Closed-form design of maxflat R-regular FIR Mth-band filters with arbitrary group delay using waveform moments

Mth-band filters have been found numerous applications in multirate signal processing systems, filter banks and wavelets. In this paper, a new closed-form expression is presented for the impulse response of the maxflat R-regular FIR Mth-band filters with arbitrary group delay. The filter coefficients are directly obtained by solving a linear system of Vandermonde equations that are derived from the regularity conditions via waveform moments. Moreover, the group delay of the proposed FIR Mth-band filters can be arbitrarily specified. Finally, some design examples are presented to demonstrate the effectiveness of the proposed maxflat R-regular FIR Mth-band filters.