \bu @@Formula... Conversion: \bu @@Spectrum: To Ltas (1-to-1) \bu @@Spectrum: To Spectrogram Synthesis: \bu @@Spectrum: To Sound A command to modify every selected @Spectrum object. The complex values in the #Spectrum are multiplied by real-valued sine shapes and straight lines, according to the following figure: %%From frequency% (standard value: 500 Hz) the lower edge of the pass band (%f__1_ in the figure). The value zero is special: the filter then acts as a low-pass filter. %%To frequency% (standard value: 1000 Hz) the upper edge of the pass band (%f__2_ in the figure). The value zero is special: the filter then acts as a high-pass filter. %Smoothing (standard value: 100 Hz) the width of the region between pass and stop (%w in the figure). Usage Because of its symmetric Hann-like shape, the filter is especially useful for decomposing the Spectrum into consecutive bands. For instance, we can decompose the spectrum into the bands 0-500 Hz, 500-1000 Hz, 1000-2000 Hz, and 2000-"0" Hz: By adding the four bands together, we get the original spectrum again. A complementary filter is described at @@Spectrum: Filter (stop Hann band)...@. See the @Filtering tutorial for information on the need for smoothing and a comparative discussion of various filters. the lower edge of the stop band (%f__1_ in the figure). The value zero is special: the filter then acts as a high-pass filter. the upper edge of the stop band (%f__2_ in the figure). The value zero is special: the filter then acts as a low-pass filter. the width of the region between stop and pass (%w in the figure). This filter is the complement from the pass-band filter (@@Spectrum: Filter (pass Hann band)...@). For instance, we can decompose the spectrum into the above stop-band spectrum and a band from 500 to 1000 Hz: By adding the two spectra together, we get the original spectrum again. A command for changing the data in all selected @Spectrum objects. A command to query the selected @Spectrum object. If the complex spectrum is given by %S(%f), the %%n%th central spectral moment is given by \in__0_^\oo (%f \-- %f__%c_)^%n |%S(%f)|^%p %df divided by the "energy" \in__0_^\oo |%S(%f)|^%p %df In this formula, %f__%c_ is the spectral centre of gravity (see @@Spectrum: Get centre of gravity...@). Thus, the %%n%th central moment is the average of (%f \-- %f__%c_)^%n over the entire frequency domain, weighted by |%S(%f)|^%p. For %p = 2, the weighting is done by the power spectrum, and for %p = 1, the weighting is done by the absolute spectrum. A value of %p = 2/3 has been seen as well. %Moment the number %n in the formulas above. A number of 3 gives you the third central spectral moment. It is not impossible to ask for fractional moments, e.g. %n = 1.5. %Power the quantity %p in the formula above. Common values are 2, 1, or 2/3. For %n = 1, the central moment should be zero, since the centre of gravity %f__%c_ is computed with the same %p. For %n = 2, you get the variance of the frequencies in the spectrum; the standard deviation of the frequency is the square root of this. For %n = 3, you get the non-normalized spectral skewness; to normalize it, you can divide by the 1.5 power of the second moment. For %n = 4, you get the non-normalized spectral kurtosis; to normalize it, you can divide by the square of the second moment and subtract 3. Praat can directly give you the quantities mentioned here: If the complex spectrum is given by %S(%f), where %f is the frequency, the %%centre of gravity% is given by \in__0_^\oo %f |%S(%f)|^%p %df Thus, the centre of gravity is the average of %f over the entire frequency domain, weighted by |%S(%f)|^%p. For %p = 2, the weighting is done by the power spectrum, and for %p = 1, the weighting is done by the absolute spectrum. A value of %p = 2/3 has been seen as well. Argument the quantity %p in the formulas above. Common values are 2, 1, or 2/3. Interpretation The spectral centre of gravity is a measure for how high the frequencies in a spectrum are on average. For a sine wave with a frequency of 377 Hz, the centre of gravity is 377 Hz. You can easily check this in Praat by creating such a sine wave (@@Create Sound...@), then converting it to a Spectrum (@@Sound: To Spectrum...@), then querying the mean frequency. For a white noise sampled at 22050 Hz, the centre of gravity is 5512.5 Hz, i.e. one half of the @@Nyquist frequency@. Related measures The centre of gravity is used in the computation of spectral moments: The (normalized) kurtosis of a spectrum is the fourth central moment of this spectrum, divided by the square of the second central moment, minus 3. See @@Spectrum: Get central moment...@. the quantity %p in the formula for the centre of gravity and the second and fourth central moment. Common values are 2, 1, or 2/3. The kurtosis is a measure for how much the shape of the spectrum around the %%centre of gravity% is different from a Gaussian shape. For a white noise, the kurtosis is 6/5. The (normalized) skewness of a spectrum is the third central moment of this spectrum, divided by the 1.5 power of the second central moment. See @@Spectrum: Get central moment...@. the quantity %p in the formula for the centre of gravity and the second and third central moment. Common values are 2, 1, or 2/3. The skewness is a measure for how much the shape of the spectrum below the %%centre of gravity% is different from the shape above the mean frequency. For a white noise, the skewness is zero. The standard deviation of a spectrum is the square root of the second central moment of this spectrum. See @@Spectrum: Get central moment...@. the quantity %p in the formula for the centre of gravity and the second central moment. Common values are 2, 1, or 2/3. The standard deviation is a measure for how much the frequencies in a spectrum can deviate from the %%centre of gravity%. For a sine wave, the standard deviation is zero. For a white noise, the standard deviation is the @@Nyquist frequency@ divided by \Vr12. A command for converting each selected @Spectrum object into an @Ltas object without loss of frequency resolution. Each band %b__%i_ in the Ltas is computed from a single frequency sample %s__%i_ in the Spectrum as follows: %b__%i_ = 2 ((Re (%s__%i_))^2 + (Im (%s__%i_))^2) / 4.0\.c10^^-10^ If the original Spectrum is expressible in Pa / Hz (sound pressure in air), the Ltas values are in "dB/Hz" relative to the auditory threshold at 1000 Hz (2\.c10^^-5^ Pa). A command for creating a @Sound object from every selected @Spectrum object. The reverse of the Fourier transform described in @@Sound: To Spectrum...@. If the Spectrum is expressed in Pa/Hz, the Sound will be in Pascal. The frequency integral over the Sound equals the time integral over the Spectrum. If you perform this command on a Spectrum object that was created earlier with @@Sound: To Spectrum...@, the resulting Sound is equal to the Sound that was input to ##Sound: To Spectrum...#. A command to create a @Spectrogram object from every selected @Spectrum object. Format conversion. The Spectrogram will have only one frame (time slice). The values are computed as the sum of the squares of the real and imaginary parts of the Spectrum. One of the @editors in P\s{RAAT}. It allows you to view, zoom, and play a @Spectrum object. Clicking on one of the (maximally) 8 rectangles above or below the drawing area lets you play a @Sound that is synthesized from a band-filtered part of the @Spectrum. You can also copy the Spectrum, band-filtered with the @@frequency selection@, or the Sound synthesized from this Spectrum, to the list of objects. Ltas ppgb Ltas: Get bin number from frequency... Ltas: Get bin width Ltas: Get frequency from bin number... Ltas: Get frequency of maximum... Ltas: Get frequency of minimum... Ltas: Get highest frequency Ltas: Get lowest frequency Ltas: Get maximum... Ltas: Get mean... Ltas: Get minimum... Ltas: Get number of bins Ltas: Get standard deviation... Ltas: Get value at frequency... Ltas: Get value in bin... Sound: To Spectrogram... Sound: To Ltas (pitch-corrected)... Sound: To Spectrum... Spectrogram Spectrogram: Formula... Spectrogram: Paint... Spectrogram: To Spectrum (slice)... Spectrum Spectrum: Filter (pass Hann band)... Spectrum: Filter (stop Hann band)... Spectrum: Formula... Spectrum: Get central moment... Spectrum: Get centre of gravity... Spectrum: Get kurtosis... Spectrum: Get skewness... Spectrum: Get standard deviation... 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See the @Formulas tutorial for explanations and examples. A command in the @@New menu@ to create a @Sound as the sum of a number of sine waves with equidistant frequencies. Arguments %Name the name of the resulting Sound object. %%Starting time%, %%End time% (s) the time domain of the resulting Sound. %%Sampling frequency% (Hz) the sampling frequency of the resulting Sound. %Phase determines whether the result is a sum of %sines or a sum of %cosines, i.e., whether the zero crossings or the maxima of the components are synchronized. This choice has little perceptual consequences. %%Frequency step% (Hz) the distance between the components. In first approximation, this is the perceived fundamental frequency. %%First frequency% (Hz) the lowest frequency component. If you supply a value of 0, %firstFrequency is taken equal to %frequencyStep. %%Ceiling% (Hz) the frequency above which no components are used. If you supply a value of 0 or a value above the Sound's @@Nyquist frequency@, %ceiling is taken equal to the Nyquist frequency. %%Number of components determines how many sinusoids are used. If you supply a value of 0 or a very high value, the maximum number of components is used, limited by %ceiling. Example 1: a pulse train A series of pulses at regular intervals, sampled after low-pass filtering at the Nyquist frequency, can be regarded as a sum of cosine waves. For instance, a 100-Hz pulse train, sampled at 22050 Hz, can be created with: Create Sound from tone complex... train 0 1 22050 Cosine 100 0 0 0 Supplying the value 0 for %firstFrequency yields an unshifted harmonic complex. Example 2: a shifted harmonic complex Some experiments on human pitch perception (%%residue pitch%) use a number of sinusoidal components with harmonically related frequencies that are all shifted by a constant amount. For instance, to get a sum of sine waves with frequencies 105 Hz, 205 Hz, and 305 Hz, you would use: Create Sound from tone complex... train 0.3 1 22050 Sine 100 105 0 3 or Create Sound from tone complex... train 0.3 1 22050 Sine 100 105 350 0 whichever you prefer. Some of these experiments are described in @@Plomp (1967)@ and @@Patterson & Wightman (1976)@. Algorithm For the `sine' phase, the resulting Sound is given by the following formula: %x(%t) = \su__%i=1..%numberOfComponents_ sin (2%\pi\.c(%firstFrequency + (%i\--1)\.c%frequencyStep)\.c%t) More flexibility? Suppose you wanted to vary the relative strengths of the frequency components. You could achieve this by creating a Sound with the command discussed here, take its Fourier transform, run a formula on the resulting Spectrum, and take the inverse Fourier transform. A more general approach is described shortly. Suppose you need a sum of sine waves with frequencies 105, 205, 305, ..., 1905 Hz, and with relative amplitudes 1, 1/2, 1/3, ..., 1/19. You could build a script that computes the various components, and add them to each other as you go along. Instead of calling 19 scripts, however, you can achieve this with the following more general script: form Add waves with decreasing amplitudes Number_of_components 19 endform \# Create a Matrix with frequency and amplitude information in each row: Create simple Matrix... freqAndGain number_of_components 2 0 Formula... if col = 1 then row * 100 + 5 else 1 / row fi \# Create a large Matrix with all the component sine waves: Create Matrix... components 0 1 10000 1e-4 0.5e-4 1 number_of_components number_of_components 1 1 0 Formula... Matrix_freqAndGain [2] * sin (2 * pi * Matrix_freqAndGain [1] * x) \# Integrate: Formula... self + self [row - 1, col] \# Publish last row: To Sound (slice)... number_of_components Scale amplitudes... 0.99 A command in the @@Read menu@ of the #Objects window. You use this if you want to get the two channels of a @stereo sound file as two separate @Sound objects in the list. Praat will name the two channels %left and %right. A command in the @@New menu@ to record a @Sound. Creates a @SoundRecorder window, except on very old Macintoshes with 8-bit audio, where it presents a native Macintosh sound-recorder window. A command in the @@New menu@ to record a @Sound. Creates a @SoundRecorder window. One of the @@types of objects@ in P\s{RAAT}. For tutorial information, see all of the @Intro. Commands Creation: \bu @@Record mono Sound...@ (from microphone or line input, with the @SoundRecorder) \bu @@Record stereo Sound...@ \bu @@Create Sound...@ (from a formula) \bu @@Create Sound from tone complex... \bu @@Create Sound from gamma-tone... \bu @@Create Sound from Shepard tone... Reading and writing: \bu @@Sound files You can also use the text and binary (real-valued) formats for Sounds, like for any other class: \bu @@Write to text file... \bu @@Write to binary file... Playing: \bu @@Sound: Play \bu @@PointProcess: Hum \bu @@PointProcess: Play Viewing and editing: \bu @SoundEditor, @ManipulationEditor, @TextGridEditor, @PointEditor, @PitchTierEditor, @SpectrumEditor Queries: structure: \bu @@time domain \bu @@Get number of samples \bu @@Get sampling period \bu @@Get sampling frequency \bu @@Get time from sample number... \bu @@Get sample number from time... content: \bu @@Sound: Get value at time... \bu @@Sound: Get value at sample number... shape: \bu @@Sound: Get minimum... \bu @@Sound: Get time of minimum... \bu @@Sound: Get maximum... \bu @@Sound: Get time of maximum... \bu @@Sound: Get absolute extremum... \bu @@Sound: Get nearest zero crossing... statistics: \bu @@Sound: Get mean... \bu @@Sound: Get root-mean-square... \bu @@Sound: Get standard deviation... energy: \bu @@Sound: Get energy... \bu @@Sound: Get power... in air: \bu @@Sound: Get energy in air \bu @@Sound: Get power in air \bu @@Sound: Get intensity (dB) Modification: \bu @@Matrix: Formula... \bu @@Sound: Set value at sample number... \bu @@Sound: Filter with one formant (in-line)... \bu @@Sound: Pre-emphasize (in-line)... \bu @@Sound: De-emphasize (in-line)... Annotation (see @@Intro 7. Annotation@): \bu @@Sound: To TextGrid... Periodicity analysis: \bu @@Sound: To Pitch... \bu @@Sound: To Pitch (ac)... \bu @@Sound: To Pitch (cc)... \bu @@Sound: To Pitch (shs)... \bu @@Sound: To Harmonicity (ac)... \bu @@Sound: To Harmonicity (cc)... \bu @@Sound: To PointProcess (periodic, cc)... \bu @@Sound: To PointProcess (periodic, peaks)... \bu @@Sound & Pitch: To PointProcess (cc) \bu @@Sound & Pitch: To PointProcess (peaks)... \bu @@Sound: To Intensity... Spectral analysis: \bu @@Sound: To Spectrum... \bu @@Sound: To Spectrogram... \bu @@Sound: To Formant (burg)... \bu @@Sound: To Formant (sl)... \bu @@Sound: LPC analysis \bu @@Sound: To LPC (autocorrelation)... \bu @@Sound: To LPC (covariance)... \bu @@Sound: To LPC (burg)... \bu @@Sound: To LPC (marple)... Filtering (see @Filtering tutorial): \bu @@Sound: Filter (pass Hann band)... \bu @@Sound: Filter (stop Hann band)... \bu @@Sound: Filter (formula)... \bu @@Sound: Filter (one formant)... \bu @@Sound: Filter (pre-emphasis)... \bu @@Sound: Filter (de-emphasis)... \bu @@LPC & Sound: Filter... \bu @@LPC & Sound: Filter (inverse) \bu @@Sound & Formant: Filter \bu @@Sound & FormantTier: Filter Conversion: \bu @@Sound: Resample... Enhancement: \bu @@Sound: Lengthen (PSOLA)...@: lengthen by a constant factor \bu @@Sound: Deepen band modulation...@: strenghten intensity modulations in each critical band Combination: \bu @@Sounds: Convolve \bu @@Sounds: Concatenate Synthesis \bu @@Source-filter synthesis@ tutorial \bu @Manipulation (@PSOLA etc.) \bu @@Spectrum: To Sound \bu ##Pitch: To Sound... \bu @@PointProcess: To Sound (pulse train)... \bu @@PointProcess: To Sound (hum)... \bu ##Pitch & PointProcess: To Sound... \bu @@Articulatory synthesis@ tutorial \bu @@Artword & Speaker: To Sound... Inside a Sound With @Inspect, you will see that a Sound contains the following data: %x__%min_ starting time, in seconds. %x__%max_ > %x__%min_ end time, in seconds. %n__%x_ the number of samples (\>_ 1). %dx sample period, in seconds. The inverse of the sampling frequency (in Hz). %x__1_ the time associated with the first sample (in seconds). This will normally be in the range [%xmin, %xmax]. The time associated with the last sample (i.e., %x__1_ + (%nx \-- 1) %dx)) will also normally be in that range. Mostly, the sound starts at %t = 0 seconds and %x__1_ = %dx / 2. Also, usually, %x__%max_ = %n__%x_ %dx. %z [1] [1..%n__%x_] the amplitude of the sound (stored as single-precision floating-point numbers). For the most common applications (playing and file I-O), Praat assumes that the amplitude is greater than -1 and less than +1. For some applications (modelling of the inner ear; articulatory synthesis), Praat assumes that the amplitude is expressed in Pascal units. If these interpretations are combined, we see that the maximum peak amplitude of a calibrated sound is 1 Pascal; for a sine wave, this means 91 dB SPL. Limitations Since the Sound object completely resides in memory, its size is limited to the amount of RAM in your computer. For sounds longer than a few minutes, you could use the @LongSound object instead, which you can view in the @LongSoundEditor. A command to change the spectral slope of every selected @Sound object. The reverse of @@Sound: Pre-emphasize (in-line)...@. For an example, see @@Source-filter synthesis@. This is the in-line version of @@Sound: Filter (de-emphasis)...@, i.e., it does not create a new Sound object but modifies an existing object. Argument %%From frequency% (Hz) the frequency %F above which the spectral slope will decrease by 6 dB/octave. The de-emphasis factor %\al is computed as %\al = exp (-2 %\pi %F \De%t) where \De%t is the sampling period of the sound. Every sample %x__%i_ of the sound, except %x__1_, is then changed, going up from the second sample: %x__%i_ = %x__%i_ + %\al %x__%i-1_ A command to enhance the fast spectral changes, like %F__2_ movements, in each selected @Sound object. %Enhancement (dB) the maximum increase in the level within each critical band. The standard value is 20 dB. the lowest frequency that shall be manipulated. The bottom frequency of the first critical band that is to be enhanced. The standard value is 300 Hertz. %%To frequency% (Hz) the highest frequency that shall be manipulated (the last critical band may be narrower than the others). The standard value is 8000 Hz. %%Slow modulation% (Hz) the frequency %f__%slow_ below which the intensity modulations in the bands should not be expanded. The standard value is 3 Hz. %%Fast modulation% (Hz) the frequency %f__%fast_ above which the intensity modulations in the bands should not be expanded. The standard value is 30 Hz. %%Band smoothing% (Hz) the degree of overlap of each band into its adjacent bands. Prevents %ringing. The standard value is 100 Hz. Suppose we have the standard settings of the arguments. The resulting sound will composed of the unfiltered part of the original sound, plus all manipulated bands. First, the resulting sound becomes the original sound, stop-band filtered between 300 and 8000 Hz: after a forward Fourier transform, all values in the @Spectrum at frequencies between 0 and 200 Hz and between 8100 Hz and the Nyquist frequency of the sound are retained unchanged. The spectral values at frequencies between 400 and 7900 Hz are set to zero. Between 200 and 400 Hz and between 7900 and 8100 Hz, the values are multiplied by a raised sine, so as to give a smooth transition without ringing in the time domain (the raised sine also allows us to view the spectrum as a sum of spectral bands). Finally, a backward Fourier transform gives us the filtered sound. The remaining part of the spectrum is divided into %%critical bands%, i.e. frequency bands one Bark wide. For instance, the first critical band run from 300 to 406 Hz, the second from 406 to 520 Hz, and so on. Each critical band is converted to a pass-band filtered sound by means of the backward Fourier transform. Each filtered sound will be manipulated, and the resulting manipulated sounds are added to the stop-band filtered sound we created earlier. If the manipulation is the identity transformation, the resulting sound will be equal to the original sound. But, of course, the manipulation does something different. Here are the steps. First, we compute the local intensity of the filtered sound %x (%t): %intensity (%t) = 10 log__10_ (%x^2 (%t) + 10^^-6^) This intensity is subjected to a forward Fourier transform. In the frequency domain, we administer a band filter. We want to enhance the intensity modulation in the range between 3 and 30 Hz. We can achieve this by comparing the very smooth intensity contour, low-pass filtered at %f__%slow_ = 3 Hz, with the intensity contour that has enough temporal resolution to see the place-discriminating %F__2_ movements, which is low-pass filtered at %f__%fast_ = 30 Hz. In the frequency domain, the filter is %H (%f) = exp (- (%\al%f / %f__%fast_)^2) - exp (- (%\al%f / %f__%slow_)^2) where %\al equals \Vrln 2 \~~ 1 / 1.2011224, so that %H (%f) has its -6 dB points at %f__%slow_ and %f__%fast_: Now, why do we use such a flat filter? Because a steep filter would show ringing effects in the time domain, dividing the sound into 30-ms chunks. If our filter is a sum of exponentials in the frequency domain, it will also be a sum of exponentials in the time domain. The backward Fourier transform of the frequency response %H (%f) is the impulse response %h (%t). It is given by %h (%t) = 2%\pi\Vr%\pi %f__%fast_/%\al exp (-(%\pi%t%f__%fast_/%\al)^2) - 2%\pi\Vr%\pi %f__%slow_/%\al exp (-(%\pi%t%f__%slow_/%\al)^2) This impulse response behaves well: We see that any short intensity peak will be enhanced, and that this enhancement will suppress the intensity around 30 milliseconds from the peak. Non-Gaussian frequency-domain filters would have given several maxima and minima in the impulse response, clearly an undesirable phenomenon. After the filtered band is subjected to a backward Fourier transform, we convert it into power again: %power (%t) = 10^^%filtered / 2^ The relative enhancement has a maximum that is smoothly related to the basilar place: %ceiling = 1 + (10^^%enhancement / 20^ - 1) \.c (1/2 - 1/2 cos (%\pi %f__%midbark_ / 13)) where %f__%midbark_ is the mid frequency of the band. Clipping is implemented as %factor (%t) = 1 / (1 / %power (%t) + 1 / %ceiling) Finally, the original filtered sound %x (%t), multiplied by this factor, is added to the output. A command to filter every selected @Sound object. The resulting Sound object has a lower spectral slope. The reverse of @@Sound: Filter (pre-emphasis)...@. For an example, see @@Source-filter synthesis@. where \De%t is the sampling period of the sound. The new sound %y is then computed recursively as: %y__1_ = %x__1_ %y__%i_ = %x__%i_ + %\al %y__%i-1_ A command to convert every selected @Sound object into a filtered sound. The filtering is done in the frequency domain. This command is equivalent to the following sequence: 1. @@Sound: To Spectrum...@ yes 2. @@Matrix: Formula... 3. @@Spectrum: To Sound For a comparative discussion of various filtering methods, see the @Filtering tutorial. The example formula is the following: if x<500 or x>1000 then 0 else self fi; rectangular band This formula represents a rectangular pass band between 500 Hz and 1000 Hz (%x is the frequency). Rectangular bands are %not recommended, since they may lead to an appreciable amount of %#ringing in the time domain. The transition between stop and pass band should be smooth, as e.g. in @@Sound: Filter (pass Hann band)...@. A command to filter every selected @Sound object, with a single formant of a specified frequency and bandwidth. Two recursive filter coefficients are computed as follows: %p = \--2 exp (\--%\pi %bandwidth %dt) cos (2%\pi %frequency %dt) %q = exp (\--2%\pi %bandwidth %dt) where %dt is the sample period. The new signal %y is then computed from the old signal %x and itself as %y__1_ := %x__1_ %y__2_ := %x__2_ \-- %p %y__1_ \At%n \>_ 3: %y__n_ := %x__n_ \-- %p %y__%n-1_ \-- %q %y__%n-2_ After filtering, the sound %y is scaled so that its absolute extremum is 0.9. This filter has an in-line version: @@Sound: Filter with one formant (in-line)...@. A command to filter every selected @Sound object in-line, with a single formant of a specified frequency and bandwidth. This is the in-line version of @@Sound: Filter (one formant)...@, i.e. it does not create a new Sound object but modifies the selected object. 1. @@Sound: To Spectrum... 2. @@Spectrum: Filter (pass Hann band)... For a complementary filter, see @@Sound: Filter (stop Hann band)...@. 2. @@Spectrum: Filter (stop Hann band)... For a complementary filter, see @@Sound: Filter (pass Hann band)...@. A command for changing the data in all selected @Sound objects. See the @Formulas tutorial for examples and explanations. A @query to the selected @Sound object. Return value the absolute extremum (in Pascal) within a specified time window. Settings %%Time range% (s) the time range (%t__1_, %t__2_). Values outside this range are ignored. If %t__1_ is not less than %t__2_, the entire time domain of the sound is considered. %%Interpolation the interpolation method (None, Parabolic, Sinc) of the @@vector peak interpolation@. The standard is Sinc70 because a Sound object is normally a sampled band-limited signal, which can be seen as a sum of sinc functions. the energy. If the unit of sound amplitude is Pa (Pascal), the unit of energy will be Pa^2\.cs. Setting The energy is defined as \in__%%t%1_^^%%t%2^ %x^2(%t) %dt where %x(%t) is the amplitude of the sound. See also For an interpretation of the energy as the sound energy in air, see @@Sound: Get energy in air@. For the power, see @@Sound: Get power...@. The energy in air, expressed in Joule/m^2. The energy of a sound in air is defined as 1 / (%\roc) \in %x^2(%t) %dt where %x(%t) is the sound pressure in units of Pa (Pascal), %\ro is the air density (apx. 1.14 kg/m^3), and %c is the velocity of sound in air (apx. 353 m/s). For an air-independent interpretation of the energy, see @@Sound: Get energy...@. For the power, see @@Sound: Get power in air@. the intensity in air, expressed in dB relative to the auditory threshold. The intensity of a sound in air is defined as 10 log__10_ { 1 / (%T %P__0_^2) \in%dt %x^2(%t) } where %x(%t) is the sound pressure in units of Pa (Pascal), %T is the duration of the sound, and %P__0_ = 2\.c10^^-5^ Pa is the auditory threshold pressure. For the intensity in Watt/m^2, see @@Sound: Get power in air@. For an auditory intensity, see @@Excitation: Get loudness@. A command available in the #Query menu if you select a @Sound object. The Info window will show the maximum amplitude (sound pressure in Pascal) within a specified time window. the time range (%t__1_, %t__2_). Values outside this range are ignored, except for purposes of interpolation. If %t__1_ is not less than %t__2_, the entire time domain of the sound is considered. the interpolation method (None, Parabolic, Cubic, Sinc) of the @@vector peak interpolation@. The standard is Sinc70 because a Sound object is normally a sampled band-limited signal, which can be seen as a sum of sinc functions. A command available in the #Query menu if you select a @Sound object. The Info window will show the mean amplitude (sound pressure in Pascal) within a specified time range. Mathematical definition The mean amplitude between the times %t__1_ and %t__2_ is defined as 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ %x(%t) %dt where %x(%t) is the amplitude of the sound in Pa. A command available in the #Query menu if you select a @Sound object. The Info window will show the minimum amplitude (sound pressure in Pascal) within a specified time window. A command available in the #Query menu if you select a @Sound object. The Info window will show the time associated with the zero crossing nearest to a specified time point. It is @undefined if there are no zero crossings or if the specified time is outside the time domain of the sound. Linear interpolation is used between sample points. %Time (s) the time for which you want to get the time of the nearest zero crossing. A command available in the #Query menu if you select a @Sound object. The Info window will show the power within a specified time window. If the unit of sound amplitude is Pa (Pascal), the unit of power will be Pa^2. The power is defined as 1/(%t__2_-%t__1_) \in__%%t%1_^^%%t%2^ %x^2(%t) %dt For an interpretation of the power as the sound power in air, see @@Sound: Get power in air@. For the total energy, see @@Sound: Get energy...@. A command available in the #Query menu if you select a @Sound object. The Info window will show the power in air, expressed in Watt/m^2. The power of a sound in air is defined as 1 / (%\rocT) \in %x^2(%t) %dt where %x(%t) is the sound pressure in units of Pa (Pascal), %\ro is the air density (apx. 1.14 kg/m^3), %c is the velocity of sound in air (apx. 353 m/s), and %T is the duration of the sound. For an air-independent interpretation of the power, see @@Sound: Get power...@. For the energy, see @@Sound: Get energy in air@. For the intensity in dB, see @@Sound: Get intensity (dB)@. A command available in the #Query menu if you select a @Sound object. The Info window will show the root-mean-square (rms) value of the sound pressure, expressed in Pascal. The root-mean-square value is defined as \Vr { 1/(%t__2_-%t__1_) \in__%%t%1_^^%%t%2^ %x^2(%t) %dt } A command available in the #Query menu if you select a @Sound object. The Info window will show the standard deviation (in Pascal) of the sound pressure within a specified window. If the sound contains less than 2 samples, the value is @undefined. The standard deviation is defined as 1/(%t__2_-%t__1_) \in%__%%t%1_^^%%t%2^ (%x(%t) - %\mu)^2 %dt where %x(%t) is the amplitude of the sound, and %\mu is its mean. For our discrete Sound object, the standard deviation is approximated by 1/(%n-1) \su__%i=%m..%m+%n-1_ (%x__%i_ - %\mu)^2 where %n is the number of sample centres between %t__1_ and %t__2_. Note the "minus 1". A command available in the #Query menu if you select a @Sound object. The Info window will show the time (in seconds) associated with the maximum pressure in a specified time range. A command available in the #Query menu if you select a @Sound object. The Info window will show the time (in seconds) associated with the minimum pressure in a specified time range. A command available in the #Query menu if you select a @Sound object. The Info window will show the amplitude (sound pressure in Pascal) at a specified sample number. If the sample number is less than 1 or greater than the number of samples, the result is @undefined. %%Sample number the sample number at which the value is to be evaluated. A command available in the #Query menu if you select a @Sound object. The Info window will show an estimate of the amplitude (sound pressure in Pascal) at a specified time. If that time is outside the samples of the Sound, the result is equal to the value of the nearest sample; otherwise, the result is an interpolated value. the time at which the value is to be evaluated. the interpolation method, see @@vector value interpolation@. The standard is Sinc70 because a Sound object is normally a sampled band-limited signal, which can be seen as a sum of sinc functions. A command to convert each selected @Sound object into a longer new @Sound object. %%Minimum frequency% (Hz) the minimum pitch used in the periodicity analysis. The standard value is 75 Hz. For the voice of a young child, set this to 150 Hz.The shortest voiceless interval in the PSOLA decomposition is taken as 1.5 divided by %%minimum frequency%. %%Maximum frequency% (Hz) the maximum pitch used in the periodicity analysis. The standard value is 600 Hz. For an adult male voice, set this to 300 Hz. %Factor the factor with which the sound will be lengthened. The standard value is 1.5. If you take a value less than 1, the resulting sound will be shorter than the original. A value larger than 3 will not work. Pitch-synchronous overlap-and-add. Your system's way of controlling where sounds will be played, and how loud. On Windows, double-click the loudspeaker icon in the Start bar. On MacOS X, go to System Preferences, then to Sound, then to Output Volume (you can put a loudspeaker icon in OSX's menu bar here). On HP-UX, try the ##Use internal loudspeaker...# preference in Praat's Preferences menu. A command to play @Sound objects. Availability You can choose this command after selecting one or more Sounds. Purpose To play the selected Sounds through the internal or external loudspeakers, the headphones, or the analog or digital outputs of your computer. Behaviour All of the Sounds selected are played, in the order in which they appear in the list. If the sampling frequency of the Sound does not match any of the system's sampling frequencies, a fast but inaccurate conversion is performed via linear interpolation. Usage The output level and the choice of the output device(s) depend on the settings in your @@audio control panel@. A command to filter each selected @Sound object. The resulting Sound object has a higher spectral slope. The reverse of @@Sound: Filter (de-emphasis)...@. the frequency %F above which the spectral slope will increase by 6 dB/octave. The pre-emphasis factor %\al is computed as where \De%t is the sampling period of the sound. The new sound %y is then computed as: %y__%i_ = %x__%i_ - %\al %x__%i-1_ The reverse of @@Sound: De-emphasize (in-line)...@. This is the in-line version of @@Sound: Filter (pre-emphasis)...@, i.e., it does not create a new Sound object but modifies an existing object. where \De%t is the sampling period of the sound. Every sample %x__%i_ of the sound, except %x__1_, is then changed, going down from the last sample: %x__%i_ = %x__%i_ - %\al %x__%i-1_ A command that creates new @Sound objects from the selected Sounds. High-precision resampling from any sampling frequency to any other sampling frequency. %%Sampling frequency the new sampling frequency, in Hertz. %Precision the depth of the interpolation, in samples (standard is 50). This determines the quality of the interpolation used in resampling. If %Precision is 1, the method is linear interpolation, which is inaccurate but fast. If %Precision is greater than 1, the method is sin(%x)/%x ("%sinc") interpolation, with a depth equal to %Precision. For higher %Precision, the algorithm is slower but more accurate. If %%Sampling frequency% is less than the sampling frequency of the selected sound, an anti-aliasing low-pass filtering is performed prior to resampling. A new Sound will appear in the list of objects, bearing the same name as the original Sound, followed by the sampling frequency. For instance, the Sound "hallo" will give a new Sound "hallo_10000". A command to change a specified sample of the selected @Sound object. the sample whose value is to be changed. Specify any value between 1 and the number of samples in the Sound. If you specify a value outside that range, you will get an error message. %%New value the value that is to be put into the specified sample. Scripting Example: select Sound hallo Set value at sample number... 100 1/2 This sets the value of the 100th sample to 0.5. An @@Editors|Editor@ for viewing and editing a @Sound object. Most of the functions of this editor are described in the @Intro. The markers To set the cursor, use the left mouse button. A horizontal line will also be shown; this line crosses the cursor line at the sound's function value. This function value is the sinc-interpolated value, and is generally different from the value that you would expect when looking at the linearly interpolated version of the sampled sound. To select a part of the time domain, use the @@time selection@ mechanism. Playing To play any part of the sound, click on one of the rectangles below or above the sound window (there can be 1 to 8 of these rectangles), or choose a Play command from the View menu. Publishing To perform analyses on the selection, or save it to a file, create an independent Sound as a copy of the selection, by clicking on the button that will copy the selection to the List of Objects; the resulting Sound will be called "Sound untitled". Editing \bu Cut: cut the selection to the clipboard. \bu Copy: copy the selection to the clipboard. \bu Paste: paste the clipboard to the cursor. \bu Zero: set the selected samples to zero. \bu Reverse: reverse the selected part of the sound. You can undo these commands with Undo (Command-Z). The Group button To synchronize a SoundEditor window with other windows that show a time signal, push the Group button in all the windows that you want to synchronize. You cannot Cut from or Paste into a synchronized SoundEditor window. With the Praat SoundRecorder window you can record a mono or stereo sound for subsequent viewing and analysis in Praat. The SoundRecorder appears on your screen if you choose @@Record mono Sound...@ or @@Record stereo Sound...@ from the @@New menu@. Depending on your system, the SoundRecorder window may allow you to choose the sampling frequency, the input gain, and the input device (microphone, line, or digital). The sound input level is monitored continuously with one or two meters. The resulting sound has 16 bits per sample, like sounds on an audio CD. To record the sound, use the Record and Stop buttons in the SoundRecorder window. Click ##Save to list# to copy the recorded sound to the object window (or ##Save left channel to list# or ##Save right channel to list# to copy the left or right channel if you have a stereo sound). The name of the resulting Sound object will be taken from the text field next to the button clicked. Size of the recording buffer The size of the recording buffer determines how many seconds of sound you can record. For instance, if the recording buffer is 20 megabytes (the standard value), you can record 220 seconds in stereo (440 seconds in mono) at a sampling frequency of 22050 Hz, or 110 seconds in stereo (220 seconds in mono) at a sampling frequency of 44100 Hz. You can change the size of the recording buffer with ##Sound input prefs...# from the Preferences menu. If you recorded a very long sound, it is probable that you cannot copy it to the list of objects. In such a case, you can still write the sound to disk with one of the Write commands in the File menu. You can then open such a long sound file in P\s{RAAT} with @@Open long sound file...@ from the Read menu. Recording sounds in Windows In Windows, you can choose your input device with the help of the recording mixer that is supplied by Windows or comes with your sound card. There will usually be a loudspeaker icon in the Start bar; double-click it, and you will see the %playing mixer (if there is no loudspeaker icon, go to ##Control Panels#, then ##Sounds and Audio Devices#, then #Volume, then #Advanced; do not blame us for how Windows XP works). In the playing mixer, choose #Properties from the #Option menu, then click #Recording, then #OK. You are now in the %recording mixer. You can watch the input level only while recording. The File menu A very long recorded sound can be too big to copy it to the list of objects. Fortunately, the File menu contains commands to save the recording (or just the left or right channel) to a sound file on disk, so that you will never have to lose your recording. Sound pressure calibration Your computer's sound-recording software returns integer values between -32768 and 32767. Praat divides them by 32768 before putting them into a Sound object, so that the values in the Sound objects are always between -1 and +1. The Praat program considers these numbers to be air pressures in units of Pascal, but they are probably not the actual true air pressures that went into the microphone. For how to obtain the true air pressures, perform a @@sound pressure calibration@. A command to concatenate all selected @Sound objects into a single large Sound. All sounds must have equal sampling frequencies. They are concatenated in the order that they appear in the list of objects. How to concatenate directly to a file If the resulting sound does not fit into memory, use one of the commands in the @@Write menu@. See @@How to concatenate sound files@. A command to convolve two @Sound objects with each other. The convolution of two time signals %A(%t) and %B(%t) is defined as (%A * %B) (%t) \=3 \in %A(%\ta) %B(%t-%\ta) %d%\ta Convolution is commutative, i.e. the convolution of %A and %B equals the convolution of %B and %A. Since convolution in the time domain amounts to multiplication in the frequency domain, both sounds are FFT-ed, the resulting spectra are multiplied, and the resulting product spectrum is FFT-ed back to give the convoluted sound. Create Sound... ppgb Create Sound from tone complex... Read two sounds from stereo file... Record mono Sound... Record stereo Sound... Sound Sound: De-emphasize (in-line)... Sound: Deepen band modulation... Sound: Filter (de-emphasis)... Sound: Filter (formula)... Sound: Filter (one formant)... Sound: Filter with one formant (in-line)... Sound: Filter (pass Hann band)... Sound: Filter (stop Hann band)... Sound: Formula... Sound: Get absolute extremum... Sound: Get energy... Sound: Get energy in air Sound: Get intensity (dB) Sound: Get maximum... Sound: Get mean... Sound: Get minimum... Sound: Get nearest zero crossing... Sound: Get power... Sound: Get power in air Sound: Get root-mean-square... Sound: Get standard deviation... Sound: Get time of maximum... Sound: Get time of minimum... Sound: Get value at sample number... Sound: Get value at time... Sound: Lengthen (PSOLA)... audio control panel Sound: Play Sound: Filter (pre-emphasis)... Sound: Pre-emphasize (in-line)... Sound: Resample... Sound: Set value at sample number... SoundEditor SoundRecorder Sounds: Concatenate Sounds: Convolve w w w w w >w hw w w Ңw ܢw (w fw w w w !w Ew Ow pw "w 2w w w Aw bw jw |w w *w qw w w w sw w jw w "w 2w w w jw bw jw |w w w ܩw w w w Dw w w w jw w "w 2w w w ޫw w jw w "w 2w w w Mw Ew w w "w *w w w w bw w w ۮw Bw :w Ңw Iw w Ѱw w w *w ?w Pw [w w w ?w Kw w ղw w !w +w Fw Pw fw nw w w dzw γw w w w w &w Bw pw }w εw w )w Fw xw w ߶w w (w 7w w Ew Zw w w >w w w w w @w >w ¼w ¼w w w :w w w ľw ̾w w mw w w _w w w 7w ~w w w w =w Nw w w w w w sw w w w Rw Ңw ew sw w w w w Mw w w w )w *w Qw w ?w w Pw w w Ew Nw `w w w w w w Fw zw w w w w w w w Ew w Tw ~w w w w Aw w w w w "w Xw Ow cw w w w w w w w w rw Xw Ow cw w w w 0w Xw Ow tw w w w w uw w w w Xw Ow tw aw fw w ľw qw w w w w Kw w Nw w w ľw ̾w w w w Ww _w qw w w w w w w `w pw )w aw jw w w w w ľw w w @w Ew w w -w Vw w w -w cw Aw Gw w ľw w w w w ľw w Ew %w gw w }w w w rw w w w Lw w ľw w Aw w w w rw Ew %w gw w }w w w w w w w w w Jw w w w w w Kw w w w ľw dw w w Ew gw w }w x w x Aw =x x >x x x x ľw ̾w w mx -x Ex [x x x ľw ̾w w mx x x [x 3 x A command in the @@New menu@ to create an empty @PitchTier object. The resulting object will have the specified name and time domain, but contain no formant points. To add some points to it, use @@PitchTier: Add point...@. For an example, see @@Source-filter synthesis@. One of the @@types of objects@ in P\s{RAAT}. A Harmonicity object represents the degree of acoustic periodicity, also called Harmonics-to-Noise Ratio (HNR). Harmonicity is expressed in dB: if 99\% of the energy of the signal is in the periodic part, and 1\% is noise, the HNR is 10*log10(99/1) = 20 dB. A HNR of 0 dB means that there is equal energy in the harmonics and in the noise. Harmonicity can be used as a measure for: \bu The signal-to-noise ratio of anything that generates a periodic signal. \bu Voice quality. For instance, a healthy speaker can produce a sustained [a] or [i] with a harmonicity of around 20 dB, and an [u] at around 40 dB; the difference comes from the high frequencies in [a] and [i], versus low frequencies in [u], resulting in a much higher sensitivity of HNR to jitter in [a] and [i] than in [u]. Hoarse speakers will have an [a] with a harmonicity much lower than 20 dB. We know of a pathological case where a speaker had an HNR of 40 dB for [i], because his voice let down above 2000 Hz. Harmonicity commands Creation: \bu @@Sound: To Harmonicity (cc)...@: cross-correlation method (preferred). \bu @@Sound: To Harmonicity (ac)...@: autocorrelation method. A command for changing the data in all selected @Harmonicity objects. See the @Formulas tutorial for examples and explanations. A @query to the selected @Harmonicity object. Return value the maximum value, expressed in dB. Arguments %%From time% (s), %%To time% (s) the selected time domain. Values outside this domain are ignored. If %%To time% is not greater than %%From time%, the entire time domain of the Harmonicity object is considered. %%Interpolation the interpolation method (None, Parabolic, Cubic, Sinc) of the @@vector peak interpolation@. The standard is Parabolic because of the usual nonlinearity (logarithm) in the computation of harmonicity; sinc interpolation would be too stiff and may give unexpected results. the mean value, expressed in dB. Setting %%Time range% (s) the time range (%t__1_, %t__2_). Values outside this range are ignored. If %t__1_ is not less than %t__2_, the entire time domain of the Harmonicity is considered. Algorithm The mean harmonicity between the times %t__1_ and %t__2_ is defined as 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ %dt %x(%t) where %x(%t) is the harmonicity (in dB) as a function of time. Frames in which the value is undefined (i.e. in silent intervals) are ignored. If all the frames are silent, the returned value is @undefined. the minimum value, expressed in dB. Settings the time range (%t__1_, %t__2_). Values outside this range are ignored, except for purposes of interpolation. If %t__1_ is not less than %t__2_, the entire time domain of the Harmonicity is considered. the standard deviation, expressed in dB. The standard deviation between the times %t__1_ and %t__2_ is defined as 1/(%t__2_ - %t__1_) \in__%%t%1_^^%%t%2^ %dt (%x(%t) - %\mu)^2 where %x(%t) is the harmonicity (in dB) as a function of time, and %\mu its mean. For our discrete Harmonicity object, the standard deviation is approximated by 1/(%n-1) \su__%i=%m..%m+%n-1_ (%x__%i_ - %\mu)^2 where %n is the number of frame centres between %t__1_ and %t__2_. Note the "minus 1". A @query to the selected @Harmonicity object for the time associated with its maximum value. the time (in seconds) associated with the maximum HNR value. the time (in seconds) associated with the minimum HNR value. A @query to the selected @Harmonicity object to . an estimate (in dB) of the value at a specified time. If this time is outside the time domain or outside the samples of the Harmonicity, the result is @undefined. %Time (s) the time at which the value is to be evaluated. the interpolation method, see @@vector value interpolation@. The standard is Cubic because of the usual nonlinearity (logarithm) in the computation of harmonicity; sinc interpolation would be too stiff and may give unexpected results. the value in a specified frame, expressed in dB. If the index is less than 1 or greater than the number of frames, the result is @undefined. %%Frame number the frame whose value is to be looked up. One of the @@types of objects@ in P\s{RAAT}. For tutorial information, see @@Intro 4. Pitch analysis@. A Pitch object represents periodicity candidates as a function of time. It does not mind whether this periodicity refers to acoustics, perception, or vocal-cord vibration. It is sampled into a number of %frames centred around equally spaced times. Pitch commands \bu @@Sound: To Pitch...@: preferred method (autocorrelation). \bu @@Sound: To Pitch (ac)...@: autocorrelation method (all parameters). \bu @@Sound: To Pitch (cc)...@: cross-correlation method. Drawing: \bu @@Pitch: Draw...@ Viewing and editing: \bu @PitchEditor Synthesis: \bu @@Pitch: To PointProcess@: create points in voiced intervals. \bu @@Sound & Pitch: To PointProcess (cc)@: near locations of high amplitude. \bu @@Sound & Pitch: To PointProcess (peaks)...@: near locations of high amplitude. Conversion: \bu @@Pitch: To PitchTier@: time-stamp voiced intervals. \bu @@Pitch & TextTier: To PitchTier...@: interpolate values at specified times. Inside a Pitch object With @Inspect, you will see the following attributes: %x__%min_ starting time, in seconds. %x__%max_ end time, in seconds. %n__%x_ the number of frames (\>_ 1). %dx time step = frame length = frame duration, in seconds. %x__1_ the time associated with the first frame, in seconds. This will usually be in the range [%xmin, %xmax]. The time associated with the last frame (i.e., %x__1_ + (%n__%x_ \-- 1) %dx)) will also usually be in that range. %ceiling a frequency above which a candidate is considered voiceless. %frame__%i_, %i = 1 ... %n__%x_ the frames (see below). Attributes of a pitch frame Each frame contains the following attributes: %nCandidates the number of candidates in this frame (at least one: the `unvoiced' candidate). %candidate__%j_, %j = 1 ... %nCandidates the information about each candidate (see below). Attributes of each candidate Each candidate contains the following attributes: %frequency the candidate's frequency in Hz (for a voiced candidate), or 0 (for an unvoiced candidate). %strength the degree of periodicity of this candidate (between 0 and 1). Interpretation The current pitch contour is determined by the path through all first candidates. If the first candidate of a certain frame has a frequency of 0, or a frequency above %ceiling, this frame is considered voiceless. A command for drawing the selected @Pitch objects into the @@Picture window@. %%From time% (seconds), %%To time% (seconds) the time domain along the horizontal axis. If these are both zero, the time domain of the #Pitch itself is taken (autowindowing). %%Minimum frequency% (Hz), %%Maximum frequency% (Hz) the frequency range along the vertical axis. %%MaximumFrequency% must be greater than %%minimumFrequency%. Behaviour In unvoiced frames, nothing will be drawn. In voiced frames, the pitch frequency associated with the frame is thought to represent the time midpoint of the frame, but frequencies will be drawn at all time points in the frame, as follows: \bu If two adjacent frames are both voiced, the frequency of the time points between the midpoints of the frames is linearly interpolated from both midpoints. \bu If a voiced frame is adjacent to another voiced frame on one side, and to a voiceless frame on the other side, the frequencies in the half-frame on the unvoiced side will be linearly extrapolated from the midpoints of the two voiced frames involved. \bu If a voiced frame is adjacent to two unvoiced frames, a horizontal line segment will be drawn at the frequency of the midpoint. A command that converts every selected @Pitch object. A command that converts a @Pitch object into a @PitchTier object. The #PitchTier object will contain as many points as there were voiced frames in the #Pitch. The %time of each point is the time associated with the centre of the corresponding %frame of the #Pitch contour. The %frequency of the point is the pitch frequency associated in this frame with the current path through the candidates. A command that uses a @Pitch object to generate a @PointProcess. Purpose to interpret an acoustic periodicity contour as the frequency of an underlying point process (such as the sequence of glottal closures in vocal-fold vibration). 1. A @PitchTier is created with @@Pitch: To PitchTier@. 2. The algorithm of @@PitchTier: To PointProcess@ generates points along the entire time domain of the PitchTier. 3. The PitchTier is removed (it never appeared in the List of Objects). 4. The voiced/unvoiced information in the Pitch is used to remove all points that lie within voiceless frames. One of the @Editors in P\s{RAAT}, for viewing and modifying a @Pitch object. What the Pitch editor shows In the window of the PitchEditor, you will see the following features: \bu Digits between 0 and 9 scattered all over the drawing area. Their locations represent the pitch %#candidates, of which there are several for every time frame. The digits themselves represent the goodness of a candidate, multiplied by ten. For instance, if you see a "9" at the location (1.23 seconds, 189 Hertz), this means that in the time frame at 1.23 seconds, there is a pitch candidate with a value of 189 Hertz, and its goodness is 0.9. The number 0.9 may be the relative height of an autocorrelation peak, a cross-correlation peak, or a spectral peak, depending on the method by which the Pitch object was computed. \bu A %#path of red disks. These disks represent the best path through the candidates, i.e. our best guess at what the pitch contour is. The path will usually have been determined by the %%path finder%, which was called by the pitch-extraction algorithm, and you can change the path manually. The path finder takes into account the goodness of each candidate, the intensity of the sound in the frame, voiced-unvoiced transitions, and frequency jumps. It also determines whether each frame is voiced or unvoiced. \bu A %%##voicelessness bar%# at the bottom of the drawing area. If there is no suitable pitch candidate in a frame, the frame is considered voiceless, which is shown as a blue rectangle in the voicelessness bar. \bu A line of digits between 0 and 9 along the top. These represent the relative intensity of the sound in each frame. Moving the marks To move the cursor hair or the beginning or end of the selection, use the @@time selection@ mechanism. Changing the path To change the path through the candidates manually, click on the candidates of your choice. The changes will immediately affect the Pitch object that you are editing. To make a voiced frame voiceless, click on the voicelessness bar. To change the path automatically, choose `Path finder...' from the `Edit' menu; this will have the same effect as filling in different values in the @@Sound: To Pitch (ac)...@ dialog, but is much faster because the candidates do not have to be determined again. Resynthesis To hum any part of the pitch contour, click on one of the buttons below or above the data area (there can be 1 to 8 of these buttons), or use a Play command from the View menu. Changing the ceiling To change the ceiling, but not the path, choose `Change ceiling...' from the `Edit' menu; if the new ceiling is lower than the old ceiling, some formerly voiced frames may become unvoiced; if the new ceiling is higher than the old ceiling, some formerly unvoiced frames may become voiced. One of the @@types of objects@ in P\s{RAAT}. A PitchTier object represents a time-stamped pitch contour, i.e. it contains a number of (%time, %pitch) points, without voiced/unvoiced information. For instance, if your PitchTier contains two points, namely 150 Hz at a time of 0.5 seconds and 200 Hz at a time of 1.5 seconds, then this is to be interpreted as a pitch contour that is constant at 150 Hz for all times before 0.5 seconds, constant at 200 Hz for all times after 1.5 seconds, and linearly interpolated for all times between 0.5 and 1.5 seconds (i.e. 170 Hz at 0.7 seconds, 210 Hz at 1.1 seconds, and so on). PitchTier objects are used for two purposes: for manipulating the pitch curve of an existing sound (see @@Intro 8.1. Manipulation of pitch@) and for synthesizing a new sound (see @@Source-filter synthesis 1. Creating a source from pitch targets@, and for an example @@Source-filter synthesis 3. The ba-da continuum@). PitchTier commands From scratch: \bu @@Create PitchTier... \bu @@PitchTier: Add point... Copy from another object: \bu @@Pitch: To PitchTier@: trivial copying of voiced frames. \bu @@PointProcess: Up to PitchTier...@: single value at specified times. \bu @@Pitch & TextTier: To PitchTier...@: copying interpolated values at specified points. Synthesize from another object: \bu @@PointProcess: To PitchTier...@: periodicity analysis. Extract from a @Manipulation object: \bu @@Manipulation: Extract pitch tier@ \bu @PitchTierEditor: with or without a Sound. \bu @ManipulationEditor \bu @@PitchTier: Down to PointProcess@: copy the times. \bu @@PitchTier: To PointProcess@: area-1 pulse generation (used in @PSOLA). \bu @@Manipulation: Replace pitch tier@ Queries: \bu @@time domain \bu @@Get low index from time... \bu @@Get high index from time... \bu @@Get nearest index from time... \bu @@PitchTier: Get mean (curve)... \bu @@PitchTier: Get mean (points)... \bu @@PitchTier: Get standard deviation (curve)... \bu @@PitchTier: Get standard deviation (points)... \bu @@Get area...@: the number of periods Modification: \bu @@Remove point... \bu @@Remove point near... \bu @@Remove points between... \bu @@PitchTier: Stylize... A command to add a point to each selected @PitchTier. the time at which a point is to be added. %Pitch (Hz) the pitch value of the requested new point. The tier is modified so that it contains the new point. If a point at the specified time was already present in the tier, nothing happens. A command to degrade every selected @PitchTier to a @PointProcess. The times of all the pitch points are trivially copied, and so is the time domain. The pitch information is lost. A @query to the selected @PitchTier object. the mean of the curve within a specified time window. Attributes the time window. Values outside this window are ignored. If %%To time% is not greater than %%From time%, the entire time domain of the tier is considered. The curve consists of a sequence of line segments. The contribution of the line segment from (%t__1_, %f__1_) to (%t__2_, %f__2_) to the area under the curve is 1/2 (%f__1_ + %f__2_) (%t__2_ \-- %t__1_) The mean is the sum of these values divided by %toTime \-- %fromTime. For a PitchTier that was created from a @Pitch object, this command gives the same result as ##Get mean....# for the original Pitch object (but remember that the median, as available for Pitch objects, is more robust). To get the mean in the entire curve, i.e. weighted by the durations of the line pieces, Use @@PitchTier: Get mean (points)...@ instead. the mean of the points within a specified time window. To get the mean in the entire curve, i.e. weighted by the durations of the line pieces, Use @@PitchTier: Get mean (curve)...@ instead. the standard deviation in the curve within a specified time window. the selected time domain. Values outside this domain are ignored. If %%To time% is not greater than %%From time%, the entire time domain of the tier is considered. The curve consists of a sequence of line segments. The contribution of the line segment from (%t__1_, %f__1_) to (%t__2_, %f__2_) to the variance-multiplied-by-time is [ 1/4 (%f__1_ + %f__2_)^2 + 1/12 (%f__1_ \-- %f__2_)^2 ] (%t__2_ \-- %t__1_) The standard deviation is the square root of: the sum of these values divided by %toTime \-- %fromTime. To get the standard deviation in the points only, i.e. not weighted by the durations of the line pieces, Use @@PitchTier: Get standard deviation (points)...@ instead. the standard deviation in the points within a specified time window. For a PitchTier that was created from a @Pitch object, this command gives the same result as ##Get standard deviation....# for the original Pitch object (but remember that variation measures based on quantiles, as available for Pitch objects, are more robust). To get the standard deviation in the entire curve, i.e. weighted by the durations of the line pieces, Use @@PitchTier: Get standard deviation (curve)...@ instead. A command that modifies the selected @PitchTier object (or the pitch curve in the @ManipulationEditor). to end up with a much simplified pitch curve. %%Frequency resolution% (standard: 2.0 semitones) the minimum amount by which every remaining pitch point will lie above or below the line that connects its two neigbours. 1. Look up the pitch point that is closest to the straight line that connects its two neighbouring points. 2. If this pitch point is further away from that straight line than %%frequency resolution%, we are finished: the curve cannot be stylized any further. 3. If we are not finished, the pitch point we found in step 1 is removed. 4. Go back to step 1. A command that uses a @PitchTier object to generate a @PointProcess. Points are generated along the entire time domain of the #PitchTier, because there is no voiced/unvoiced information. The area between two adjacent points under the linearly interpolated pitch contour, is always 1. One of the @Editors in P\s{RAAT}, for viewing and manipulating a @PitchTier object, which is optionally shown together with a @Sound object. Objects The editor shows: \bu The @Sound, if you selected a Sound object together with the PichTier object before you clicked #Edit. \bu The @PitchTier: blue points connected with blue lines. Playing To play (a part of) the %resynthesized sound: @click on any of the 8 buttons below and above the drawing area, or choose a Play command from the View menu. To play the %original sound instead, use @@Shift-click@. Adding a point @Click at the desired time location, and choose ##Add point at cursor# or type ##Command-P#. Removing points To remove one or more pitch points, make a @@time selection@ and choose ##Remove point(s)# from the ##Point# menu. If there is no selection, the point nearest to the cursor is removed. A command to compute a @PitchTier from a @PointProcess. Argument %%Maximum interval% (s) the maximum duration of a period; intervals longer than this are considered voiceless. A pitch point is constructed between each consecutive pair of points in the #PointProcess, if these are more than %maximumInterval apart. The associated pitch value will be the inverse of the duration of the interval between the two points. A command that creates a @Harmonicity object from every selected @Sound object. to perform a short-term HNR analysis. The algorithm performs an acoustic periodicity detection on the basis of an accurate autocorrelation method, as described in @@Boersma (1993)@. %%Time step% (standard value: 0.01 s) the measurement interval (frame duration), in seconds. %%Minimum pitch% (standard value: 75 Hz) determines the length of the analysis window. %%Silence threshold% (standard value: 0.1) frames that do not contain amplitudes above this threshold (relative to the global maximum amplitude), are considered silent. %%Number of periods per window% (standard value: 4.5) 4.5 is best for speech: HNR values up to 37 dB are guaranteed to be detected reliably; 6 periods per window raises this figure to more than 60 dB, but the algorithm becomes more sensitive to dynamic changes in the signal. Usage You will normally use @@Sound: To Harmonicity (cc)...@ instead of this command, because that has a much better time resolution (though its sensitivity is 60, not 80 dB). The algorithm performs an acoustic periodicity detection on the basis of a forward cross-correlation analysis. For information on the arguments, see @@Sound: To Harmonicity (ac)...@. A command that creates a @Pitch object from every selected @Sound object. to perform a pitch analysis, optimized for speech. The arguments that control the recruitment of the candidates are: %%Time step% (standard value: 0.0) the measurement interval (frame duration), in seconds. If you supply 0, P\s{RAAT} will use a time step of 0.75 / (%%pitch floor%), e.g. 0.01 seconds if the pitch floor is 75 Hz; in this example, P\s{RAAT} computes 100 pitch values per second. %%Pitch floor% (standard value: 75 Hz) candidates below this frequency will not be recruited. This parameter determines the length of the analysis window: it will be 3 longest periods long, i.e., if the pitch floor is 75 Hz, the window will be 3/75 = 0.04 seconds long. Note that if you set the time step to zero, the analysis windows for consecutive measurements will overlap appreciably: P\s{RAAT} will always compute 4 pitch values within one window length, i.e., the degree of %oversampling is 4. A post-processing algorithm seeks the cheapest path through the candidates. The argument that determines the cheapest path is: %%Pitch ceiling% (standard value: 600 Hz) candidates above this frequency will be ignored. This is the algorithm described at @@Sound: To Pitch (ac)...@, with all the parameters not mentioned above set to their standard values. to perform a pitch analysis based on an autocorrelation method. Normally, you will instead use @@Sound: To Pitch...@, which uses the same method. The command described here is mainly for experimenting with the parameters, or for the analysis of non-speech signals, which may require different standard settings of the parameters. The algorithm performs an acoustic periodicity detection on the basis of an accurate autocorrelation method, as described in @@Boersma (1993)@. This method is more accurate, noise-resistant, and robust, than methods based on cepstrum or combs, or the original autocorrelation methods. The reason why other methods were invented, was the failure to recognize the fact that if you want to estimate a signal's short-term autocorrelation function on the basis of a windowed signal, you should divide the autocorrelation function of the windowed signal by the autocorrelation function of the window: %r__%x_ (%\ta) \~~ %r__%xw_ (%\ta) / %r__%w_ (%\ta) candidates below this frequency will not be recruited. This parameter determines the effective length of the analysis window: it will be 3 longest periods long, i.e., if the pitch floor is 75 Hz, the window will be effectively 3/75 = 0.04 seconds long. %%Very accurate% (standard value: %off) if %off, the window is a Hanning window with a physical length of 3 / (%%pitch floor%). If %on, the window is a Gaussian window with a physical length of 6 / (%%pitch floor%), i.e. twice the effective length. A post-processing algorithm seeks the cheapest path through the candidates. The arguments that determine the cheapest path are: %%Silence threshold% (standard value: 0.03) frames that do not contain amplitudes above this threshold (relative to the global maximum amplitude), are probably silent. %%Voicing threshold% (standard value: 0.45) the strength of the unvoiced candidate, relative to the maximum possible autocorrelation. To increase the number of unvoiced decisions, increase this value. %%Octave cost% (standard value: 0.01 per octave) degree of favouring of high-frequency candidates, relative to the maximum possible autocorrelation. This is necessary because even (or: especially) in the case of a perfectly periodic signal, all undertones of %F__0_ are equally strong candidates as %F__0_ itself. To more strongly favour recruitment of high-frequency candidates, increase this value. %%Octave-jump cost% (standard value: 0.35) degree of disfavouring of pitch changes, relative to the maximum possible autocorrelation. To decrease the number of large frequency jumps, increase this value. In contrast with what is described in the article, this value will be corrected for the time step: multiply by 0.01 s / %TimeStep to get the value in the way it is used in the formulas in the article. %%Voiced / unvoiced cost% (standard value: 0.14) degree of disfavouring of voiced/unvoiced transitions, relative to the maximum possible autocorrelation. To decrease the number of voiced/unvoiced transitions, increase this value. In contrast with what is described in the article, this value will be corrected for the time step: multiply by 0.01 s / %TimeStep to get the value in the way it is used in the formulas in the article. to perform a pitch analysis based on a cross-correlation method. The algorithm performs an acoustic periodicity detection on the basis of a forward cross-correlation analysis. the measurement interval (frame duration), in seconds. If you supply 0, P\s{RAAT} will use a time step of 0.25 / (%%pitch floor%), e.g. 0.00333333 seconds if the pitch floor is 75 Hz; in this example, P\s{RAAT} computes 300 pitch values per second. candidates below this frequency will not be recruited. This parameter determines the length of the analysis window: it will be 1 longest period long, i.e., if the pitch floor is 75 Hz, the window will be 1/75 = 0.01333333 seconds long. The other arguments are the same as for @@Sound: To Pitch (ac)...@. The preferred method for speech is @@Sound: To Pitch...@. The command described here is mainly for experimenting, or for applications where you need short time windows. A command that analyses the selected @Sound objects, and creates @PointProcess objects. This command combines the actions of @@Sound: To Pitch (ac)...@ and @@Sound & Pitch: To PointProcess (cc)@. This command combines the actions of @@Sound: To Pitch (ac)...@ and @@Sound & Pitch: To PointProcess (peaks)...@. A command to create a @PointProcess from the selected @Sound and @Pitch objects. The voiced intervals are determined on the basis of the voiced/unvoiced decisions in the @Pitch object. For every voiced interval, a number of %points (or glottal pulses) is found as follows: 1. The first point %t__1_ is the absolute extremum of the amplitude of the #Sound, between %t__%mid_ \-- %T__0_ / 2 and %t__%mid_ + %T__0_ / 2, where %t__%mid_ is the midpoint of the interval, and %T__0_ is the period at %t__%mid_, as can be interpolated from the #Pitch contour. 2. From this point, we recursively search for points %t__%i_ to the left until we reach the left edge of the interval. These points must be located between %t__%i\--1_ \-- 1.2 %T__0_(%t__%i\--1_) and %t__%i\--1_ \-- 0.8 %T__0_(%t__%i\--1_), and the cross-correlation of the amplitude in its environment [%t__%i_ \-- %T__0_(%t__%i_) / 2; %t__%i_ + %T__0_(%t__%i_) / 2] with the amplitude of the environment of the existing point %t__%i\--1_ must be maximal (we use parabolic interpolation between samples of the correlation function). 3. The same is done to the right of %t__1_. 4. Though the voiced/unvoiced decision is initially taken by the #Pitch contour, points are removed if their correlation value is less than 0.3; furthermore, one extra point may be added at the edge of the voiced interval if its correlation value is greater than 0.7. 1. The first point %t__1_ is the absolute extremum (or the maximum, or the minimum, depending on your %%Include maxima% and %%Include minima% settings) of the amplitude of the #Sound, between %t__%mid_ \-- %T__0_ / 2 and %t__%mid_ + %T__0_ / 2, where %t__%mid_ is the midpoint of the interval, and %T__0_ is the period at %t__%mid_, as can be interpolated from the #Pitch contour. 2. From this point, we recursively search for points %t__%i_ to the left until we reach the left edge of the interval. These points are the absolute extrema (or the maxima, or the minima) between the times %t__%i\--1_ \-- 1.2 %T__0_(%t__%i\--1_) and %t__%i\--1_ \-- 0.8 %T__0_(%t__%i\--1_). The periods that are found in this way are much more variable than those found by @@Sound & Pitch: To PointProcess (cc)@, and therefore less useful for PSOLA analysis. Create PitchTier... ppgb Harmonicity Harmonicity: Formula... Harmonicity: Get maximum... Harmonicity: Get mean... Harmonicity: Get minimum... Harmonicity: Get standard deviation... Harmonicity: Get time of maximum... Harmonicity: Get time of minimum... Harmonicity: Get value at time... Harmonicity: Get value in frame... Pitch Pitch: Draw... Pitch: Interpolate Pitch: Smooth... Pitch: To PitchTier Pitch: To PointProcess PitchEditor PitchTier PitchTier: Add point... PitchTier: Down to PointProcess PitchTier: Get mean (curve)... PitchTier: Get mean (points)... PitchTier: Get standard deviation (curve)... PitchTier: Get standard deviation (points)... PitchTier: Stylize... PitchTier: To PointProcess PitchTierEditor PointProcess: To PitchTier... Sound: To Harmonicity (ac)... Sound: To Harmonicity (cc)... Sound: To Pitch... Sound: To Pitch (ac)... Sound: To Pitch (cc)... Sound: To PointProcess (periodic, cc)... Sound: To PointProcess (periodic, peaks)... Sound & Pitch: To PointProcess (cc) Sound & Pitch: To PointProcess (peaks)... ,*x q*x +x ?+x ,x ,x ,x ,x -x -x -x -x >-x B-x y-x }-x P.x l.x .x .x .x .x 3/x >/x ~/x /x /x /x $0x /0x W0x b0x 0x 0x 0x 0x 1x 1x 1x 62x @2x a2x 2x 2x 13x G3x k4x u4x 1x 1x O5x 62x @2x a2x 2x 2x k4x u4x 5x 5x 6x +7x 7x 6x 7x +x n8x 62x 8x 8x @9x L9x y9x 9x 9x 9x ;x ;x l<x 9x <x 62x 8x 8x @2x <x y9x 9x =x =x =x 9x P>x 62x 8x 8x @2x <x y9x 9x l>x v>x >x >x >x -?x 9x ?x 62x 8x 8x @2x <x y9x 9x =x =x ?x @x @x @x 9x O@x g@x 9x Ax 62x 8x 8x @2x <x y9x 9x 1Ax ;Ax ;x Bx Cx 9x -Dx 62x 8x 8x @2x <x y9x 9x WDx @x 8x 8x @2x Dx y9x 9x =x Ex 9x Fx ^Fx @x 8x 8x @2x Dx y9x 9x =x Ex 9x Fx Fx 62x 8x 8x @9x `Gx Gx 9x Gx Gx 9x Gx ;x 7Ix 4Jx Jx Kx FLx \Lx 62x Mx kNx ~Nx pOx Ox CPx [Px Px Qx Rx 0Rx Sx Tx Tx Tx LWx ^Wx Xx Xx ;x .Zx `[x [x #\x Y\x \x I]x v]x ^x ^x ^x ^x ^x _x _x :_x _x _x _x _x `x `x ?`x a`x `x `x `x `x _x `x `x 0ax 8ax ax ax ax ax Rbx dbx bx bx +cx Ocx cx ^x 62x cx cx %dx Gdx 1x ex ex 1x ex Zfx 62x gx 4gx hx hx Bjx ]jx lx lx {ox ox ;x rx sx ux dvx lvx 62x vx ;x wx ux dvx lvx 62x vx ;x xx zx zx ^x {x zx ^x {x J|x ^x |x J|x ^x :}x A command in the @@New menu@ to create an empty @FormantTier object. The resulting object will have the specified name and time domain, but contain no formant points. To add some points to it, use @@FormantTier: Add point...@. For an example, see @@Source-filter synthesis@. One of the @@types of objects@ in P\s{RAAT}. A Formant object represents spectral structure as a function of time: a %%formant contour%. Unlike the time-stamped @FormantTier object, it is sampled into a number of %frames centred around equally spaced times, Each frame contains frequency and bandwidth information about several formants. Inside a Formant object With @Inspect, you will see the following attributes: %xmin starting time, in seconds. %xmax end time, in seconds. %nx the number of frames (\>_ 1). %dx time step = frame length = frame duration, in seconds. %x1 the time associated with the first frame, in seconds. This will usually be in the range [%xmin, %xmax]. The time associated with the last frame (i.e., %x1 + (%nx \-- 1) %dx)) will also usually be in that range. %frame__%i_, %i = 1 ... %nx the frames (see below). Attributes of a formant frame Each %frame__%i_ contains the following attributes: %intensity an indication of the maximum intensity (a squared sound amplitude) in this frame. %nFormants the number of formants in this frame (usually between 2 and 6). %formant__%j_, %j = 1 ... %nFormants the information about each formant (see below). Attributes of each formant Each %formant__%j_ contains the following attributes: %frequency the formant's centre frequency (in Hz). %bandwidth the formant's bandwidth (in Hz). See also ##Linear Prediction# A command for converting each selected @Formant object into a @FormantTier object. The resulting FormantTier contains a point for each original frame. The number of formants in the result is limited to 10. The intensity information is lost. A command to draw the selected @Formant objects to the @@Picture window@. Behaviour Every formant value is drawn as a small circle, filled with the current colour. Arguments %%From time% (s), %%To time% (s) the time domain of the drawing. If %%To time% is not greater than %%From time%, the entire formant contour is drawn. %%Maximum frequency% (Hz) the height of the %y axis. For speech, 5000 Hz is a usual value. %%Dynamic range% (dB) determines the signal intensity (as stored in each formant frame) below which no formants will be drawn. If zero, all formants will be drawn. The standard value is 30 dB, which would mean that formants in frames with intensities less than the maximum intensity minus 30 dB will not be drawn. %%Garnish determines whether axes, numbers, and texts ("Time", "Formant frequency") will be drawn in the margins around the picture. Turn this button off if you prefer to garnish your picture by yourself with the @Margins menu. Every formant value is drawn as one or two short line segments, connected, if possible, with a line segment of the corresponding formant values in the adjacent frames. Usage Unlike @@Formant: Speckle...@, this procedure assumes that e.g. the second formant in frame %i has something to do with the second formant in frame %i+1. To make this assumption more plausible, use @@Formant: Track...@ first. A command to modify each selected @Formant object with a specified formula. For what you can do with formulas, see @@Matrix: Formula...@. The %%i%th row contains the values of the %%i%th bandwidth contour. See @@Formant: Formula (frequencies)...@ for more information. For what you can do with formulas, see @@Matrix: Formula...@. The %%i%th row contains the values of the %%i%th frequency contour. A @query to the selected @Formant object for the bandwidth of the specified formant at the specified time. %%Formant number the ordinal number of the formant, counting up from 0 Hz. Specify "2" for %F__2_ etc. %%Time% (s) the time at which to evaluate the bandwidth. %Units the units of the result (Hertz or Bark). Return value the estimated bandwidth in Hertz or Bark. If %Time is not within half a frame width of any frame centre, or If the specified %%Formant number% is greater than the number of formants in the frame, the return value is @undefined; otherwise, the formant is considered to belong to the frame whose centre is nearest to the specified time. Algorithm If possible (i.e. if the adjacent frame has enough formants), a linear interpolation is performed between the centre of the frame and the centre of the adjacent frame. With Bark units, the Hertz-to-Bark transformation is performed on the two frequencies %F \+_ 1/2 %B (after interpolation), and the result is the difference between these two values A @query to ask the selected @Formant object for the maximum value of the specified formant. the maximum, in Hertz or Bark. the selected time domain. Values outside this domain are ignored. If %%To time% is not greater than %%From time%, the entire time domain of the formant contour is considered. %Interpolation the interpolation method (none or parabolic). See @@vector peak interpolation@. A @query to ask the selected @Formant object for the mean value of the specified formant. the mean, in Hertz or Bark. Scripting You can use this command to put the mean into a script variable: select Formant hallo mean = Get mean... 2 0 0 Hertz In this case, the value will not be written into the Info window. A @query to ask the selected @Formant object for the minimum value of the specified formant. the minimum, in Hertz or Bark. A @query to ask the selected @Formant object for the number of formants in a specified frame. Argument %%Frame number the frame number whose formant count is sought. the number of formants. A @query to ask the selected @Formant object for an estimation of the specified quantile of the distribution that underlies the attested values of the specified formant. the quantile, in Hertz or Bark. %Quantile the fraction (between 0 and 1) of the values of the underlying distribution expected to lie below the result. For instance, if %Quantile is 0.10, the algorithm estimates the formant value below which 10\% of all formant values are expected to lie. To get an estimate of the %median of the underlying distribution, specify a quantile of 0.50. First, the available formant values within the selected time domain are collected in an array. This array is then sorted and the @@quantile algorithm@ is performed. With Bark units, the Hertz-to-Bark transformation is performed before the quantile algorithm. A @query to ask the selected @Formant object for the standard deviation of the attested values of the specified formant within a specified time domain. the standard deviation, in Hertz or Bark. A @query to ask the selected @Formant object for the time associated with the maximum value of a specified formant within a specified time domain. the selected time domain. Values outside this domain are ignored, except for interpolation. If %%To time% is not greater than %%From time%, the entire time domain of the formant contour is considered. the interpolation method (None or Parabolic). See @@vector peak interpolation@. the time expressed in seconds. If no relevant formants are found, the value is @undefined. A @query to ask the selected @Formant object for the time associated with the minimum value of a specified formant within a specified time domain. A @query to ask the selected @Formant object for the frequency of the specified formant at the specified time. the time at which to evaluate the formant frequency. %Units) %%Interpolation the interpolation method, see @@vector value interpolation@. Always Linear. the bandwidth in Hertz or Bark. If %Time is not within half a frame width of any frame centre, or if the specified %%Formant number% is greater than the number of formants in the frame, the value is @undefined; otherwise, the formant is considered to belong to the frame whose centre is nearest to the specified time. If possible (i.e. if the adjacent frame has enough formants), a linear interpolation is performed between the centre of the frame and the centre of the adjacent frame. With Bark units, the Hertz-to-Bark transformation is performed before interpolation. A command to extract a specified number of formant tracks from each selected @Formant object. The tracks represent the cheapest paths through the measured formant values in consecutive frames. How to use In order to be capable of producing three tracks (i.e. F1, F2, and F3), there must be at least three formant candidates in %every frame of the Formant object. The typical use of this command, therefore, is to analyse five formants with @@Sound: To Formant (burg)...@ and then use the tracking command to extract three tracks. When to use, when not This command only makes sense if the whole of the formant contour makes sense. For speech, formant contours make sense only for vowels and the like. During some consonants, the Formant object may have fewer than three formant values, and trying to create three tracks through them will fail. You will typically use this command for the contours in diphthongs, if at all. To be able to interpret the arguments, you should know that the aim of the procedure is to minimize the sum of the %costs associated with the three tracks. %%Number of tracks the number of formant tracks that the procedure must find. If this number is 3, the procedure will try to find tracks for F1, F2, and F3; if the Formant object contains a frame with less than three formants, the tracking procedure will fail. %%Reference F1% (Hertz) the preferred value near which the first track wants to be. For average (i.e. adult female) speakers, this value will be around the average F1 for vowels of female speakers, i.e. 550 Hz. %%Reference F2% (Hertz) the preferred value near which the second track wants to be. A good value will be around the average F2 for vowels of female speakers, i.e. 1650 Hz. %%Reference F3% (Hertz) the preferred value near which the third track wants to be. A good value will be around the average F3 for vowels of female speakers, i.e. 2750 Hz. This argument will be ignored if you choose to have fewer than three tracks, i.e., if you are only interested in F1 and F2. %%Reference F4% (Hertz) the preferred value near which the fourth track wants to be. A good value may be around 3850 Hz, but you will usually not want to track F4, because traditional formant lore tends to ignore it (however inappropriate this may be for the vowel [i]), and because Formant objects often contain not more than three formant values in some frames. So you will not usually specify a higher %%Number of tracks% than 3, and in that case, this argument will be ignored. %%Reference F5% (Hertz) the preferred value near which the five track wants to be. In the unlikely case that you want five tracks, a good value may be around 4950 Hz. %%Frequency cost% (per kiloHertz) the local cost of having a formant value in your track that deviates from the reference value. For instance, if a candidate (i.e. any formant in a frame of the Formant object) has a formant frequency of 800 Hz, and the %%Frequency cost% is 1.0/kHz, the cost of putting this formant in the first track is 0.250, because the distance to the reference F1 of 550 Hz is 250 Hz. The cost of putting the formant in the second track would be 0.850 (= (1.650 kHz - 0.600 kHz) \.c 1.0/kHz), so we see that the procedure locally favours the inclusion of the 800 Hz candidate into the F1 track. But the next two cost factors may override this local preference. %%Bandwidth cost% the local cost of having a bandwidth, relative to the formant frequency. For instance, if a candidate has a formant frequency of 400 Hz and a bandwidth of 80 Hz, and the %%Bandwidth cost% is 1.0, the cost of having this formant in any track is (80/400) \.c 1.0 = 0.200. So we see that the procedure locally favours the inclusion of candidates with low relative bandwidths. %%Transition cost% (per octave) the cost of having two different consecutive formant values in a track. For instance, if a proposed track through the candidates has two consecutive formant values of 300 Hz and 424 Hz, and the %%Transition cost% is 1.0/octave, the cost of having this large frequency jump is (0.5 octave) \.c (1.0/octave) = 0.500. This command uses a Viterbi algorithm with multiple planes. For instance, if the selected Formant object contains up to five formants per frame, and you request three tracks, the Viterbi algorithm will have to choose between ten candidates (the number of combinations of three out of five) for each frame. The formula for the cost of e.g. track 3, with proposed values %F__2%i_ (%i = 1...%N, where %N is the number of frames) is: \su__%i=1..%N_ %frequencyCost\.c\|f%F__3%i_ \-- %referenceF3\|f/1000 + + \su__%i=1..%N_ %bandWidthCost\.c%B__3%i_/%F__3%i_ + + \su__%i=1..%N-1_ %transitionCost\.c\|flog__2_(%F__3%i_/%F__3,%i+1_)\|f Analogous formulas compute the cost of track 1 and track 2. The procedure will assign those candidates to the three tracks that minimize the sum of three track costs. One of the @@types of objects@ in P\s{RAAT}. A FormantTier object represents spectral structure as a function of time: a %%formant contour%. Unlike the evenly sampled @Formant object, it consists of a number of formant %points (or %targets), sorted by time. Each point contains contains several formant/bandwidth pairs. For examples, see @@Source-filter synthesis@. FormantTier commands Creation: From scratch: \bu @@Create FormantTier... \bu @@FormantTier: Add point... Copy from another object: \bu @@Formant: Down to FormantTier@: trivial copying of frames to points. Conversion: \bu @@FormantTier: Down to PointProcess@: copy times. Synthesis: \bu @@Sound & FormantTier: Filter@: see @@Source-filter synthesis@. Queries: \bu @@Get low index from time... \bu @@Get high index from time... \bu @@Get nearest index from time... Modification: \bu @@Remove point... \bu @@Remove point near... \bu @@Remove points between... FormantTier attributes With @Inspect, you will see the following attribute: %points when you open this, you see the %size (the number of points) and a series of points (%item [%i], %i = 1...%n). Attributes of a formant point Each point contains the following attributes: %time the time associated with this formant target, in seconds. Also used to sort the targets. %numberOfFormants the number of formant/bandwidth pairs (never more than 10). %formant [0..%numberOfFormants-1] the formant frequencies in Hertz. ##Caution:# the frequency of the %%i%th formant is in %formant [%i-1]! %bandwidth [0..%numberOfFormants-1] the formant bandwidths in Hertz. ##Caution:# the bandwidth of the %%i%th formant is in %bandwidth [%i-1]! A command to add a point to each selected @FormantTier. %Time (s) the time at which a point is to be added. %%Frequencies and bandwidths (Hz) the frequency and bandwidth values of the requested new point. To get three formants at 500, 1500, and 2500 Hz with bandwidths of 50, 100, and 150 Hz, respectively, you specify "500 50 1500 100 2500 150". The tier is modified so that it contains the new point. If a point at the specified time was already present in the tier, nothing happens. A command to degrade every selected @FormantTier to a @PointProcess. The times of all the formant points are trivially copied, and so is the time domain. The formant information is lost. A command that creates a @Formant object from every selected @Sound object. It performs a short-term spectral analysis, approximating the spectrum of each analysis frame by a number of formants. %%Time step% (seconds) the time between the centres of consecutive analysis frames. If the sound is 2 seconds long, and the time step is 0.01 seconds, there will be approximately 200 analysis frames. The actual number is somewhat lower (usually 195), because we cannot measure very well near the edges. If you set the time step to 0.0 (the standard), Praat will use a time step that is equal to 25 percent of the analysis window length (see below). %%Maximum number of formants% for most analyses of human speech, you will want to extract 5 formants per frame. This, in combination with the %%Maximum formant% argument, is the only way in which this procedure will give you results compatible with how people tend to interpret formants for vowels, i.e. in terms of vowel height (F1) and vowel place (F2). %%Maximum formant% (Hertz) the ceiling of the formant search range. It is crucial that you set this argument to a value suitable for your speaker. The standard value of 5500 Hz is suitable for an average adult female. For a male, use 5000 Hz; if you use 5500 Hz for an adult male, you may end up with too few formants in the low frequency region, e.g. analysing an [u] as having a single formant near 500 Hz whereas you want two formants at 300 and 600 Hz. For a young child, use a value much higher than 5500 Hz, for instance 8000 Hz (experiment with it on steady vowels). %%Window length% (seconds) the effective duration of the analysis window. The actual length is twice this value, because Praat uses a Gaussian-like analysis window with sidelobes below -120 dB. For instance, if the %%Window length% is 0.025 seconds, the actual Gaussian window duration is 0.050 seconds. This window has values below 4\% outside the central 0.025 seconds, and its frequency resolution (-3 dB point) is 1.298 / (0.025 s) = 51.9 Hz, as computed with the formula given at @@Sound: To Spectrogram...@. This is comparable to the bandwidth of a Hamming window of 0.025 seconds, which is 1.303 / (0.025 s) = 52.1 Hz, but that window (which is the window most often used in other analysis programs) has three spectral lobes of about -42 dB on each side. %%Pre-emphasis from% (Hertz) the +3 dB point for an inverted low-pass filter with a slope of +6 dB/octave. If this value is 50 Hz, then frequencies below 50 Hz are not enhanced, frequencies around 100 Hz are amplified by 6 dB, frequencies around 200 Hz are amplified by 12 dB, and so forth. The point of this is that vowel spectra tend to fall by 6 dB per octave; the pre-emphasis creates a flatter spectrum, which is better for formant analysis because we want our formants to match the local peaks, not the global spectral slope. See the @@source-filter synthesis@ tutorial for a technical explanation, and @@Sound: Pre-emphasize (in-line)...@ for the algorithm. The sound will be resampled to a sampling frequency of twice the value of %%Maximum formant%, with the algorithm described at @@Sound: Resample...@. After this, pre-emphasis is applied with the algorithm described at @@Sound: Pre-emphasize (in-line)...@. For each analysis window, Praat applies a Gaussian-like window, and computes the LPC coefficients with the algorithm by Burg, as given by @@Childers (1978)@ and @@Press et al. (1992)@. This algorithm can initially find formants at very low or high frequencies. In order for you to be able to identify the traditional F1 and F2, all formants below 50 Hz and all formants above %%Maximum formant% minus 50 Hz, are removed. If you don't want this, you may experiment with @@Sound: To Formant (keep all)...@ instead. If you prefer an algorithm that always yields the requested number of formants, nicely distributed across the frequency domain, you may try the otherwise rather unreliable Split-Levinson procedure @@Sound: To Formant (sl)...@. A command that creates a @Formant object from every selected @Sound object. Not recommended for general use. Purpose to perform a short-term spectral analysis, approximating the spectrum of each frame by a number of formants. The same as with @@Sound: To Formant (burg)...@. The same as with @@Sound: To Formant (burg)...@. In contrast with that command, however, all formant values are kept, even those below 50 Hz and those above %%Maximum formant% minus 50 Hz. Although this makes the identification of the traditional F1 and F2 more difficult, this might give better results in resynthesis (see @@Sound & Formant: Filter@), but it usually generates funny values instead. The algorithm is based on the implementation of the `Split Levinson' algorithm by @@Willems (1986)@. This algorithm will always find the requested number of formants in every frame, even if they do not exist. The standard routine (@@Sound: To Formant (burg)...@) yields much more reliable formant values, though it is more sensitive to the %%Maximum formant% argument. Because of the general funny behaviour of the Split-Levinson algorithm, we did not bother to implement an analysis of the bandwidths. They are all set arbitrarily to 50 Hz. A command to create a new Sound from the selected @Sound and @Formant objects. The resulting Sound is scaled so that its maximum absolute amplitude is 0.99. If you don't want this, use @@Sound & Formant: Filter (no scale)@ instead. Unlike what happens in @@Sound & Formant: Filter@, the resulting Sound is not scaled. This allows generation of a series of signals with controlled relative intensities. A command to create a new Sound from the selected @Sound and @FormantTier objects. The resulting Sound is scaled so that its maximum absolute amplitude is 0.99. If you don't want this, use @@Sound & FormantTier: Filter (no scale)@ instead. Unlike what happens in @@Sound & FormantTier: Filter@, the resulting Sound is not scaled. This allows generation of a series of signals with controlled relative intensities. Create FormantTier... ppgb Formant Formant: Down to FormantTier Formant: Speckle... Formant: Draw tracks... Formant: Formula (bandwidths)... Formant: Formula (frequencies)... Formant: Get bandwidth at time... Formant: Get maximum... Formant: Get mean... Formant: Get minimum... Formant: Get number of formants Formant: Get quantile... Formant: Get standard deviation Formant: Get time of maximum... Formant: Get time of minimum... Formant: Get value at time... Formant: Track... FormantTier FormantTier: Add point... FormantTier: Down to PointProcess Sound: To Formant (burg)... Sound: To Formant (keep all)... Sound: To Formant (sl)... Sound & Formant: Filter Sound & Formant: Filter (no scale) Sound & FormantTier: Filter Sound & FormantTier: Filter (no scale) ěx x x x 8x Lx px }x ̜x ڜx Px x x tx x Ğx x x ?x `x ՠx x ]x tx x x ӡx ݡx x x 7x x x ӡx ݡx ^x dx zx x x %x Sx ֤x Bx x x x x 1x x (x x x ox x x px }x ̜x ڜx x x ٩x x =x Sx x x x x x x 4x :x gx qx x x px }x ̜x ڜx x [x x }x x x (x ~x x yx x x px x Fx Xx x x x x ȹx x \x xx Kx x x мx tx x )x qx x x "x Mx ix %x x ;x x x -x Xx vx x Yx px x x x x x x x x x x gx !x x x x 6x Xx x x ,x rx x x &x x Bx wx x x x x }x x x Mx }x x x px x x 1x x zx x x mx x x x x Hx x x x x x _x ix x x ,x Yx x (x Lx tx x x x x x x {x x x (x x x zx x x x ӡx -x Ix Qx x x x x 4x x gx x x gx x Px x %x x /x x ?x x x 0x x x \x x x x x x >x Cx Jx Qx Yx ax gx rx }x x x x x x fx x x x >x Cx Jx Qx Yx ax gx x (x x 6x Ix x 0x cx gx x (x x 6x >x Cx Jx Qx Yx ax x vx x 7x Qx Rx x gx x xx >x Cx Jx Qx Yx x x &x x x gx x x -x 5x Jx Qx Vx [x _x dx hx A command to create a @TextGrid from scratch. Arguments %%From time (seconds) the starting time, usually 0 seconds. %%To time (seconds) the end time, usually the duration. %%Tier names a list of the names of the tiers that you want to create, separated by spaces. %%Point tiers a list of the names of the tiers that you want to be %%point tiers%; the rest of the tiers will be %%interval tiers%. One of the @@types of objects@ in P\s{RAAT}. An IntervalTier represents a series of contiguous intervals in time. Each interval contains a a string. Creating a IntervalTier object in Praat An IntervalTier object is normally extracted from a @TextGrid object, which may contain several tiers. From scratch: 1. Select an object with a time domain, e.g., a Sound or a Pitch. 2. Click ##To IntervalTier#. The resulting IntervalTier will have the same time domain as the original Sound (or Pitch), e.g., if the Sound object starts at 0.0 seconds and has a duration of 2.1 seconds, the resulting IntervalTier will also have an %xmin of 0.0 and an %xmax of 2.1 seconds. The resulting IntervalTier will have one interval in it, extending from %xmin to %xmax. Editing an IntervalTier in Praat You would edit an IntervalTier by converting it to a @TextGrid and invoking a @TextGridEditor, perhaps with a Sound. Drawing an IntervalTier You can draw an IntervalTier alone or together with a Sound or Pitch object, after converting it to a TextGrid. Inside an IntervalTier With @Inspect, you will see the following attributes: %x__%min_ the starting time, in seconds. %x__%max_ the end of the time domain, in seconds. %intervals a sorted collection of text intervals. The attributes of a text interval are: %text an ASCII text string. Though %text is a system-independent ASCII text string, it may, as everywhere in Praat, contain @@Special symbols@ like Greek letters, mathematical symbols, style information, and Phonetic symbols, which will be visible when the string is drawn into the Picture window or viewed in a @TextGridEditor. A command to merge all selected @IntervalTier objects into a new @TextGrid object. You can also merge with @TextTier objects: @@TextTier(s) & IntervalTier(s): To TextGrid@ A command to convert an old-style #Label object, which you have probably read from an old file, into a new-style @TextGrid object. The Sound is needed to supply the TextGrid with a finite time domain, which old-style Label objects lacked. A command that creates a @PitchTier object from one selected @Pitch and one selected @TextTier object. Purpose to return the frequencies in the Pitch contour at the times specified by the TextTier. Argument %%Check voicing% (standard: on) determines whether, if the time of a mark is not within a voiced frame, you will get a message like "No periodicity at time %xxx.", and no PitchTier is created. If this button is off, the resulting pitch frequency will be 0.0 Hz. Normal behaviour For all the times of the marks in the TextTier, a pitch frequency is computed from the information in the Pitch, by linear interpolation. All the resulting time-frequency pairs are put in a new PitchTier object. The time domain of the resulting PitchTier is a union of the domains of the original Pitch and TextTier functions. A command to create an empty @TextGrid from every selected @PointProcess. The only information in the PointProcess that is used, is its starting and finishing times. Example If %%Tier names% is "a b c", and %%Point tiers% is "b", the resulting TextGrid object will contain an interval tier named "a", a point tier named "b", and another interval tier named "c". A command to create a @TextGrid with voiced/unvoiced information from every selected @PointProcess. %%Maximum period% (s) the maximum interval that will be consider part of a larger voiced interval. %%Mean period% (s) half of this value will be taken to be the amount to which a voiced interval will extend beyond its initial and final points. %%Mean period% must be less than %%Maximum period%, or you may get intervals with negative durations. If %%Maximum period% is 0.02 s, and %%Mean period% is 0.01 s, and the point process is 0.1 seconds long, with points at 20, 28, 39, 61, and 72 milliseconds, the resulting TextGrid object will contain an interval tier with "U" intervals at [0 ms, 15 ms], [44 ms, 56 ms], and [77 ms, 100 ms], and "V" intervals at [15 ms, 44 ms] and [56 ms, 77 ms]. A command to promote every selected @PointProcess to a @TextTier. %Text the text that will be placed in every point. Behaviour The times of all the points are trivially copied, and so is the time domain. The text information will be the same for every point. A command to create a @TextGrid without any labels, copying the time domain from the selected @Sound. If %%Tier names% is "a b c", and "Point tiers" is "b", the resulting TextGrid object will contain an interval tier named "a", a point tier named "b", and another interval tier named "c". One of the @@types of objects@ in P\s{RAAT}. For checking the spelling in texts and @TextGrid objects. 1. How to create a SpellingChecker object You normally read in a SpellignChecker with @@Read from file...@ from the Read menu. 2. How to check the spelling of a @TextGrid A SpellingChecker object can be used fur purposes of spelling checking. In order to check the spellings in a @TextGrid object, you first view the TextGrid in an editor window by selecting the TextGrid together with the SpellingChecker object, and clicking Edit. In most cases, you will also want to select a @Sound or @LongSound object before clicking Edit, so that a representation of the sound is also visible (and audible) in the editor. Thus, you typically select three objects and click Edit. The editor then allows you to check the spellings (command ##Check spelling# from the Search menu). 3. How to create a SpellingChecker object for the first time If you are the maintainer of a word list for spelling checking, you will want to convert this list to a SpellingChecker object that you can distribute among the transcribers of your corpus. The first step is to create a @WordList object from your text file, as described on the @WordList man page. Then you simply click ##To SpellingChecker#. A button labelled ##Edit...# appears. This command allows you to set the following attributes of the SpellingChecker object: %%Allow all parenthesized this flag determines whether text between parentheses is ignored in spelling checking. This would allow the transcriber to mark utterances in foreign languages, which cannot be found in the lexicon. %%Separating characters determines the set of characters (apart from the space character) that separate words. The standard is ".,;:()". If a string like "error-prone" should be considered two separate words, you will like to change this to ".,;:()-". For the Corpus of Spoken Dutch (CGN), the hyphen is not a separator, since words like "mee-eter" should be checked as a whole. If a string like "Mary's" should be considered two separate words, include the apostrophe. %%Allow all names determines whether all words that start with a capital are allowed. For the CGN, this is on, since the lexicon does not contain many names. %%Name prefixes a space-separated list that determines what small groups of characters can precede names. For the CGN, this is "'s- d' l'", since names like %%'s-Gravenhage%, %%d'Ancona%, and %%l'H\o^pital% should be ignored by the spelling checker. %%Allow all words containing a space-separated list of strings that make a word correct even if not in the lexicon. For the CGN, this is "* xxx", since words like %%keuje*d% and %%verxxxing% should be ignored by the spelling checker. %%Allow all words starting with a space-separated list of prefixes that make a word correct even if not in the lexicon. For the CGN, this is empty. %%Allow all words ending in a space-separated list of suffixes that make a word correct even if not in the lexicon. For the CGN, this is "-", since the first word in %%verzekerings- en bankwezen% should be ignored by the spelling checker. One of the @@types of objects@ in P\s{RAAT}, used for %annotation (segmentation and labelling). For tutorial information, see @@Intro 7. Annotation@. Description A #TextGrid object consists of a number of %tiers. There are two kinds of tiers: an %%interval tier% is a connected sequence of labelled intervals, with %boundaries in between. A %%point tier% is a sequence of labelled points. How to create a TextGrid @@Sound: To TextGrid...@ (takes the time domain from the Sound) @@LongSound: To TextGrid...@ (takes the time domain from the LongSound) @@PointProcess: To TextGrid...@ (takes the time domain from the PointProcess) @@PointProcess: To TextGrid (vuv)...@ (labels voiced and unvoiced intervals) @@Create TextGrid...@ From merging any number of existing tiers: @@TextTier(s): To TextGrid@ @@IntervalTier(s): To TextGrid@ From merging an existing TextGrid with existing tiers or TextGrids: @@TextGrid & TextTier: Append@ @@TextGrid & IntervalTier: Append@ @@TextGrid & TextGrid: Merge@ Conversion from an old-style Label object: @@Label & Sound: To TextGrid@ How to edit a TextGrid You select a TextGrid alone or together with a @Sound or @LongSound, and click #Edit. A @TextGridEditor will appear on your screen, containing the TextGrid and an optional copy of the Sound or LongSound. How to draw a TextGrid You can draw a TextGrid to the @@Picture window@ with: ##TextGrid: Draw... ##TextGrid & Sound: Draw... ##TextGrid & Pitch: Draw... ##TextGrid & Pitch: Draw separately... A command to ask the selected @TextGrid object how many of the specified labels it contains in the specified tier. %%Tier number the number (1, 2, 3...) of the tier whose labels you want to investigate. %%Label text the text on the labels that you want to count. The number of intervals or points with label %%Label text% in tier %%Tier number% is written into the @@Info window@. If the specified tier does not exist, the number will be 0. Scripting You can use this command to put the number into a script variable: select TextGrid hallo number_of_a = Count labels... 1 a In this case, the value will not be written into the Info window. A command to append the selected @IntervalTier to the selected @TextGrid. A command to merge two selected @TextGrid objects into a new @TextGrid. A command to append the selected @TextTier to the selected @TextGrid. One of the @Editors in P\s{RAAT}, for editing a @TextGrid object. You can optionally include a copy of a @Sound or @LongSound in this editor, by selecting both the TextGrid and the Sound or LongSound before clicking #Edit. The Sound or LongSound is shown in the upper part of the window, the tiers in the lower part. A text window at the top shows the text of the %#selected interval or point, i.e. the interval or point at the location of the cursor. All tiers are visible, and if you do not zoom in, all boundaries, points, and texts are visible, too. You can do many of the same things that you can do with a @SoundEditor or @LongSoundEditor. Positioning the cursor or the selection marks To position the cursor hair, @click in the #Sound, on a boundary, on a point, or inside an interval. To select any part of the time domain, use the @@time selection@ mechanism; if you do this by clicking in a tier, the selected time domain will snap to the nearest boundary or point. Creating new intervals, boundaries, points, or tiers To create a new interval, create a new boundary in an interval tier. To create a new boundary or point in a tier, @click inside the cursor circle in that tier, or choose one of the commands in the Boundary/Point menu to insert a boundary at the cursor time on the selected tier (shortcut: Enter) or on any tier (shortcuts: Command-F1 through Command-F9). The original text in the interval that is split, is divided up between the two resulting intervals, depending on the position of the text cursor in the text window. To create a new tier, choose ##Add interval tier# or ##Add point tier# from the #Tier menu. Playing an entire interval, or part of it As in many other editors, you can play a stretch of sound by clicking in any of the rectangles around the drawing area. To play an interval of an interval tier, you first @click inside it. This will make the interval %selected, which means that the visible part of the interval will be drawn in yellow. The cursor will be positioned at the start of the interval, and the time selection will comprise exactly the interval. This means that you can use the Tab key to play the interval. If you press it while a sound is playing, the Tab key will halt the playing sound, and the cursor will move to the time at which the sound stopped playing. This helps you to divide up a long sentence into parts that you can remember long enough to write them down. The Tab key will play the selected interval. Editing the text in an interval or at a point To edit the label text of an interval or point: 1. Select that interval or point by clicking in or on it. The text currently in the interval or point will appear in the text window. 2. Just type the text, and use the mouse and the arrow keys to navigate the text window. Everything you type will become visible immediately in the text window as well as in the selected interval or point. You can use all the @@Special symbols@ that you can use elsewhere in Praat, including mathematical symbols, Greek letters, superscripts, and phonetic symbols. Selecting a tier To select a tier, click anywhere inside it. Its number and name will be drawn in red, and a pointing finger symbol (\pf) will appear on its left. Selecting a boundary or point To select a boundary on an interval tier, @click in its vicinity or inside the following interval; the boundary will be drawn in red. The text in the interval will appear in the text window. To select a point on a point tier, @click in its vicinity; it will be drawn in red. The text of the point will appear in the text window. Moving one or more boundaries or points To move a boundary or point to another time position, @drag it with the mouse. To move all the boundaries and points with the same time (on different tiers) to another time position, @@Shift-drag@ them. To move boundaries or points to the exact time position of a boundary or point on an other tier, @drag them into that other tier and into the vicinity of that boundary or point. To move boundaries or points to the exact time position of the cursor, @drag them into the vicinity of the cursor. Removing a boundary, point, or tier To remove a selected #boundary, choose #Remove from the #Boundary menu. This creates a new interval which is the union of the two intervals originally adjoining the boundary; the new text of this interval is the concatenation of the two original texts, except if these were equal, in which case the new text equals both original texts. To remove a selected #point, choose #Remove from the #Point menu. To remove a selected #tier, choose ##Remove entire tier# from the #Tier menu. Extracting a part of the sound To copy the selected part of the Sound or LongSound as a Sound to the @@List of Objects@, choose ##Extract sound selection# from the #File menu. You can specify whether you want the time domain of the resulting Sound to match the starting and finishing times of the selection or whether you want the time domain of the resulting Sound to start at zero seconds. If you are viewing a LongSound, you can save the selected part of it to a 16-bit sound file (AIFF, AIFC, WAV, NeXT/Sun, NIST) with a command from the File menu. Accelerations To write the @TextGrid object to a text file without going to the @@Object window@: choose ##Write TextGrid to text file...# from the #File menu. Searching The Search menu contains the command #Find (Command-F), which will allow you to specify a text whose first occurrence will then be looked for in the currently selected tier (starting from the currently selected text in the currently selected interval). The command ##Find again# (Command-G) will search for the next occurrence of the same search text. Checking the spelling You can check the spelling of the intervals in your tiers by including a @SpellingChecker object as you launch the editor: select TextGrid + (Long)Sound + SpellingChecker, then click Edit. The Search menu will contain the command ##Check spelling# (Command-L), which will search for the next word that does not occur in its lexicon. One of the @@types of objects@ in P\s{RAAT}. A TextTier object represents a marked point process, i.e., it contains a series of (%time, %text) points, sorted by time. Each point is marked with a text string. Though this is a system-independent ASCII text string, it may, as everywhere in Praat, contain @@Special symbols@ like Greek letters, mathematical symbols, style information, and Phonetic symbols, which will be visible when the string is drawn into the Picture window or viewed in a @TextGridEditor. Creating a TextTier object in Praat A TextTier object is usually extracted from a @TextGrid object, which may contain several tiers. 2. Click "To TextTier". The resulting TextTier will have the same time domain as the original Sound (or Pitch), e.g., if the Sound object starts at 0.0 seconds and has a duration of 2.1 seconds, the resulting TextTier will also have an %xmin of 0.0 and an %xmax of 2.1 seconds. The resulting TextTier will have 0 points in it. Editing a TextTier in Praat To edit a TextTier, first convert it into a @TextGrid. You invoke a @TextGridEditor in either of two ways: \bu Select a TextGrid and click ##Edit#. \bu Select a TextGrid and a @Sound and click ##Edit#. In the latter case, a copy of the Sound object will be visible in the editor. The @TextGridEditor will allow you to add marks to a TextTier object, move marks around, edit the texts in the marks, and remove marks. Drawing a TextTier You can draw a TextTier together with a Pitch object, by selecting one TextTier and one Pitch object, and choosing "Draw...". The mark texts will appear just above the pitch contour. Class description If you select a TextTier and click ##Inspect# or ##Write to console#, you will see that a TextTier object contains the following attributes: the starting time. the end of the time domain. %points a collection of text points, sorted by their times. A command to add a point to each selected @TextTier. %Time (s) the time at which a point is to be added. the text of the requested new point. The tier is modified so that it contains the new point. If a point at the specified time was already present in the tier, nothing happens. A command to degrade every selected @TextTier to a @PointProcess. The times of all the text points are trivially copied, and so is the time domain. The text information is lost. A command to merge all selected @TextTier objects into a new @TextGrid object. You can also merge with @IntervalTier objects: A command to merge all selected @TextTier and @IntervalTier objects into a new @TextGrid object. One of the @@types of objects@ in P\s{RAAT}. An object of class WordList contains a sorted list of strings in a system-independent format. WordList objects can be used for spelling checking after conversion to a @SpellingChecker object. 1. How to create a WordList object You will normally create a WordList object by reading a binary WordList file. You'll use the generic @@Read from file...@ command from the Read menu. See below under 3 for how to create such a file. 2. What you can do with a Wordlist object The main functionality of a WordList is its ability to tell you whether it contains a certain string. If you select a WordList, you can query the existence of a specific word by using the ##Has word# command. You supply the word and press OK. If the WordList does contain the word, the value "1" will be written to the Info window; otherwise, the value "0" will be written. 3. How to create a binary WordList file You can create a binary (compressed) WordList file from a simple text file that contains a long list of words. Perhaps such a text file has been supplied by a lexicographic institution in your country; because of copyright issues, such word lists cannot be distributed with the Praat program. To convert the simple text file into a compressed WordList file, you basically take the following steps: Read Strings from raw text file... lexicon.iso Genericize Sort To WordList Write to binary file... lexicon.WordList I'll explain these steps in detail. For instance, a simple text file may contain the following list of words: cook cooked cookie cookies cooking cooks Copenhagen K\o/bnhavn M\u"nchen Munich \aongstr\o"m These are just 11 words, but the procedure will work fine if you have a million of them, and enough memory in your computer. You can read the file into a @Strings object with @@Read Strings from raw text file...@ from the Read menu in the Objects window. The resulting @Strings object contains 11 strings in the above order, as you can verify by viewing them with @Inspect. In general, the Strings object will occupy a lot of memory, and be slow to read in. For instance, a certain list of more than 300,000 Dutch word forms occupies 3.6 MB on disk, and will occupy at least 7 MB of memory after it is read in. The extra 3.4 MB arise because the Strings object contains a pointer to each of the strings, and each of the strings is in a separately allocated part of the memory heap. Moreover, it takes 8 seconds on an average 1999 computer to read this object into memory. For these reasons, we will use the WordList object if we need a sorted list for spelling checking. If you select the Strings, you can click the ##To WordList# button. However, you will get the following complaint: String "K\o/bnhavn" not generic. Please genericize first. This complaint means that the strings are still in your computer's native text format, which is ISO-Latin1 for Unix and Windows computers, or Mac encoding for Macintosh computers. So you press the #Genericize button. You can see that the Strings object changes to K\bso/bnhavn M\bsu\" nchen \bsaongstr\bso\" m The strings are now in the generic system-independent format that is used everywhere in Praat to draw strings (see @@Special symbols@). You can again try to click the ##To WordList# button. However, you will get a complaint again: String "Copenhagen" not sorted. Please sort first. This complaint means that the strings have not been sorted in ASCII sorting order. So you click #Sort, and the Strings object becomes: The strings are now in the ASCII order, in which capitals come before lower-case letters, and backslashes come in between these two series. Clicking ##To WordList# now succeeds, and a WordList object appears in the list. If you write it to a text file (with the Write menu), you will get the following file: File type = "ooTextFile" Object class = "WordList" string = "Copenhagen M\bsu\" \" nchen \bsaongstr\bso\" \" m cooks\"r Note that the double quotes (\" ) that appear inside the strings, have been doubled, as is done everywhere inside strings in Praat text files. After you have created a WordList text file, you can create a WordList object just by reading this file with @@Read from file...@ from the Read menu. The WordList object has two advantages over the Strings object. First, it won't take up more memory than the original word list. This is because the WordList is stored as a single string: a contiguous list of strings, separated by new-line symbols. Thus, our 300,000-word list will take up only 3.6 MB, and be read in 4 seconds. However, disk storage and reading can again be improved by compressing the word list. We can take advantage of the sorting, by noting for each entry how many leading characters are equal to those of the previous entry. The list then becomes something equivalent to 0 K\bso/bnhavn 0 M\bsu\" nchen 1 unich 0 \bsaongstr\bso\" m 0 cook 4 ed 4 ie 6 s 5 ng 4 s You can write the WordList compressed in this way to a binary file with @@Write to binary file...@. For our 300,000-word list, this file takes up only 1.1 MB and can be read into memory (with @@Read from file...@) in a single second. When read into memory, the WordList object is again expanded to 3.6 MB to allow rapid searching. Create TextGrid... ppgb IntervalTier IntervalTier(s): To TextGrid Label & Sound: To TextGrid Pitch & TextTier: To PitchTier... PointProcess: To TextGrid... PointProcess: To TextGrid (vuv)... PointProcess: Up to TextTier... Sound: To TextGrid... SpellingChecker TextGrid TextGrid: Count labels... TextGrid & IntervalTier: Append TextGrid & TextGrid: Merge TextGrid & TextTier: Append TextGridEditor TextTier TextTier: Add point... TextTier: Down to PointProcess TextTier(s): To TextGrid TextTier(s) & IntervalTier(s): To TextGrid WordList HOMESHARE HOMEPATH HOMEDRIVE %s\%s\Message.txt w Cannot create message file "%s" (no privilege to write to directory, or disk full). %s PraatShell1 %s Program %s not running (or an old version). Program %s returns error. x x ,q x m[ x q 0x s Trying to read "%s". Procrustes Configurations_to_Procrustes: Configurations must have the same number of points and the same dimension. The eigenvectors must have the same dimension. Eigenvector range too large. y y j y y *y *y j y 5y @y hj y v[ y lj y v[ *y lj y w[ |y y Py Od@< .@ . ? dy=>z[ y y (y label value intercept parameters: size parameters [%ld]: Trying to read "%s". RegressionParameter Regression parameters Ordered Intercept: : Coefficient of independent variable LinearRegression Not enough columns (has to be more than 1). Solution is not unique (more parameters than cases). LogisticRegression No data in either class. Cannot determine result. No data in class %s. Cannot determine result. Logistic regression has not converged in 100 iterations. The results are unreliable. p y u y } y y y y y y y j y y y y y y y y y y hy y [ y lj Ly ? b@ I@ ? @ (@? ?ffffff9@ R@? @ @333333? f@name ranking disharmony string numberOfConstraints marks my numberOfConstraints OTMulti constraints OTConstraint index numberOfCandidates candidates OTCandidate my numberOfCandidates Number of constraints: %ld Number of candidates: %ld Number of violation marks: %ld %ld constraints " " %.17g %.17g %ld candidates " %d No constraints. No candidates. The forms "%s" and "%s" do not match any candidate. (OTMulti: Get winner (two):) Not performed. Learning with full knowledge... Processing partial pair %ld out of %ld: { "%s", "%s" } Only %ld partial pairs out of %ld were processed. OTMulti did not complete learning from partial pairs. (no matching candidates) %s%s \Vr \pf \<- * ! \-> (OTGrammar_setRanking): No constraint %ld. Cannot remove last constraint. No constraint "%s". No winner (OTMulti_generateOptimalForm:) Not performed. (OTMulti_Strings_generateOptimalForms:) Not performed. (OTMulti_generateOptimalForms:) Not performed. @& .> ? 4@5[ y 0Rj H y Evaluate 2.0 Evaluation noise Evaluate (noise 2.0) Evaluate (tiny noise) Edit ranking constraint 100.0 Ranking value Disharmony Select a constraint first. OTGrammar: Learn one... Learn one Learn forward backward bidirectionally 0.1 Plasticity Rel. plasticity spreading Remove constraint Reset all rankings Ranking OT learning Partial forms: form1Text form2Text -- edit ot -- Edit Evaluate... Edit ranking... Reset all rankings... Learn one... -- remove -- OT learning tutorial Help %%ranking value %disharmony \sp %s@@%ld|%s@ %.3f %.3f OTMultiEditor OTMultiEditor not created. wy wy j dy uy y [ wy lj y numberOfElements p Permutation my numberOfElements %s: Range must be in [1, %d] Number of elements: %d (Permutation::readAscii:) Number of elements must be >= 1. (Permutation::readAscii:) All values must be unique and in the [1, %d] range. Permutation_swap %s: Blocksize must be in [1, %d] range. %s: Start and finish positions of the two blocks must be in [1,%d] range. Permutation_permuteRandomly Permutation_rotate Permutation_swapOneFromRange Permutation_swapOneFromRange: Impossible to satisfy "forbid same" constraint within the chosen range. Permutation_permuteBlocksRandomly %s: It is not possible to fit an integer number of blocks in the range. (The last block is only of size %d). Permutation_interleave %s: There is not an integer number of blocks in the range. (The last block is only of size %d instead of %d). %s: Offset must be smaller than blocksize. Permutation_reverse TableOfReal_and_Permutation_permuteRows: The number of rows in the table and the number of elements in the Permutation must be equal. `(y (y (y )y *y *y *y +y +y .+y \+y +y +y +y +y *,y 8,y t,y ,y ,y -y D-y f-y -y -y -y .y ^.y .y .y .y .y .y 5/y L/y /y (0y M0y U0y 0y M0y 0y 1y .y <1y D1y y1y 1y 1y &2y .y <1y 2y 2y 2y D3y R3y y1y 4y e5y .y <1y 5y M0y 5y c6y 6y <1y 6y 6y 7y |7y 7y 7y 7y y1y 8y :y :y ;y 6y <y <y 6y r<y <y <y y1y =y =y ~>y ?y W?y 9Ay 6y FCy 5y OCy ]Cy Cy Cy y1y Dy Dy Ey Ey ,Fy 6y <1y eFy Fy Fy y1y Fy KGy Gy Hy M0y IHy Iy HIy Iy =Jy M0y Jy iKy Ky y1y Ly Ly Ny Ny Py @Qy Qy Qy Qy M0y Ry FTy Ty M0y Ty Ty Ty Uy Ty Uy Ty Uy Uy HUy Uy Ty Uy rUy Uy Uy Uy Uy Uy Uy Uy Uy Qy Vy Wy M0y QWy dXy Ty Ty Uy Ty Uy Ty Uy Xy HUy Uy Ty Uy rUy Uy Uy Uy Uy Uy Uy Xy OYy Uy Uy Uy Ty Ty Ty Yy .Zy M0y hZy HUy Uy Ty Uy rUy Uy Uy Uy Uy Uy Uy Zy HUy Uy Ty Uy rUy Uy Uy Zy One of the @@types of objects@ in P\s{RAAT}. A Permutation object with %n elements consists of some ordering of the numbers 1,2...%n. Interpretation A permutation like for example (2,3,5,4,1) is an %arrangement of the five objects 1, 2, 3, 4, and 5. It tells us that the second object is in the first position, the third object is in the second position, the fifth object in the third position and so on. If we combine a Permutation together with an other object, like a Strings for example, we may force a @@Strings & Permutation: Permute strings|new arrangement of the strings@, according to the specification in the Permutation. Commands Creation: \bu @@Create Permutation...@ Query: \bu ##Get number of elements# \bu @@Permutation: Get value...|Get value...@ \bu @@Permutation: Get index...|Get index...@ Modification: \bu @@Permutation: Sort|Sort@ \bu @@Permutation: Swap blocks...|Swap blocks...@ \bu @@Permutation: Swap one from range...|Swap one from range...@ Permutations: \bu @@Permutation: Permute randomly...|Permute randomly...@ \bu @@Permutation: Permute randomly (blocks)...|Permute randomly (blocks)...@ \bu @@Permutation: Interleave...|Interleave...@ \bu @@Permutation: Rotate...|Rotate...@ \bu @@Permutation: Reverse...|Reverse...@ \bu @@Permutation: Invert|Invert@ Successive permutations: \bu @@Permutations: Multiply|Multiply@ Usage @@Strings & Permutation: Permute strings@ to rearrange the strings in a Strings object. @@TableOfReal & Permutation: Permute rows@ to rearrange the rows in a TableOfReal object. A command to create a @Permutation of the numbers 1,2, ..., %numberOfElements. Arguments %Name determines the name of the new permutation. %%Number of elements% determines the number of elements in the permutation. %%Identity Permutation determines whether the permution will be a randomly chosen one, or the @@identity permutation@. The identity permutation is (1,2,3,...,%numberOfElements), i.e. the numbers 1 to %numberOfElements in their natural order. Get the value at the index position. Example The query for the value at index 3 for the permutation (3,2,4,5,1) gives 4. Get the index position of the value. The query for the index of value 3 for the permutation (3,2,4,5,1) gives 1. Reverse the elements in the given range. %%Range defines the range of elements that will be reversed. Examples 1. With the %range [0,0], the permutation (1,2,3,4,5) will generate (5,4,3,2,1). 2. With the %range [3,0], the permutation (1,2,3,4,5) will generate (1,2,5,4,3). An element, randomly chosen from a range, will be permuted with an element at a given index position. defines the range of indices from which one will be randomly chosen. %%Index% defines the special index position whose element will be interchanged with the one chosen from the range. %%Forbid same when on, forbids the randomly chosen position and the index position to be the same. This switch is only of relevance when the chosen range happens to overlap the index position. With range [0,0], an index of 3, "Forbid same" %off and (1,2,3,4,5) as the starting permutation, the outcome might be one of the five permutations (3,2,1,4,5), (1,3,2,4,5), (1,2,3,4,5), (1,2,4,3,5), (1,2,5,4,3). If "Forbid same" were chosen as %on, the (1,2,3,4,5) permutation is forbidden and the only outcome could be one of other four permutations. Generates a random permutation for the elements in the given range. defines the range of elements that will be permuted. With a range of [3,6], the permutation (1,2,3,4,5,6,7) generates one of the 24 possible permutations, for example (1,2,(4,5,3,6),7). Generates a new @Permutation by randomly permuting blocks of size %blocksize. Parameters defines the range of elements whose blocks will be permuted. %%Block size defines the size of the blocks that will be permuted. There must fit an integer number of blocks in the chosen range. %%Permute within blocks% when %on, the elements in each block are also randomly permuted. %%No doublets% guarantees that the first element in each block does not equal the last element of the previous block modulo the block size. E.g. the numbers 3, 6, 9 are all equal modulo 3. This parameter only has effect when "Permute within blocks" is %on. 1. With range [0,0], a block size of 3 and "Permute within blocks" %off, the permutation ((1,2,3),(4,5,6),(7,8,9)) generates one of the six possible permutations, for example ((4,5,6),(7,8,9),(1,2,3)). (The option "No doublets" will be ignored and the parentheses are only there to indicate the blocks.) 2. With range [0,0], a block size of 3, "Permute within blocks" %on and "No doublets" %off, the permutation ((1,2,3),(4,5,6),(7,8,9)) might generate ((5,4,6),(9,8,7),(3,1,2)). 3. With the same options as 2 but "No doublets" %on, the previously given outcome is forbidden because the last element of the first block (6) and the first element of the next block (9) are equal modulo 3 (the blocksize). A valid outcome might then be ((5,4,6),(8,9,7),(3,1,2)). A command to swap blocks in the selected @Permutation. %From, %To define the two starting positions from where elements are to be swapped. The blocks may overlap. determines the number of pairs to swap. Behaviour The elements at the %from and %to position are swapped. If blocksize is greater than one, the two elements at %from+1 and %to+1 will be swapped. This goes on until the last two elements in each block have been swapped. 1. Swap two blocks: with %from = 1, %to = 4, and %blocksize = 2, the permutation (1,2,3,4,5) will be modified to (4,5,3,1,2). 2. Swap two elements: with %from = 1, %to = 4, and %blocksize = 1, the permutation (1,2,3,4,5) will be modified to (4,2,3,1,5). 3. Swap two overlapping blocks: with %from = 1, %to = 3, and %blocksize = 3, the permutation (1,2,3,4,5) will be modified to (3,4,5,2,1). Generates a new @Permutation by interleaving elements from successive blocks. We always start with the first element in the first block. When the offset is zero, the next element will be the first element of the second block, then the first element of the third block. After the first element of the last block, we start again with the second elements in each block. And so on. (In card playing, with two blocks of 26 cards each, this is called a faro shuffle and eight successive faro shuffles will return the deck to precisely the order in which you began.) If the offset differs from zero and equals 1 for example, we start with the first element in the first block, then the second element in the second block, the third element in the third block and so on. When the last element of a block is reached and the number of blocks is not exhausted the next element will be the first from the next block. When the last block is reached, we start the same cycle again with the next lower element in the first block (which by the way need not be the second element, see also example 4). %%Range% %%Block size% defines the size of a block. There must fit an integer number of blocks in the chosen range. %%Offset% defines the relative positions of selected elements in successive blocks. 1. With range [0,0], a block size of 3, and an offset of 0, the permutation ((1,2,3),(4,5,6),(7,8,9)) will generate (1,4,7,2,5,8,3,6,9). 2. With range [0,0], a block size of 3, and an offset of 1, the permutation ((1,2,3),(4,5,6),(7,8,9)) will generate (1,5,9,2,6,7,3,4,8). 3. With range [0,0], a block size of 3, and an offset of 2, the permutation ((1,2,3),(4,5,6),(7,8,9)) will generate (1,6,8,2,4,9,3,5,7). 4. With range [0,0], a block size of 4, and an offset of 1, the permutation ((1,2,3,4),(5,6,7,8)) will generate (1,6,3,8,2,7,4,5). A circular shift of all elements within the given range. defines the range of elements that will be circularly permuted. %%Step size define how many positions each element will be shifted. 1. With a step of size 2 and range [1,5], the permutation (1,2,3,4,5) will generate (4,5,1,2,3). 2. With a step of size 2 and range [2,5], the permutation ((1),(2,3,4,5)) will generate ((1),(4,5,2,3)) 3. With a step of size -1 and range [0,0], the permutation (1,2,3,4,5) will generate (2,3,4,5,1). Generates the inverse of the selected @Permutation. If the permutation is (1,5,3,2,4) the generated inverse will be (1,4,3,5,2). If we @@Permutations: Multiply|multiply@ these two permutations the result will be the identity permutation (1,2,3,4,5). Apply the selected @@Permutation@s one after the other. Permutations are %not commutative, i.e. applying permutation %p__1_ after %p__2_ might not give the same outcome as applying %p__2_ after %p__1_. Sorts the elements ascending, i.e. set the selected @@Permutation@ to the @@identity permutation@. Generate a new @TableOfReal with a row ordering determined by the @Permutation. If the selected TableOfReal has 5 rows and the permutation is (5,4,3,2,1) the first row of the new TableOfReal equals the fifth row of the selected, the second row of new equals the fourth row of the selected and so on. Generate a new @Strings with a strings ordering determined by the @Permutation. The number of strings in the #Strings and the number of elements in the #Permutation have to be equal. 1. If the selected Strings has the 4 strings ordered as "heed", "hid", "hood", "hud", and the permutation is (4,3,2,1), the new Strings has the ordering "hud", "hood", "hid", "heed". 2. In the example that is discussed in the @@ExperimentMFC|listening experiment@ section, we have four stimuli "heed.wav", "hid.wav", "hood.wav", "hud.wav" that we want to present three times to each subject with a <PermuteBalancedNoDoublets> randomization strategy, i.e. stimuli presented in blocks of four, randomized, and no two successive stimuli equal. This type of randomization can easily be accomplished with a Permutation object and a Strings. 1. Fill the Strings object with 12 strings, i.e. three repetitions of the four stimuli. 2. Create a Permutation object with 12 elements and perform ##@@Permutation: Permute randomly (blocks)...|Permute randomly (blocks)...@ 0 0 4 yes yes#. We randomly permute blocks of size 4 and permute randomly within these blocks and make sure that on the transition from on block to the other no two stimuli are equal. (Of course, the random permutation of the blocks makes no difference here since all the blocks have the same content.) 3. Select the Strings and the Permutation together and chose ##Permute strings#. Now the new Strings will contain the new ordering of the stimuli. Generates a @Permutation with the same number of elements as the @Strings. Parameter %Sort determines whether the Permutation will have an element ordering that can be used to sort the Strings alphabetically. If "Sort" is %on, and the selected Strings contains 4 strings ordered as "hud", "hid", "hood", "heed", the generated Permutation will be (4,2,3,1). If you now select the String and the Permutation together and chose @@Strings & Permutation: Permute strings|Permute strings@, the new Strings will have the strings ordered alphabetically as "heed", "hid", "hood", "hud". You can also sort the Strings alphabetically descending, by first @@Permutation: Reverse...|reversing@ the elements in the Permutation before you select the Permutation and the Strings together. One of the @@Types of objects|types of objects@ in the P\s{RAAT} program. Generates an @Index from the selected @Strings. We start from the following #Strings: 6 (number of strings) "hallo" "dag allemaal" "tot morgen" This will give us the following #Index: 1 (number of columns) "" (no column name) 6 (number of elements) 2 1 3 Generates a @Permutation from the selected @Index by randomly permuting blocks of equivalent elements. Suppose your data consists of groups of equivalent elements and the number of elements in the groups are not equal. You want to make random ordering of your data such that the elements in a group stay together. The following example shows you how. %%Permute within classes determines whether the elements within a class will be randomly permuted. Suppose your data, for example a @Strings, consists of groups of equivalent elements and the number of elements in the groups are not equal. You want to make a random ordering of your data such that the elements in a group stay together. The following example shows you how. We start from the following Strings: We chose @@Strings: To Index|To Index@ which will give us the following #Index: We chose ##To Permutation# and with "Permute within classes" %off, this might generate the permutation (2,4,6,1,3,5). Selecting the Permutation and the Strings together and chosing @@Strings & Permutation: Permute strings|Permute strings@ will generate the following Strings: We see that the permutation always keeps equal strings together. Creates a new @Index by copying a part of selected Index. Given the following Index: The command ##Extract part... 1 2# gives you the new Index: Note that all classes stay intact and may have zero references like for example the "tot morgen" class. Permutation djmw Create Permutation... identity permutation Permutation: Get value... Permutation: Get index... Permutation: Reverse... Permutation: Swap one from range... Permutation: Permute randomly... Permutation: Permute randomly (blocks)... Permutation: Swap blocks... Permutation: Interleave... Permutation: Rotate... Permutation: Invert Permutations: Multiply Permutation: Sort TableOfReal & Permutation: Permute rows Strings & Permutation: Permute strings Strings: To Permutation... Index Strings: To Index Index: To Permutation... Index: Extract part... _y _y j _y _y hj _y _y `y `y `y ^y A[ _y lj ^y =[ `y ^y 0_y classes numberOfElements classIndex Index Ordered my numberOfElements StringsIndex Number of elements: %d Index_extractPart: range should be in interval [1,%d]. @ ?Sound_and_LPC_to_LPC_robust %s: Time domains differ. %s: Sampling intervals differ. %s: Analysis window too short. %s: Incorrect retrieved analysis width LPC analysis LPC analysis of frame %ld out of %ld Sound_to_LPC: analysis results of %ld frame(s) out of %ld could not be optimised. %d iterations. Average %s per frame. -NAN -nan NAN nan 0x0p0 -INF -inf INF inf ? ? 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" t 00000000T1X1\1`1111 2222283<3@3D33333|4444 5$5(5,5D5555555555p6t6x6|6666 " 444,4044484\4`4d4h446 666$74787P7|7777 8888; ;$;<;h;;;;;;<D<d<<<<====l>p>t>x>8?<?@?D????? " D 00001111X2\2`2d2(3777848`88889<9h99: ::: # T 7778<8h88888889 9 99;;;;;<H<L<P<<0=4=8=====p>t>x>|>? # 000x1666 777 7777 7 7$7(7,7074787<7@7D7H7L7P7T7X7\7`7d7h7l7p7t7x7|777777777777777777777777777777777 888 8888 8 8$8(8,8084888<8@8D8H8L8P8T8X8\8`8d8h8l8p8t8x8|8888888888888888888;;;H<== =4=8=<=@== 0# 444505\5x5|5555P6 @# 7778$888L8`8t8888888 99(9<9P9d9x9999999::,:@:T:h:|::::; ;D;l;;;;;;;; < <4<H<\<p<<<<<<<=$=8=L=`=t====== >>(><>P>d>x>>>>>>??,?@?T?h??????? 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???? ? ?$?(?,?0?4?8?<?@?D?H?L?P?T?X?\?`?d?h?l?p?t?x?|????????????????????????????????? 4 000 0000 0 0$0(0,0004080<0@0D0H0L0P0T0X0\0`0d0h0l0p0t0x0|000000000000000000000000000000000 1 06 x \;p;;;;;;;;<$<8<L<`<t<<<<<< ==(=<=P=d=x======>,>@>T>h>|>>>>>>? ?0?D?X?l??????? @6 0 0H0\0p0000001$181L1`1t111111 22(2<2P2d2x22222233,3T3h3|3333334 404D4X4l4444444 5 545\5p55555556$686L6`6t6666666 77(7<7P7d7x777777788,8@8T8h8|88888889 909D9X9l99999999 : :4:H:\:p::::::::;$;8;L;t;;;;;; <<(<<<P<d<x<<<<<<<==,=@=T=h=|======> >0>D>X>l>>>>>>>> ? ?4?H?\?p??????? P6 H 0$0L0`0t0000000 11(1P1d1x11111122,2@2T2h2|22222223 303X3l33333333 4 444T4\4p44444445$585L5`5t555555 6(6<6P6d6x666666677,7@7T7h77777778 808D8X8l8888888 9 949H9\9p9999999:$:8:L:`:t:::::: ;;(;<;P;d;x;;;;;;<<,<@<T<|<<<<<<= =0=D=X=l=== 6 t ;;;;; < <4<H<\<p<<<<<<<<=$=8=L=`=t======= >>(><>P>d>x>>>>>>>??,?@?T?h?|????? 6 000X0l00000000 1 141H1\1p111111112$282L2`2t2222222 33(3<3P3d3x333333344,4@4T4h4|44444445 505D5X5l55555555 6 646H6\6p666666667$787L7`7t7777777 88(8<8P8d8x888888899,9@9T9h9|9999999 :0:D:X:l::::::: ; ;4;H;\;p;;;;;;;;<$<8<L<`<t<<<<<<< ==(=H=P=d=x======>>,>@>T>h>|>>>>>>? ?0?D?X?l??????? 6 p 0 040H0\0p0000001$181L1`1t111111 22<2P2x22222223,3@3T3h3|3333333404D4X4l4444444 5 545H5\5p55555556$6L6`6t666666 77(7<7P7d77777788,8@8T8h8|8888889 909X9l9999999 : :4:H:\:p:::::::;$;8;L;t;;;;;; <<(<<<d<x<<<<<<==,=@=T=h=|=====> >0>D>X>l>>>>>>> ? ?4?H?\?p??????? 6 0$080`0t0000000 11(1<1P1d111111122,2@2T2|22222223 303D3X3l3333333 4 444H4\4p44444444$585L5`5555555 p7 h ;;;<,<@<T<h<|<<<<<< =0=D=X=l======= > >4>H>\>p>>>>>>>?$?8?`?t??????? 7 00(0<0d0x00000001,1@1T1h1|1111112 202D2X2222222 3 343H3\3p333333334$484L4`4t4444444 55(5<5P5d5x555555566,6@6T6h6|6666667 707D7X7l777777 848H8\8p88888889$9L9`9t9999999 ::(:<:P:d:x::::::;;,;@;T;h;|;;;;;;;< <0<D<X<l<<<<<<<< = =4=H=\=p=======>$>8>L>t>>>>>> ??(?<?P?d?x?????? 7 H 00,0@0h0|00000001 101X1l1111111 2 242H2\2p22222223$383L3t3333333 44(4<4P4x44444455,5@5T5h5|55555556 606X6l6666666 7 747H7\7p77777778$888L8`8t8888888 99(9<9P9d9x9999999::,:@:T:|:::::::; ;0;D;X;l;;;;;; <4<H<\<p<<<<<<<=$=8=L=`=t== 8 ? 8 00@0T0h0|00000001 101D1X1l11111111 2 242H2\2p2222223$383L3`3t333333 44(4<4P4d4x44444455,5T5h5|5555556 606D6X6l6666666 7 747H7\7p77777778$888L8`8t888888 99(9<9P9d9x999999::,:@:T:|:::::::; ;0;D;X;l;;;;;;; < <4<H<\<<<<<<<<=$=8=L=`======= >>(><>P>d>>>>>>>??,?@?T?h?|?????? 8 0 000D0X0l00000000 1 141H1\1p111111112$2L2`2t2222222 33(3<3P3d3x333333344,4@4T4h4|44444445 5D5X5l5555555 6 646\6p666666667$787L7`7t777777 88<8P8d8x88888899@9T9h999999: 8 p 001$181L1`1t111111 22(2<2P2d2x222222233,3@3T3h3|3333334 404X4l4444444 5 545H5p55555555686L6`6t666666 77(7<7P7x77777778,8@8T8h8|88888889 909D9X9l9999999 : :4:H:\:p::::::::;$;8;L;`;t;;;;;;; <<<<P<d<x<<<<<<<==,=T=|=====> >0>D>X>l>>>>>>>> ? ?4?H?\?p???????? 8 ( 0$080L0`0t00000001(1<1P1d1x111111122,2@2T2h2|2222222303D3X3l3333333 444H4\44444445$585L5`5t5555555 66(6<6P6d6x666666677,7@7T7h7|77777778 808D8X8l88888888 9 949H9\9p99999999:$:8:L:`:t::::::: ;;(;<;P;d;x;;; 8 ====0>4>8>>???? 9 x 0`0p0t0000001111111L2P2T2X22(3,3033556h66667(7,7D7p77777777888L8P8T88H=L=P== 9 0$0(0@0l00000`1h5|55555556 606D6X6l66666666 7 747H7\7p77777778$8L8t8888889(9<9P9d9x999999::,:@:T:h::::::: ;0;D;X;l;;;;;;;; < <H<\<p<<<<<<<<=$=L=`=t======= >>(><>P>d>>>>>>>??,?@?h?|????? 9 000D0l00000000 141H1\1p1111112$282L2`2t2222222 33(3<3P3d3x33333344,4@4T4h4|44444445 505D5X5l55555555 6 646H6\666666667$787L7`7t7777777 88(8<8 P9 0 \=l=p====== >8>H>L>>>>,?0?4?8?? `9 X << <$<(<0<T<\<t<x<|<<<<<<<<x=|=<?@?d?h?l?p?t?x?|???????????? p9 @ L0\0`0d0h0l0p0|000011111111 2222 2h8l888 9 00