Adaptive estimation of zeros of time-varying z-transforms

Abstract

In the present paper, a method is proposed for adaptive estimation and tracking of roots of time-varying, complex, and univariate polynomials, e.g. z-transform polynomials that arise from finite signal sequences. The objective with the method is to alleviate the computational burden induced by factorization. The estimation is done by solving a set of linear equations; the number of equations equals the order of the polynomial. To avoid potential drifting of the estimations, it is proposed to verify with Aberth-Ehrlich’s factorization method at given intervals. A numerical experiment supplements theory by estimating roots of time-varying polynomials of different order. As a function of order, the proposed method has a lower run time than Lindsey-Fox and computing eigenvalues of companion matrices. The estimations are quite accurate, but tend to drift slightly in response to increasing coefficient pertubation lengths.