Least-squares approach to IIR digital filters and an application to equiripple solutions

Masahiro Okuda, Masaaki Ikehara, Shin Ichi Takahashi

Research output: Contribution to journalArticle

Abstract

This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.

Original languageEnglish
Pages (from-to)28-36
Number of pages9
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume81
Issue number7
Publication statusPublished - 1998 Jul

Fingerprint

Chebyshev approximation
IIR filters
Digital filters
Least squares approximations
Computer simulation

Keywords

  • Equiripple approximation
  • Gram-Schmidt orthogonalization
  • IIR digital filter
  • Weighted modified least-squares method

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "Least-squares approach to IIR digital filters and an application to equiripple solutions",
abstract = "This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.",
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AB - This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.

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