Design of FIR filters based on interval analysis

The paper describes optimization technique based on the interval analysis and its application in filter design. In particular, it considers the design of linear-phase FIR filters whose coefficients can be expressed as sums of powers of two (SPT). The optimization based on the interval analysis is attractive because it results in global solution. It is originally developed for optimizing functions of continuous variables. On the other hand, the design of filters with SPT coefficients is an integer-programming problem. Therefore, the basic optimization algorithm is modified to deal with the discrete variable space. The convergence rate of the proposed algorithm is analyzed for various filter complexities. Furthermore, the design of a decimation filter for low-delay software radio receivers is described.