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as window size gets larger, this almost always makes the system stable ? choice of LP analysis parameters – need 2 poles (for 1 kHz) for each vocal tract resonance below Fs/2 – need 34 poles to represent source shape and radiation load – use values of p ≈ 1314 25 Prediction Error Signal Behavior 1( ) ( ) ( ) ( )() t h e p re d ictio n e rr o r sig n a l is co m p u t e d a s sh o u ld b e la rg e a t t h e b e g in n in g o f e a ch p itch p e ri o d (v o ice d sp e e ch ) = g o o d sig n a l f o r p itch d e t e ct io n ca n p e rpkke n s n s n k Gu nen??? ? ? ??()f o rm a u t o co rr e la t io n o n a n d d e t e ct la rg e st p e a k e rr o r sp e ct ru m is a p p ro x im a t e ly f la t s o e f f e ct s o f f o rm a n t s o n p itch d e t e ct io n a rem in im iz e den26 LP Analysis of Speech ? note error signal near time=0 for autocorrelation method 27 Frequency Domain Interpretation 1202()1| ( ) | |2 co n si d e r se t o f p r e d i cto r co e f f i ci e n t s f r o m a u t o co r r e l a t i o n m e t h o d w i t h m e a n sq u a r e d e r r o r o r i n t h e f r e q u e n cy d o m a i n ( f r o m Pa r se v a l 39。 / 。s) a r e d e t e r m in e d ( co m p u t e d ) b y ( o v e r a f in itn ce s b e t w e e n t h e a ct u a l s p e e ch sa m p le sand e in t e rt h e linvae a yl) r l pk??r e d ict e d o n e s4 Basic Principles of LP 1()()()1 u s e t h e t i m e v a r y i n g d i g i ta l f i l te r t o r e p r e s e n t th e g l o tt a l p u l s e sha p e , th e v o c a l t r a c t IR a n dth e r a d i a ti o n e ff e c ts, i .e ., sy s te m e x c i te d b y a n i m p u l s e t r a i n f o r pkkkS z GHzUzaz????? ?v o i c e d spe e c h o r a r a n d o m seq u e n c e f o r u n v o i c e d spe e c h a l r e a d y k n o w h o w t o e s ti m a te p i tch p e r i o d a n d V /U V t h i s a l l p o l e m o d e l i s a n a tu r a l r e p r e s e n ta ti o n f o r n o n n a s a l v o i c e d spe e c h , b u t a l s o w o r k s r e a s o n a b l y w e l l f o rn a s a l s a n d u n v o i c e d sou n d s ( e v e n w i th o u t e x p l i c i t z e r o s ) = r e c a l l t h a t a l o t o f p o l e s can a p p r o x i m a te z e r o s1( ) ( ) ( )pkks n a s n k G u n?? ? ??H(z) 5 LP Basic Equations 111()( ) ( ) ( )()()( ) ( ) ( ) ( ) ( )thppkkkkkpkkpSzs n s n k P z zSzene n s n s n s n s n k????????? ? ? ? ??? ? ? ? ????? a o r de r li ne ar p r ed i ctor is a sy stem o f t he fo r m th e pr ed i cti on e r r or , , is o f t he fo r m th e pr1()( ) 1(),1( ) ( ) ( )pkkkkkEzA z zSza k pe n G u n A z????? ? ?? ? ? ????ed i cti on e r r or is th e ou tp ut o f a sy stem w i th tr an sfer fu nction if th e spee ch si gn al ob ey s the p r od ucti on m od el ex actly , a nd if an d is a n ()()()HzGHzAz?i nv er se fil te r fo r , . , 6 LP Estimation Issues kk????? n e e d t o d e t e rm in e { } d ir e ct ly f ro m sp e e ch su ch t h a t t h e y g iv e g o o d e st im a t e s o f t h e t im e v a ry in g sp e ct ru m n e e d t o e st im a t e { } f ro m sh o rt se g m e n t s o f sp e e ch n e e d t o m in im iz e m e a n sq u a re d p re d ickka??t io n e rr o r o v e r sh o rt se g m e n t s o f sp e e ch re su ltin g { } a ss u m e d t o b e t h e a ct u a l { } in t h e sp e e ch p ro d u ct io n m o d e l= in t e n d t o sh o w t h a t a ll o f t h is e f f icie n t ly ,re lia b ly , ca nand b e d o n ea cc u ra t e l f o r sy p e e ch7 Solution for {αk} ? ?2221( ) ( ) ( )( ) ( )( ) ( ) sh o rttim e a v e ra g e p re d ictio n e rr o r is d e f in e d a s se le ct se g m e n t o f sp e e ch in t h e v icin i t y o f sa m p le t h e kn n n nmmpn k nmknE e m s m s ms m s m k