Statistical Speech Analysis and Nonlinear Modeling

Transcription

1 Lmerck, 16th Aprl 23 Statstcal Analyss and Nnlnear Mdelng Nasss Katsamans & Petrs Marags Natnal Techncal Unversty f Athens Schl f Electrcal & Cmputer Engneerng CVSP Grup COST277 Meetng,

2 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns The prblem: Analyss based n the AM-FM mdel The methd: Statstcal Multband Demdulatn usng Kalman Flters and Energy Separatn

3 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns References: AFM Mdel and ESA, Marags,, Kaser, Quater IEEE Trans. Aud 1993 Statstcal Multband Demdulatn, Lu, Derschuk IEEE Trans. Sgnal Prc Pa, Derschuk IEEE Trans. Sgnal Prc.. 2

4 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Descrptn f the Algrthm Kalman- The Kalman-ESA mdel Instantaneus Frequency and Ampltude Estmatn Basc Varatn Mdfed Measurement Equatn Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns

5 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Based n the AM-FM mdel: yt () = at ()cs(2π ft + 2 πf m, q( τ) dτ+ θ) Fr a lnger tme nterval: φ () t t φ () t = θ + 2 π [ f ( τ) + v ( τ)] dτ The speech sgnal (multcmpnent( multcmpnent): K st () = a()cs t φ () t = 1 t

6 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Dynamc System, fr each cmpnent: fn () = fn ( 1) + qwn ( 1) f f an () = α an ( 1) + qw( n 1) a a a vn () = α vn ( 1) + qw( n 1) v v v φ( n) = φ( n 1) + 2 πt( f( n 1) + v( n 1)) s The measurement equatn: K yn ( ) = a( n)cs( φ( n)) + run ( ) = 1

7 Intrductn Cntents Algrthm Descrptn Kalman- Kalman- ESA Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Fr each cmpnent: Sgnal Bandpass Flterng & Demdulatn Algrthm (ESA) f, bw aˆ vˆ f a v φ Kalman Flter Nse (WGN) yˆ

8 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Instantaneus Frequency & Ampltude Estmatn (IFAE) s(k) : multcmpnent AFM sgnal s(k) Wndwng f () n bw () n ESA Gabr Flter a() n IF ( n)

9 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns State Equatns: f() n = f( n 1) + q w ( n 1) f f an () IFAE = IFAE (, s f( n 1), bw, n) + Q wifae() n IF () n φ( n) = φ( n 1) + 2 πtif( n 1) s Measurement Equatn: K yn ( ) = a( n)cs( φ( n)) + run ( ) = 1

10 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns State Equatns: f ( n) = f ( n 1) + q w ( n 1) f f a ( n) = α a ( n 1) + q w ( n 1) a a a v ( n) = α v ( n 1) + q w ( n 1) v v v φ ( n) = φ ( n 1) + 2 πt ( f ( n 1) + v ( n 1)) s Measurement Equatns: K yn ( ) = a( n)cs( φ ( n)) + run ( ) = 1 y ( n) = f ( n) + v ( n) + r u ( n),1,1,1 y ( n) = a ( n) + r u ( n),2,2,2

11 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn () Mdfed Equatn () Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns The sgnal: 2 yt () = [1 κcs(2 π f t)] = 1 AM t cs(2 π( ft+ β cs(2 π f τ) dτ)) Effect f Nse Effect f the AM ndex Effect f the FM ndex FM,

12 Effect f Nse Effect f Nse IA 1-1 IF SNR(dB) SNR(dB) Nrmalzed Mean Square Errr Nrmalzed Mean Square Errr -1-2 IF 2 Nrmalzed Mean Square Errr IA SNR(dB) SNR(dB) 3 4 Nrmalzed Mean Square Errr

13 Effect f the AM ndex Nrmalzed Mean Square Errr IA 1 Nrmalzed Mean Square Errr IF amindex amindex Nrmalzed Mean Square Errr IA 2 Nrmalzed Mean Square Errr IF amindex amindex

14 Effect f the FM ndex Nrmalzed Mean Square Errr IA 1 Nrmalzed Mean Square Errr IF fmindex fmindex Nrmalzed Mean Square Errr IA 2 Nrmalzed Mean Square Errr IF fmindex fmindex

15 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn Mdfed Equatn Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Analyss Demdulatn f the separate cmpnents Phneme /ee/ n the wrd m/ee ee/tng Sgnal Recnstructn Frmant Trackng Vced Sentence Where were yu whle we were away? -Sgnal Recnstructn

16 5 IA 1 1 IF IA IF IA IA IF IF tme(sec) tme(sec)

17 Recnstructed Sgnal Recnstructed sgnals n tme,nmse=.13275,nmse=.2297,nmse= PSD f recnstructed sgnals

18 Orgnal Sgnal:

19 Intrductn Cntents Algrthm Descrptn Kalman- Estmatn Basc Varatn Mdfed Equatn Cmparsn Applcatn t Analyss Frmant Trackng Cnclusns Further Research Enhancement by means f energy estmatn Inclusn f nse Multband sgnal prcessng Better Demdulatn Natural backgrund Cmparng wth Kalman- Applcatn t Frmant Evlutn Mdelng Bandwdth Mdelng Theretcal Research System Identfcatn Better Estmatn Cmplexty Reductn