Optimal Design of CSD Coefficient FIR Filters Subject to Number of Nonzero Digits

Abstract

In a hardware implementation of FIR(Finite Impulse Response) digital filters, it is desired to reduce a total number of nonzero digits used for a representation of filter coefficients. In general, a design problem of FIR filters with CSD(Canonic Signed Digit) representation, which is efficient one for the reduction of numbers of multiplier units, is often considered as one of the 0-1 combinational problems. In such the problem, some difficult constraints make us prevent to linearize the problem. Although many kinds of heuristic approaches have been applied to solve the problem, the solution obtained by such a manner could not guarantee its optimality. In this paper, we attempt to formulate the design problem as the 0-1 mixed integer linear programming problem and solve it by using the branch and bound technique, which is a powerful method for solving integer programming problem. Several design examples are shown to present an efficient performance of the proposed method.