ACCURATE PJRNErI'ER ESTIMATION OF NOISY SPEECH-LIKE SIGNALS RAMDAS KUMARESAN and LXJNALD W. TLJFPS Department of Electrical Engineering University of Rhode Island Kingston, RI 02881 ABH1IArr Ass'.im 1 rir thd3t 55 hC) i't seirierit of ob'.e r'd speech st :t rap be modeled the tio:t :i.iii''.JI.sC? 1's''porist? oi •:t :i.riei1' ss'L;rITi wt:' C))t31Ii t.lio Fc).t. tr I or' :ttinnt; of t.ho i'.•j.eiTi froli thE €T'C)5 nt a poiurioiniiii. of tii pt:)tric)ni:L a.i S T't 5C'I1I (L c' y'tiiii-rri bw two ftC ,tHTh1'3 ii'.ii'iti decompositiori of' sri est:imated c'orrt:! IsLiort matrix. The speech—i ike srtal is used :i. ri the reversed time di rertloit to ider,tifii the sinnai T'elSted reros nt' the poisriomial from the rest • Experimental results conPariflr. the accuracw of the oie parameters obtained bw different methods are iveri. INTRODUCTION: Speech sirials are modeled cuite succesfuliw as the output of a linear swstem (vocal tract) excited hs wide hand siirsals (1), Mariw linear prediction (LP) based algorithms (1) do riot dive accurate estimates of' the role or pole/zero parameters reresentiri the vocal tract especially when the data record is short arid roisy. If the order-of the speech model is over estimated some of' these algorithms will thve false formarit. locations (see section III). Also for nasalized speech sir'ials the parameters thven hw the LF based techriiejes seem grossly inaccurate (2) * There has beer numerous attenipts to solve this rrobleiti Recent reports of Henderson (3) and Van Blaricum (4) are closels coririected to our work. They have attempted to obtain better estimates of role locations from noisy i rn P ui Sc re sPorts e dat a ijsi ri eier;value/eier,vector deconpositior'i of an estimated correlation matni;<, The methods we present here (5,6) are in:pravemerits over their techriiGues. The salient features of our methods ar'e as follows. We have previouslw used similar ideas for resolvin closely aced spectral peaks (7,8) • I ) We model the speech dat a as an impulse response seeuerce or ecuivalentls a sum of M exponentially damped sinals with arbitrary phases arid amplitudes. 2) As in other linear prediction based methods we obtain the sole parameters of the mrulse This research was supported by the Office of Naval Research under the grant No. N0014—81—K—0144. response from the zeros o' a polynomial, similar to the prediction error filter olwnomial (1). The key point is that the accuracy of the coefficients of this polynomial is ensured h usir the eienvalue/eieniyector or emuivaler,tlv sirular value deconipositiori (SUEt) of' the corelatior,/data matrix, Once the pole parameters are determined accurately the zeros if ar,y, in the case of nasalized sounds cars be determined usiri other methods (see ref. (5)). 3) We use art L th deSree polynomial 0(z), where L is larger than H the number of exponeritials ir, the data. Also L is chosen as a sizable fraction of N, the number of data samples which is assumed small, This turns out to he an important factor in jmprovir the accuracy of the estimates, 4) Lastly, we use the data in the backward direction, to isolate the M zeros of 0(z) related to the signal parameters, called siral zeros from the rest L—M, extraneous zeros (9). I1 ESTIMATING THE POLE LOCATIONS: We shall Fresent two closelw related methods to determine the Pole locations from noisy impulse response data, A short semerit of a speech—like sirsal, (ni),nl,2.. N, assumed to be a SUITI of' H exponentially damped siniuidal sinials is observed, That is, (rr) ae5, where 5K arid a are complex r,unihers in enera1 We construct a (N—L)x(L+l) data matrix A, below usir the N sanuples of y(n) I— * * 1J(t) 'j(.) . A = / t.'L) 'j3). L* ) LNL 'N-L+).' '*' deriotes comrlex &ontJuate, In both methods we atternt to firiij a vector (1 , ' ' )' with which we form the polriomial G(z)=1+Kz. The H out of' L zeros of 0(z) estimates of k172.,. H. If the data is indeed a sum of H exporienitials and noiseless then the olvniomial 0(z), with coefficiert vector which satisfies the homosnueous etuationi will have zeros at e"5k=1,2,, H. But L has to satisfy the iruemuality ML(N—L) 1357 CH 1746•7!8210000 1357 $ 00.75 © 1982 IEEE