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Design of composite filters with equiripple passbands and least-squares stopbands

We study a class of composite 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 problem of designing a C-filter with equiripple passband and least-squares stopband subject to peak stopband gain is formulated and an algorithm for designing such a class of linear-phase FIR C-filters is proposed. The algorithm is based on an alternating convex 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 example is presented to illustrate the algorithm and demonstrate the performance of the C-filter relative to its conventional FIR counterparts.