FIR filter solution to unusual gain responses arising in Parks-McClellan algorithm

Abstract

A linear-phase FIR filter with more than two bands, designed by employing the Parks-McClellan algorithm, may exhibit an undesirable gain response in the transition band. In this paper, a practical FIR filter solution to such undesirable results is proposed, whereby a modified sampling kernel and the complementary filter concept are utilized. In particular, the proposed approach provides a closed-form design of type-1 linear-phase FIR filters satisfying the given filter specification.