Design of Least-Squares and Minimax Composite Filters

Abstract

We study a class of composite FIR filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problems of designing C-filters that are optimal in least-squares, equiripple passband and lease-squares stopband, and minimax sense are formulated, and three algorithms for designing such linear-phase FIR C-filters are proposed. The algorithms are based on an alternating optimization strategy in that the prototype and shaping filters are optimized in separate steps, which are coupled and carried out in a sequential manner to yield a satisfactory design. Design examples are presented to illustrate the algorithms and demonstrate the performance of the C-filters relative to their conventional FIR counterparts.