Table of Contents

Paper Abstract

The alternation theorem is at the core of the efficient real Chebyshev approximation algorithms. In this paper, the alternation theorem is extended from the real-only to the complex case. A new efficient algorithm is described for designing FIR filters that best approximate in the Chebyshev sense a desired complex-valued function. This algorithm is based on an ascent Remez exchange method applied to a transformation of the complex Chebyshev error, and is basically a generalization of the Parks-McClellan algorithm to the complex case. Numerical examples are presented to illustrate the performance of the proposed algorithm.