Optimal design method for FIR filter with discrete coefficients based on integer semi-infinite linear programs

The purpose of the paper is to propose a new design method of FIR filters with discrete coefficients considering optimality. In the proposed method, the design problem of FIR filters is formulated as a mixed integer semi-infinite linear programming problem (MISILP), which can be solved by a branch and bound technique. Then, it is possible to obtain the optimal discrete coefficients, and the optimality of the obtained solution can be guaranteed. It was confirmed that optimal coefficients of a linear phase FIR filter with discrete coefficients could be designed in reasonable computational time with sufficient precision based on the results of computational experiments.