Design of sharp-cutoff FIR digital filters with prescribed constant group delay

This paper addresses the design problem of sharp-cutoff FIR filters with prescribed constant group delay. The frequency-response masking (FRM) approach for designing sharp linear-phase (SLP) FIR filters is generalized to solve the design problem. The optimal interpolation factor M required in the FRM structure is determined by minimizing a proposed complexity measure of the designed sharp-cutoff FIR filter. Then the bandedge frequencies associated with each subfilter of the FRM structure can be determined. A method is proposed to find the corresponding group delay for each subfilter by solving a set of linear equations derived from the selected M and the prescribed constant group delay. After finding the required design specifications, we present a method based on a weighted least squares (WLS) algorithm for the minimax design of each subfilter. Finally, a modified discrete optimization procedure in conjunction with the WLS algorithm is proposed for designing sharp-cutoff FIR filters with powers-of-two coefficients as well as constant group delay. Several design examples are given for illustration.