Design of CSD coefficient FIR filters based on branch and bound method

In this paper, we propose a novel method for a high-speed optimal design of FIR filters with CSD coefficients. The design problem can be formulated as a mixed integer programming problem and can be optimally solved using the branch-and-bound method. Then, in such a method, many feasible solutions with similar objective function values exist, and thus enormous subproblems are generated in the branch operation. It prevents us from fast design of filters. Therefore, it is effective to limit a feasible region in advance. In the proposed method, an approximation solution obtained by the other optimization method is used to omit unnecessary subproblems from the branch operation. That is, the branch-and-bound method is begun with the branch tree constructed based on the approximation solution. As a result, a significant reduction of subproblems can be expected. Several design examples are shown to present an effectiveness of the proposed method.