Fast FIR digital filter structures using minimal number of adders and its application to filter design

This paper proposes fast FIR digital filter structures using the minimal number of adders. Filter coefficients are expressed with canonic signed digit (CSD) code and Hartley's technique is used to minimize the number of adders and subtractors. The proposed filters implemented as wired logic are fast because the structure having the shortest critical path is selected. Two algorithms are given to obtain such fast structures. In many examples the critical path length of the filter structures obtained using the proposed method is equal to that of the conventional CSD structures. This paper also presents a new design method of FIR filters using the mixed integer programming (MILP). Utilization of common expressions in Hartley's technique widens the CSD coefficient space. Thus the MILP may lead to better frequency responses. Superior frequency responses are actually obtained in many simulations.