【正文】 s t h e o r e m ) NpnnmjnnE e mE S e??????????????21( ) |( ) ( ) ( )( ) 1 w h e r e i s t h e FT o f t h e se g m e n t o f sp e e ch , a n d i s si n ce t h e i m p u l se r e sp o n se o f t h e l i n e a r sy ste m i n t h e m o d e l f o r sp e e ch p r o d u ct i o n i s o fjjjnnpj j kkkA e dS e s m A eA e e??????????????222()()| ( ) |2 | ( ) | t h e f o r m t h e n w e ca n e x p r e ss t h e e r r o r a s t h i s m e a n s t h a t m i n i m i z i n g i s e q u i v a l e n t t o m i n i m i z i n g t h e i n t e g r a l o f t h e r a t i o o f t h e e njjjnnjnGHeAeSeGEdHeE??????????????()e r g y sp e ctr u m o f t h e sp e e ch se g m e n t t o t h e m a g n i t u d e sq u a r e d o f t h e FR o f t h e l i n e a r sy ste m f o r t h e sp e e ch m o d e l si n ce w e p r e v i o u sl y sh o w e d t h a t t h e a u t o co r r e l a t i o n f u n ctio n , , o f t h e se g m e n t ofnRm?22()( ) ( ) ( ) 1l i m | ( ) | | ( ) | sp e e ch , , a n d t h e a u t o co r r e l a t i o n f u n ci t o n , , o f t h e I R , , o f t h e sy ste m f u n ctio n , a r e e q u a l f o r t h e f i r st ( ) v a l u e s, t h e n t h u s a s g e t s la r gnjjnpsmR m h m H z pH e S ep??????? ()e , w e ca n a p p r o x i m a t e t h e si g n a l sp e ctr u m w i t h a r b i t r a r i l y sm a l l e r r o r w i t h t h e a l l p o l e m o d e l , Hz28 Frequency Domain Interpretation 22| ( ) | | ( ) | 28 co m p a r i so n b e t w e e n a n d f o r p o l e f i t b e t t e r f i t s n e a r sp e ctr u m p e a k s t h a n i n sp e ctr u m v a l l e y s f o r n u m b e r o f h a r m o n i cs f i t i s t o sp e ctr a l sh a p e f o r , f ijjnH e S e ppp?????? t i s t o d e t a i l e d sh a p e o f sp e ctr u m29 Frequency Domain Interpretation p l o ts sh o w Fo u r i e r t r a n sfo r m o f se g m e n t a n d L P sp e ctr a f o r v a r i o u s o r d e r s a s in cr e a se s, m o r e d e ta i l s o f th e sp e ctr u m a r e p r e se r v e d n e e d t o ch o o se a v a l u e o f t h a t r e p r e se n ts pp? th e sp e ctr a l e ff e cts o f th e g l o tt a l p u l se , v o ca l tr a c t a n d r a d i a ti o n n o th i n g e l s e30 Comparisons of Spectral Analysis Methods Spectral Comparisons across Methods a: narrowband analysis—resolves pitch harmonics b: wideband analysis—gives a smoothed spectrum c: homomorphic smoothing—gives good indications of formant locations d: LPC fit with p=12—formants and bandwidths can readily be obtained by factoring LPC polynomial 31 LPC Synthesis 1( ) ( ) ( ) t h e b a s i c s y n th e s i s e q u a ti o n i s n e e d t o u p d a te p a r a m e te r s e v e r y 1 0 m s e c o r s o p i tc h s y n c h r o n o u s m o d e wo r k s b e s tpkks n s n k G u n???? ? ????32 Formant Analysis Using LPC ? factor predictor polynomial—assign roots to formants ? pick prominent peaks in LPC spectrum ? problems on nasals where roots are not poles or zeros 。 choose values of N1=300, N2=300, p=10 ? putation for ? covariance method ≈ N1p+p3 ≈ 4000 *,+ ? autocorrelation method ≈ N2p+p2 ≈ 3100 *,+ 24 LP Solution Comparisons ? stability – guaranteed for autocorrelation method – cannot be guaranteed for covariance method。 / so l v e m a t r i x f o r st e p 1 st e p 2 s te p 3VVVVd V V V d V V d V ddV d V d V dV d V d V dd V dV??????????????????????????????? ?? ?32 2 32 31 1 21 32 32 31 1 21 242 2 42 41 1 21 42 42 41 1 21 23 43 4//,st e p 4 i t e r a t e p r o ce d u r e t o so l v e f o r d V d V V V d V dV d V d V V V d V dd V d????? ? ? ? ?? ? ? ? ??17 Cholesky Deposition ttt 1 n o w n e e d t o so lv e f o r u sing a 2 ste p p r o ce