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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Plusieurs méthodes pour tester la stabilité des filtres numériques récursifs bidimensionnels (2D) quart de plan du premier quadrant ont été suggérées dans les années 1970 et 80. Bien que les algorithmes de lignes et de colonnes de Jury, les tests de stabilité de concaténation de lignes et de colonnes aient été considérés comme des méthodes de mappage très efficaces. Ils manquent encore de précision car ils nécessitent un nombre infini d’étapes pour conclure sur la stabilité exacte des filtres et le temps de calcul requis est également énorme. Dans cet article, nous présentons une méthode algébrique procédurale très simple ne nécessitant que deux étapes lorsqu'elle est appliquée au filtre quart de plan 2D du deuxième ordre. Nous étendons la même méthode aux filtres NSHP (Non-Symmetric Half-plan) du second ordre. De nombreux exemples sont donnés pour ces deux types de filtres ainsi que pour certains filtres numériques 2D récursifs généraux d'ordre inférieur. Nous avons appliqué notre méthode à des exemples de filtres à peine stables ou à peine instables disponibles dans la littérature et avons obtenu les mêmes décisions, montrant ainsi que notre méthode est suffisamment précise.
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Ananthanarayanan RATHINAM, Rengaswamy RAMESH, P. Subbarami REDDY, Ramaswamy RAMASWAMI, "Testing the Stability of 2-D Recursive QP, NSHP and General Digital Filters of Second Order" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 8, pp. 1408-1414, August 2010, doi: 10.1587/transfun.E93.A.1408.
Abstract: Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970's and 80's. Though Jury's row and column algorithms, row and column concatenation stability tests have been considered as highly efficient mapping methods. They still fall short of accuracy as they need infinite number of steps to conclude about the exact stability of the filters and also the computational time required is enormous. In this paper, we present procedurally very simple algebraic method requiring only two steps when applied to the second order 2-D quarter - plane filter. We extend the same method to the second order Non-Symmetric Half-plane (NSHP) filters. Enough examples are given for both these types of filters as well as some lower order general recursive 2-D digital filters. We applied our method to barely stable or barely unstable filter examples available in the literature and got the same decisions thus showing that our method is accurate enough.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1408/_p
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@ARTICLE{e93-a_8_1408,
author={Ananthanarayanan RATHINAM, Rengaswamy RAMESH, P. Subbarami REDDY, Ramaswamy RAMASWAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Testing the Stability of 2-D Recursive QP, NSHP and General Digital Filters of Second Order},
year={2010},
volume={E93-A},
number={8},
pages={1408-1414},
abstract={Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970's and 80's. Though Jury's row and column algorithms, row and column concatenation stability tests have been considered as highly efficient mapping methods. They still fall short of accuracy as they need infinite number of steps to conclude about the exact stability of the filters and also the computational time required is enormous. In this paper, we present procedurally very simple algebraic method requiring only two steps when applied to the second order 2-D quarter - plane filter. We extend the same method to the second order Non-Symmetric Half-plane (NSHP) filters. Enough examples are given for both these types of filters as well as some lower order general recursive 2-D digital filters. We applied our method to barely stable or barely unstable filter examples available in the literature and got the same decisions thus showing that our method is accurate enough.},
keywords={},
doi={10.1587/transfun.E93.A.1408},
ISSN={1745-1337},
month={August},}
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TY - JOUR
TI - Testing the Stability of 2-D Recursive QP, NSHP and General Digital Filters of Second Order
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1408
EP - 1414
AU - Ananthanarayanan RATHINAM
AU - Rengaswamy RAMESH
AU - P. Subbarami REDDY
AU - Ramaswamy RAMASWAMI
PY - 2010
DO - 10.1587/transfun.E93.A.1408
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2010
AB - Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970's and 80's. Though Jury's row and column algorithms, row and column concatenation stability tests have been considered as highly efficient mapping methods. They still fall short of accuracy as they need infinite number of steps to conclude about the exact stability of the filters and also the computational time required is enormous. In this paper, we present procedurally very simple algebraic method requiring only two steps when applied to the second order 2-D quarter - plane filter. We extend the same method to the second order Non-Symmetric Half-plane (NSHP) filters. Enough examples are given for both these types of filters as well as some lower order general recursive 2-D digital filters. We applied our method to barely stable or barely unstable filter examples available in the literature and got the same decisions thus showing that our method is accurate enough.
ER -