Simultaneous approximation for IIR digital filters with log magnitude and phase response

Masahiro Okuda, Masaaki Ikehara, Shin Ichi Takahashi

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase-squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.

Original languageEnglish
Pages (from-to)1879-1884
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number11
Publication statusPublished - 1996


  • IIR digital filter
  • Log magnitude response
  • Robust algorithm
  • Steepest decent method

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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