A Design Method for Separable-Denominator 2D IIR Filters with a Necessary and Sufficient Stability Check
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.1 pp.307-310
- Publication Date
- 2009/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.307
- Type of Manuscript
- LETTER
- Category
- Digital Signal Processing
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Keyword
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Toma MIYATA, Naoyuki AIKAWA, Yasunori SUGITA, Toshinori YOSHIKAWA, "A Design Method for Separable-Denominator 2D IIR Filters with a Necessary and Sufficient Stability Check" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 1, pp. 307-310, January 2009, doi: 10.1587/transfun.E92.A.307.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.307/_p
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@ARTICLE{e92-a_1_307,
author={Toma MIYATA, Naoyuki AIKAWA, Yasunori SUGITA, Toshinori YOSHIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Design Method for Separable-Denominator 2D IIR Filters with a Necessary and Sufficient Stability Check},
year={2009},
volume={E92-A},
number={1},
pages={307-310},
abstract={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.},
keywords={},
doi={10.1587/transfun.E92.A.307},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - A Design Method for Separable-Denominator 2D IIR Filters with a Necessary and Sufficient Stability Check
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 307
EP - 310
AU - Toma MIYATA
AU - Naoyuki AIKAWA
AU - Yasunori SUGITA
AU - Toshinori YOSHIKAWA
PY - 2009
DO - 10.1587/transfun.E92.A.307
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2009
AB - 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.
ER -
English
