Fast and stable least-squares approach for the design of linear phase FIR filters

Masahiro Okuda, Masaaki Ikehara, Shin Ichi Takahashi

    Research output: Contribution to journalArticlepeer-review

    24 Citations (Scopus)


    In this paper, we present a new numerical algorithm for solving the normal equations associated with the least-squares design of linear phase FIR filters. The usual solution methods have a computational complexity of O(N3). Moreover, solving the normal equations with Gaussian elimination commonly yields numerical errors, especially when the filter is long. Here, we convert a least-squares method into the problem of constructing a system of orthonormal functions. The proposed design algorithm needs only O(N2) computations, and numerical errors can be reduced. Some examples are given to show the excellent performance of the algorithm.

    Original languageEnglish
    Pages (from-to)1485-1493
    Number of pages9
    JournalIEEE Transactions on Signal Processing
    Issue number6
    Publication statusPublished - 1998 Dec 1


    • Computational complexity
    • Least-squares design
    • Linear-phase fir filters
    • Orthogonal functions

    ASJC Scopus subject areas

    • Signal Processing
    • Electrical and Electronic Engineering

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