Title: Stable multi-dimensional model reduction and IIR filter design

Authors: J. Abouir, A. Cuyt

Addresses: Faculte des Sciences et Techniques, Department de Mathematiques, Universite Hassan II, B.P. 146 Mohammedia, Morocco. ' Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, B-2020 Antwerpen, Belgium

Abstract: It is well-known that model reduction techniques applied to stable multi-dimensional Linear Shift-Invariant (LSI) systems with Infinite-extent Impulse Response (IIR) do not necessarily guarantee a stable reduced system. Several conditions exist to check stability a posteriori. In this paper we outline a new technique that guarantees, a priori, that the system or filter is stable. In Section 1 we establish the necessary notation and definitions to deal with multi-dimensional systems and filters. Section 2 introduces the technique of multivariate Pade-type approximation and deals with stability. In Section 3 we illustrate the use of the newly proposed technique in filter design.

Keywords: model order reduction; rational transfer function; IIR systems; digital filters; stability; linear shift invariant; LSI systems; infinite-extent impulse response; filter design.

DOI: 10.1504/IJCSM.2007.013761

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.1, pp.16 - 27

Published online: 25 May 2007 *

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