A Design Method for Separable-Denominator 2D IIR Filters with a Necessary and Sufficient Stability Check

Toma MIYATA  Naoyuki AIKAWA  Yasunori SUGITA  Toshinori YOSHIKAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.1   pp.307-310
Publication Date: 2009/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.307
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
separable-denominator 2D IIR filters,  stability criterion,  system matrix,  successive projection methods,  

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Summary: 
In this paper, we propose designing method for separable-denominator two-dimensional Infinite Impulse Response (IIR) filters (separable 2D IIR filters) by Successive Projection (SP) methods using the stability criteria based on the system matrix. It is generally known that separable 2D IIR filters are stable if and only if each of the denominators is stable. Therefore, the stability criteria of 1D IIR filters can be used for separable 2D IIR filters. The stability criteria based on the system matrix are a necessary and sufficient condition to guarantee stability in 1D IIR filters. Therefore, separable 2D IIR filters obtained by the proposed design method have a smaller error ripple than those obtained by the conventional design method using the stability criterion of Rouche's theorem.