Nonlinear Modeling and Processing of Speech with Applications to Speech Coding

111 recent years there has been increasing interest in nonlinear speech modeling. In our approach, a speech signal is modeled as a sum of jointly amplitude ( A M ) and frequency (FM) modula.ted cosines with slowly-varying ce~lt~er frecluencies. The key problem is to extra.ct the center frequency ancl the a.inplitucle and frecluency modu.lations for each forma,nt in t,he nlodel from the inea,sured speech signa,ls. In this study, we describe the speech signal in terms of stcatistical inoclels and apply statcistical nonlinear filtering techniclues (Extended Iutationally t.ract.sble manner. Using Cra,mer-R.ao 11ound techniques, we ca.n compa.re t'lle performanc(of our computationally feasible estima.tors relative to the perfornlance of the coniput,a.tionally intra.cta,ble optimal estima.tor. Recoml~ination of the amplitude aad frequency signals g;enerat.ed by our approach results in fa,it'hful recollstruction of speech in both the t i me a.nd frequency c1oma.ins. We consider two applications. The first a.pl~lication, ~: l l ich is forma.11t tra,cl;ing, is a direct application of our non1inea.r filters since the fonna.nt frecluencies are a pa.rt. of our nonlinear model. The a.pplica,t'ion of our entire frame\vorl; to speech coding is also discussed.