FIR FILTER DESIGN WITH ADDITIONAL CONSTRAINTS USING COMPLEX CHEBYSHEV-APPROXIMATION

A powerful single exchange algorithm for the solution of the complex Chebyshev approximation problem was introduced by Tang. It was picked up and modified by Alkhairy et al. for the design of digital FIR filters. In this paper we extend this algorithm to solve the approximation problem in conjunction with additional constraints, such as constraints on the filter coefficients, constraints on the magnitude response and/or its derivatives or constraints on the group delay. Since the algorithm deals with a linear optimization problem, all constraints have to be linear with respect to the filter coefficients. We show this linearization and the inclusion into the complex approximation problem and the algorithm as well. A final example will demonstrate results achieved with the modified algorithm.