Stability and margin of stability tests for multidimensional filters

Author

Curtin, Eugene ; Saba, Salim

Author_Institution

Dept. of Math., Southwest Texas State Univ., San Marcos, TX, USA

Volume

46

Issue

7

fYear

1999

fDate

7/1/1999 12:00:00 AM

Firstpage

806

Lastpage

809

Abstract

In this paper we give simplified proofs of the stability and the margin of stability criteria of Zeheb and Walach for n-dimensional recursive digital filters. We base our proofs on the method of Lagrange multipliers. Both the stability and margin of stability questions are converted into the problem of locating the zeros of a system of polynomial equations. These systems can then be solved using Buchberger´s algorithm for computing the Groebner basis of a polynomial ideal

Keywords

circuit stability; multidimensional digital filters; multiplying circuits; recursive filters; stability criteria; Buchberger´s algorithm; Groebner basis; Lagrange multipliers; Zeheb-Walach criteria; multidimensional filters; n-dimensional recursive digital filters; polynomial equations; polynomial ideal; stability; stability tests; Application software; Digital filters; Equations; Lagrangian functions; Mathematics; Multidimensional systems; Polynomials; Signal processing algorithms; Stability criteria; Testing;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.774225

Filename

774225