A generalized Remez multiple exchange algorithm for complex FIR filter design

This paper presents a generalization of Remez multiple exchange algorithm for designing optimal complex finite impulse response (FIR) filters with the Chebyshev (minimax) error criterion. Methods for implementing the two fundamental steps of Remez multiple exchange algorithm in the complex case are proposed. Specifically, it is shown that generalization of the first step, which involves solving a complex Chebyshev approximation subproblem over a set of guessed extremal points, can be implemented by solving a maximization problem with simple bound constraints using Newton´s method. In addition, generalization of the second step, which involves finding a new set of guessed extremal points, can be realized by use of a simple exchange rule derived from the concept of extremal signature