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

31 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


  • 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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