【正文】 , ) ( ) ( ) , 1 , 0( , ) ( ) ( ) , 1 ch a n g i n g t h e su m m a tion ind e x g i v e s pNn k nmkNn n nmNin n nmiNkn n nmks m s m ki k s m i s m k i p k pi k s m s m i k i p k pi k s m s m k i???????????????????????????? ? ? ? ? ? ??? ? ? ? ? ? ?? ? ? ??????,00( ) ( 1 ) k e y d i ff e r e n ce fr o m A u to cor r e l a tion M e t h o d is t h a t l i m i ts o f sum m a tioni n cl u d e t e r m s b e fo r e = w i n d o w e x te n d s sa m p l e s b a ck w a r d sfr o m t o si n ce w e a r e e x te n d i n g w i n d o w b ai p k pmps n p s n N? ? ????? ck w a r d s, d o n 39。 it is e st im a t in g f r o m t h e m o st r e ce n t v a lu e s o f b y lin e a r l y p r e d ict in g its pppNx n x n Nxnp p N x n?????m in im iz in g t h e su m o f sq u a r e d d iff e r ev a lu e f o r L P , t h e p r e d ict o r co e f f icie n t s ( t h e 39。1 Speech Signal Processing—Lecture 10 Linear Predictive Coding (LPC)Introduction 2 LPC Methods ? LPC methods are the most widely used in speech coding, speech synthesis, speech recognition, speaker recognition and verification and for speech storage – LPC methods provide extremely accurate estimates of speech parameters, and does it extremely efficiently – basic idea of Linear Prediction: current speech sample can be closely approximated as a linear bination of past samples, ., 1( ) ( ) ,f o r s o m e v a l u e o f 39。 spkkkx n x n k p??????3 LPC Methods ( ) ( )()( ) ( ) f o r p e r io d ic sig n a ls w ith p e r io d , it i s o b v io u s t h a t b u t t h a t is n o t w h a t L P is d o in g 。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