Design of discrete coefficient FIR digital filters with arbitrary amplitude and phase responses

The design of FIR digital filters with discrete coefficients in the complex frequency domain is considered. A design method based on a recently developed weighted-least-squares (WLS) algorithm is presented. First, FIR filters with continuous coefficients are designed, using the WLS algorithm to meet the desired frequency response specifications in the minimax sense. To avoid the effect of a nonuniformly distributed coefficient grid due to discretization of filter coefficients, a procedure is then performed to obtain an optimal filter gain factor. Finally, utilizing the error weighting function obtained by the WLS algorithm, an efficient discrete optimization process is performed to obtain a discrete solution in the minimax sense. The efficiency of the method is illustrated by the design of discrete-coefficient FIR filters with constant group delay and filter length greater than 60