Design of FIR filters with complex desired frequency response using a generalized Remez algorithm

Complex approximation with a generalized Remez algorithm is used to design FIR digital filters with nonconjugate symmetric frequency responses. The minimax criterion is used and the Chebychev approximation is posed as a linear optimization problem. The primal problem is converted to its dual and is solved using an efficient, quadratically convergent algorithm developed by Tang. Optimal Chebychev real-coefficient FIR filters with group delay smaller than half the filter length can be designed with slightly better magnitude responses compared to linear-phase filters. Linear-phase filters can also be designed when the group delay is specified to be half the filter length. Most importantly, the design method is capable of producing filters with complex coefficients that approximate nonconjugate symmetric frequency responses