Optimal design of FIR filter with SP2 coefficients based on semi-infinite linear programming method

In this paper, we propose a new design method of FIR filters with Signed Power of Two (SP2) coefficients. In the method proposed here, the design problem of FIR filters is formulated as a discrete semi-infinite linear programming problem (DSILP), and the DSILP is solved using a branch and bound technique. We will guarantee the optimality of the solution obtained. Hence, it is possible to obtain the optimal discrete coefficients. It is confirmed that the optimal coefficients of linear phase FIR filter with the SP2 coefficients could be designed fast with enough precisions by the computational experiments.