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.

    Keywords

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

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering

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