A Study on Weighting Scheme for Rational Remez Algorithm

Yusuke SAITO
Masahiro OKUDA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A    No.4    pp.1144-1147
Publication Date: 2011/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1144
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
IIR digital filter,  the rational Remez algorithm,  ripple ratio,  

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In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. The conventional rational Remez algorithm quickly finds the squared magnitude response of the optimal IIR digital filters, and then by factorizing it the equiripple filter is obtained. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to explicitly control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by manually changing the weights in order to achieve the ratio of the weights exactly. To address this problem, we modify the conventional algorithm and make it possible to directly control the ripple ratio. The method iteratively solves eigenvalue problems with controlling the ripple ratio. Using this method, the equiripple solutions with desired weights are obtained automatically.