A Unified Approach to the Design of Interpolated and Frequency-Response-Masking FIR Filters

We present a unified approach to the design of two well-known classes of computationally efficient digital filters, namely the interpolated and frequency-response-masking (FRM) FIR filters, that are optimized in minimax sense. The highly nonconvex minimax designs of these filters are carried out by jointly optimizing the subfilters involved using a convex-concave procedure (CCP) that yields an iterative and converging process where each iteration involves a convex problem of minimizing a linear function subject to convex quadratic constraints. We present an analysis to explain why CCP is well-suited for the design problems at hand. We also show that the CCP-based design framework is flexible to allow extension to the design of FRM filters that simultaneously promotes sparsity of the filter coefficients to reduce implementation complexity. Design examples with comparisons are presented to demonstrate the performance of the proposed design methods.