A multiple exchange Remez algorithm for complex FIR filter design in the Chebyshev sense

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