12th Annual Conference of the International Speech Communication Association

Florence, Italy
August 27-31. 2011

Adaptive Estimation of Zeros of Time-Varying Z-Transforms

C. F. Pedersen, Ove Andersen, Paul Dalsgaard

Aalborg University, Denmark

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 perturbation lengths.

Full Paper

Bibliographic reference.  Pedersen, C. F. / Andersen, Ove / Dalsgaard, Paul (2011): "Adaptive estimation of zeros of time-varying z-transforms", In INTERSPEECH-2011, 173-176.