Closed-form design of maximally flat R-regular Mth-band FIR filters

In this paper, we derive some properties of maximally flat R-regular Mth-band FIR filters. We show that the R-regularity implies maximally flat frequency response at ω=0. The R-regular constraints are a set of linear equations with complex coefficients. We can convert these complex-value equations to equivalent ones with only real coefficients. We also show that it is possible to completely determine the filter coefficients by R-regularity. Design examples are presented to illustrate the R-regularity properties and the effectiveness of the proposed approach