On error surfaces of sufficient order adaptive IIR filters: proofs and counterexamples to a unimodality conjecture

Author

Fan, Hong ; Mayeri, M.

Author_Institution

Dept. of Electr. & Comput. Eng., Cincinnati Univ., OH, USA

Volume

37

Issue

9

fYear

1989

fDate

9/1/1989 12:00:00 AM

Firstpage

1436

Lastpage

1442

Abstract

It is shown that although a conjecture proposed by S. Stearns (ibid., vol.ASSP-29, p.763-6, June 1981) concerning sufficient conditions to guarantee unimodality of error surfaces for adaptive pole-zero infinite-impulse-response (IIR) filters is valid for first- and second-order filters, it is not true in general without an additional constraint introduced by T. Soderstrom (Autom., vol.11, p.93-9, Jan. 1982). Proofs of the conjecture for a first- and second-order adaptive filters are given. Counterexamples are presented to illustrate the failure of this conjecture for higher order filters when the condition of Soderstrom is not satisfied for both matching order and overparameterizing cases

Keywords

adaptive filters; digital filters; filtering and prediction theory; adaptive IIR filters; digital filters; pole-zero infinite-impulse-response; Adaptive filters; Additive noise; Finite impulse response filter; IIR filters; Least squares approximation; Linear systems; Matched filters; Signal processing; Sufficient conditions; System identification;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.31298

Filename

31298