Design of discrete coefficient FIR and IIR digital filters with prefilter-equalizer structure using linear programming

Abstract

Optimal methods for designing multiplierless finite-impulse response (FIR) and infinite-impulse response (IIR) filters with cascaded prefilter-equalizer structures are proposed. Assuming that an FIR filter consists of a cyclotomic polynomial (CP) prefilter and an interpolated second order polynomial (ISOP) equalizer, in the proposed method, the prefilter and equalizer are simultaneously designed using mixed integer linear programming (MILP). The resulting filter is a cascaded filter with minimal complexity. For IIR filters, all-pole IIR equalizers consisting of inverse of interpolated first order polynomials (IIFOP's) are introduced, and a CP-prefilter cascaded with this type of equalizer is designed. Design examples demonstrate that the proposed methods produce a more efficient cascaded prefilter-equalizer than existing methods.