A design method for separable-denominator 2D IIR filters with a necessary and sufficient stability check

Toma Miyata, Naoyuki Aikawa, Yasunori Sugita, Toshinori Yoshikawa

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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 Rouch́e's theorem.

Original languageEnglish
Pages (from-to)307-310
Number of pages4
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 1 Jan 2009



  • Separable-denominator 2D IIR filters
  • Stability criterion
  • Successive projection methods
  • System matrix

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