Linear Prediction Analysis of Speech Sounds

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Paul Bond
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1 Lr Prdcto Alyss of Sch Souds Brl Ch 4 frcs: X Hug t l So Lgug Procssg Chtrs 5 6 J Dllr t l Dscrt-T Procssg of Sch Sgls Chtrs J W Pco Sgl odlg tchqus sch rcogto rocdgs of th I Stbr

2 Lr Prdctv Coffcts (LPC) A ll-ol fltr wth suffct ubr of ols s good roto to odl th vocl trct (fltr) for sch sgls ~ H ( z ) ( z ) ( z ) A( z ) [] [ ] [] [] [ ] X z [ ] Vocl Trct Prtrs [ ] It rdcts th currt sl s lr cobto of ts svrl st sls Lr rdctv codg LPC lyss uto-rgrssv odlg 4 SP- Brl Ch

3 4 SP- Brl Ch 3 Short-Tr Alyss: Algbr Aroch stt th corrsodg LPC coffcts s thos tht z th totl short-tr rdcto rror (u squrd rror) ( ) [] ~ Frg/Wdowg Th totl short-tr rdcto rror for scfc fr [] [] [] { } T th drvtv [] Th rror vctor s orthogol to th st vctors Ths rorty wll b usd ltr o!

4 4 SP- Brl Ch 4 Short-Tr Alyss: Algbr Aroch [] Φ Ψ : corrlto coffcts Df To b usd t g! P Φ Ψ

5 4 SP- Brl Ch 5 Short-Tr Alyss: Algbr Aroch Th u rror for th otl [] [] [] ( ) [] [] [] ~ ( ) [] [] ( ) qul Totl Prdcto rror Th rror c b otord to hl stblsh Us th rorty drvd th rvous g!

6 4 SP- Brl Ch 6 Short-Tr Alyss: Gotrc Aroch Vctor rsttos of rror d Sch Sgls Th rdcto rror vctor ust b orthogol to th st vctors [] [] - [] [] [] ( ) ( ) T T ( ) P X ( ) ( ) T T T T T T X X X X X X X X X X f l s Ths rorty hs b show rvously (P3) th st vctors r s colu vctors

7 Short-Tr Alyss: Autocorrlto Mthod [] s dtclly zro outsd - Th -squrd rror s clcultd wth ~- [] [ L] w othrws L: Fr Prod th lgth of t btw succssv frs [] L L- shft [] [ L ] ~ - - Frg/Wdowg [] ~ [][] w 4 SP- Brl Ch 7

8 4 SP- Brl Ch 8 Short-Tr Alyss: Autocorrlto Mthod Th -squrd rror wll b: [] [] [] ( ) ~ Why? P- - P- - [] [] [] ( ) ( ) [] T th drvtv:

9 4 SP- Brl Ch 9 Short-Tr Alyss: Autocorrlto Mthod Altrtvly Whr s th utocorrlto fucto of Ad Thrfor: [] [] [] P P A Toltz Mtr: sytrc d ll lts of th dgol r qul Why?

10 Short-Tr Alyss: Autocorrlto Mthod Lvso-Durb curso Itlzto Itrto: For do th followg rcurso 3 Fl Soluto: ( ) () ( ) ( ) ( ) [ ( )] [] ( ) [ ] ( ) ( ) ( ) ( ) ( ) for - ( ) ( ) whr - ( ) A w hghr ordr coffct s roducd t ch trto [] ( [] [ ] ) [ ] ( ) for 4 SP- Brl Ch

11 Short-Tr Alyss: Covrc Mthod [] s ot dtclly zro outsd - Wdow fucto s ot ld Th -squrd rror s clcultd wth ~- [] L L- shft [] [ L ] - Th -squrd rror wll b: ~ [] ( [] [] ) 4 SP- Brl Ch

12 4 SP- Brl Ch Short-Tr Alyss: Covrc Mthod [] ( ) P P P ot A Toltz Mtr: sytrc d but ot ll lts of th dgol r qul T th drvtv:

13 LPC Sctr LPC sctru tchs or closly th s th th vllys H Prsvl s thor ( w ) ( w G H ) ω ( ) ω ( ) π π X ω [] ( ) d ω G π π π π H d ω Bcus th rgos whr X ω ω > H cotrbut or to th rror th thos whr ( ) ( ) ω ω H ( ) > X ( ) 4 SP- Brl Ch 3

14 LPC Sctr LPC rovds stt of gross sh of th short-tr sctru Ordr 6 Ordr 4 Ordr 4 Ordr 8 4 SP- Brl Ch 4

15 LPC Prdcto rrors 4 SP- Brl Ch 5

16 MFCC vs LPC Cstru Coffcts MFCC outrfors LPC Cstru coffcts Prctully otvtd l-scl rrstto dd hls rcogto Hghr-ordr MFCC dos ot furthr rduc th rror rt corso wth th 3-ordr MFCC Aothr rctully otvtd fturs such s frst- d scod-ordr dlt fturs c sgfctly rduc th rcogto rrors 4 SP- Brl Ch 6

17 Howor 7 Fll 4 Try to lt th short-tr lr rdcto codg (LPC) for sch sgls You should follow th followg structos: Usg th utocorrlto thod wth Lvso-Durb curso d ctgulr/hg wdowg Alyzg th vowl (or FIAL) ortos of sch sgl wth dffrt odl ordrs (dffrt P g P6 4 4 d 8) 3 Plottg th LPC sctr s wll s th orgl sch sctru 4 Usg th sch wv fl b6_wv (o hdr PCM 6KHz rw dt) s th lr 4 SP- Brl Ch 7

18 Hts: Howor 7 Fll 4 Wh th LPC coffcts r drvd you c costruct uls rsos sgl h[] - (: fr sz) by: Th rdcto rror c b rssd by th utocorrlto fucto: 4 SP- Brl Ch 8

19 Howor 7 Fll 4 3 Th MATLb l cod: [ ]; % orgl sgl dso: fr sz y[ ]; % fltr's uls rsos h[] dso: fr sz gvlg; % vlg: th rdcto rror Xfft(5); % fst Fourr Trsfor so th fr sz < 5 Yfft(y5); % fst Fourr Trsfor X()[]; % rov th X() th DC Y()[]; % rov th Y() th DC M5; owrxbs(x(:m/))^; % th owr sctru of X logpx*log(owrx); % th owr sctru of X db owrybs(y(:m/))^; % th owr sctru of Y logpy*log(owry)*log(g); % th owr sctru of Y db % lus th g (rror) db yqust8; % l frqucy d frq(:m/)/(m/)*yqust; % rry stor th frqucy dcs fgur(); lot(frqlogpx'b'frqlogpy'r'); % lot th rsult % b: blu l for th owr sctru of th orgl sgl % r: rd l for th owr sctru of th fltr 4 SP- Brl Ch 9

20 l Fgurs of LPC Sctr Howor 7 Fll 4 Ordr 6 ctgl wdow o r-hss Ordr 4 ctgl wdow o r-hss Ordr 4 ctgl wdow o r-hss Ordr 8 ctgl wdow o r-hss Ordr 8 ctgl wdow Pr-hss Ordr 8 Hg wdow Pr-hss Ordr 8 Hg wdow o r-hss Plottd by ogr Kuo Fll 4 SP- Brl Ch

Linear Prediction Analysis of

Linear Prediction Analysis of Lr Prdcto Alyss of Sch Souds Brl Ch Drtt of Coutr Scc & Iforto grg Ntol Tw Norl Uvrsty frcs: X Hug t l So Lgug g Procssg Chtrs 5 6 J Dllr t l Dscrt-T Procssg of Sch Sgls Chtrs 4-6 3 J W Pco Sgl odlg tchqus