DESIGN OF IIR DIGITAL-FILTERS BASED ON EIGENVALUE PROBLEM

This paper presents a new method for designing IIR digital filters wit h optimum magnitude response in the Chebyshev sense and different orde r numerator and denominator. The proposed procedure is based on the fo rmulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general e igenvalue problem, we introduce a very simple selection rule for the e igenvalue to be sought for where the rational interpolation is perform ed if and only if the positive minimum eigenvalue is chosen. Therefore , the solution of the rational interpolation problem can be obtained b y computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained t hrough a few iterations, The design algorithm proposed in this paper n ot only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties o f the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate t he effectiveness of this method.