An efficient Remez-type algorithm for the design of optimum IIR filters with arbitrary partially constrained specifications

An efficient algorithm is described for the design of digital filters with optimum magnitude in the Chebyshev sense, arbitrary specifications, and arbitrary numerator and denominator orders. The filter specifications can be partially constrained. The characterization theorem of the optimum solution is given. As a conventional Remez multiple exchange algorithm applied to rational approximation problems, the proposed procedure is constructed on the basis of this characterization theorem. The resulting algorithm, being a Remez-type procedure, is much faster than other methods. The proposed algorithm can be used for designing recursive filters having several passbands and stopbands. Several examples illustrating the efficiency and flexibility of the algorithm are included