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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
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Les tendances récentes dans la conception de filtres impliquent le développement de filtres clairsemés avec des coefficients qui ont non seulement des valeurs réelles mais également des valeurs nulles. Ces filtres clairsemés peuvent atteindre des performances élevées en optimisant la sélection des coefficients nuls et en calculant les coefficients réels (non nuls). La conception d'un filtre clairsemé à réponse impulsionnelle infinie (IIR) est plus difficile que la conception d'un filtre clairsemé à réponse impulsionnelle finie (FIR). Par conséquent, les études sur la conception de filtres clairsemés IIR ont été rares. Dans cette étude, nous considérons des filtres IIR dont les coefficients impliquent une valeur nulle, appelés filtres IIR clairsemés. Premièrement, nous formulons le problème de conception comme un problème de programmation linéaire sans imposer de condition de stabilité. Par la suite, nous reformulons le problème de conception en modifiant la fonction d'erreur et préparons plusieurs polynômes dénominateurs possibles avec des pôles stables. Enfin, en intégrant ces méthodes dans des algorithmes d'amincissement successifs, nous développons un nouvel algorithme de conception des filtres. Pour démontrer l'efficacité de la méthode proposée, ses performances sont comparées à celles d'autres méthodes existantes.
Masayoshi NAKAMOTO
Hiroshima University
Naoyuki AIKAWA
Tokyo University of Science
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Masayoshi NAKAMOTO, Naoyuki AIKAWA, "Minimax Design of Sparse IIR Filters Using Sparse Linear Programming" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 8, pp. 1006-1018, August 2021, doi: 10.1587/transfun.2020EAP1096.
Abstract: Recent trends in designing filters involve development of sparse filters with coefficients that not only have real but also zero values. These sparse filters can achieve a high performance through optimizing the selection of the zero coefficients and computing the real (non-zero) coefficients. Designing an infinite impulse response (IIR) sparse filter is more challenging than designing a finite impulse response (FIR) sparse filter. Therefore, studies on the design of IIR sparse filters have been rare. In this study, we consider IIR filters whose coefficients involve zero value, called sparse IIR filter. First, we formulate the design problem as a linear programing problem without imposing any stability condition. Subsequently, we reformulate the design problem by altering the error function and prepare several possible denominator polynomials with stable poles. Finally, by incorporating these methods into successive thinning algorithms, we develop a new design algorithm for the filters. To demonstrate the effectiveness of the proposed method, its performance is compared with that of other existing methods.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1096/_p
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@ARTICLE{e104-a_8_1006,
author={Masayoshi NAKAMOTO, Naoyuki AIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Minimax Design of Sparse IIR Filters Using Sparse Linear Programming},
year={2021},
volume={E104-A},
number={8},
pages={1006-1018},
abstract={Recent trends in designing filters involve development of sparse filters with coefficients that not only have real but also zero values. These sparse filters can achieve a high performance through optimizing the selection of the zero coefficients and computing the real (non-zero) coefficients. Designing an infinite impulse response (IIR) sparse filter is more challenging than designing a finite impulse response (FIR) sparse filter. Therefore, studies on the design of IIR sparse filters have been rare. In this study, we consider IIR filters whose coefficients involve zero value, called sparse IIR filter. First, we formulate the design problem as a linear programing problem without imposing any stability condition. Subsequently, we reformulate the design problem by altering the error function and prepare several possible denominator polynomials with stable poles. Finally, by incorporating these methods into successive thinning algorithms, we develop a new design algorithm for the filters. To demonstrate the effectiveness of the proposed method, its performance is compared with that of other existing methods.},
keywords={},
doi={10.1587/transfun.2020EAP1096},
ISSN={1745-1337},
month={August},}
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TY - JOUR
TI - Minimax Design of Sparse IIR Filters Using Sparse Linear Programming
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1006
EP - 1018
AU - Masayoshi NAKAMOTO
AU - Naoyuki AIKAWA
PY - 2021
DO - 10.1587/transfun.2020EAP1096
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2021
AB - Recent trends in designing filters involve development of sparse filters with coefficients that not only have real but also zero values. These sparse filters can achieve a high performance through optimizing the selection of the zero coefficients and computing the real (non-zero) coefficients. Designing an infinite impulse response (IIR) sparse filter is more challenging than designing a finite impulse response (FIR) sparse filter. Therefore, studies on the design of IIR sparse filters have been rare. In this study, we consider IIR filters whose coefficients involve zero value, called sparse IIR filter. First, we formulate the design problem as a linear programing problem without imposing any stability condition. Subsequently, we reformulate the design problem by altering the error function and prepare several possible denominator polynomials with stable poles. Finally, by incorporating these methods into successive thinning algorithms, we develop a new design algorithm for the filters. To demonstrate the effectiveness of the proposed method, its performance is compared with that of other existing methods.
ER -