Advanced weighting scheme in the rational Remez algorithm for IIR digital filters

In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. Many methods have been proposed for the design of such filters. One of the most practical methods is the rational Remez algorithm, in which the squared magnitude response of the IIR digital filter is approximated by solving an eigenvalue problem, and then the filter is obtained by factorizing it. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to 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 trial and error 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 ratios. The method iteratively solves eigenvalue problems with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.