Complex approximation with additional constraints

A powerful signal exchange algorithm for the solution of the complex Chebyshev approximation problem was introduced by P.T.P. Tang (1988). It was picked up and modified by A. Alkhairy et al. (1991) for the design of digital FIR filters. This algorithm is extended 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. This linearization, the integration into the complex approximation problem, and the algorithm are shown. An example demonstrating results obtained with the modified algorithm is given.>