A Partial MILP Algorithm for the Design of Linear Phase FIR Filters with SPT Coefficients

摘要

This article presents a three-step method for designing linear phase FIR filters with signed-powers-of-two (SPT) coefficients. In Step one, a prototype optimal FIR filter is designed by the Remez exchange algorithm. In Step two, a scaling factor is selected by employing simple ad-hoc rules. In Step three, each coefficient of the prototype filter is scaled by the scaling factor and is quantized coarsely as the canonic-signed-digit (CSD) representation. Then, a mixed-integer-linear-programming (MILP) algorithm is applied to three least significant digits (LSDs) of the filter's coefficients to reduce the number of SPT terms. Design examples demonstrate that the proposed algorithm is able to produce linear phase fixed-point FIR filters using fewer SPT terms than the existing methods under the same normalized peak ripple magnitude (NPRM) specification.