Optimal design of CSD coefficient FIR filters subject to number of nonzero digits

Abstract

SUMMARYIn the hardware implementation of FIR (Finite Impulse Response) digital filters, it is desirable to reduce the total number of nonzero digits used for representation of the filter coefficients. In general, the design problem of FIR filters with CSD (Canonical Signed Digit) representation, which is efficient for reduction of the number of multiplier units, is often treated as a 0-1 combinational problem. In such problems, certain difficult constraints hinder linearization of the problem. Although many kinds of heuristic approaches have been used to solve the problem, the solutions obtained in such a manner cannot be guaranteed to be optimal. In this paper, we attempt to formulate the design problem as a 0-1 mixed integer linear programming problem and to solve it by using the branch and bound technique, which is a powerful method for solving integer programming problems. Several design examples are presented to illustrate the efficient performance of the proposed method.