On the simultaneous estimation of poles and zeros in speech analysis

Kopec, Oppenheim, and Tribolet have described a homomorphic technique for producing, from a speech signal, a minimum-phase estimate of the vocal-tract impulse response. Once such an estimate has been obtained, the problem of modeling the vocal tract with a pole-zero model is a classical one in nonlinear estimation theory. It is shown in this paper that Shanks' method, Kalman's method, and the iterative prefiltering method are all different linearizations of the same nonlinear problem, and the iterative prefiltering method is proposed as an approach to estimating the poles and zeros of the vocal-tract transfer function simultaneously. A simulation is described which shows the advantage of estimating poles and zeros simultaneously rather than sequentially as in Shanks' method. A preliminary example of application to real speech is also given.