Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response

Masahiro OKUDA  Masaaki IKEHARA  Shin-ichi TAKAHASHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.11   pp.1879-1885
Publication Date: 1996/11/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
IIR digital filter,  log magnitude response,  steepest decent method,  robust algorithm,  

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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.