Cancelled: A High-Efficiency FIR Filter Design Combining Cyclic-Shift Synthesis with Evolutionary Optimization

Abstract

To optimize the performance of FIR filters that have low computation complexity , this paper proposes a hybrid design consisting of two optimization levels. The first optimization level is based on cyclic-shift synthesis , in which all possible sub filters (or windowed sub filters) with distinct cycle shifts are averaged to generate a synthesized filter. Due to the fact that the ripples of these sub filters' transfer curves can be individually compensated, this synthesized filter attains improved performance (besides two uprushes occur on the edges of a transition band) and thus this synthesis actually plays the role of ‘natural optimization’. Furthermore, this synthesis process can be equivalently summarized into a 3-step closed-form procedure, which converts the multi-variable optimization into a single-variable optimization. Hence, to suppress the uprushes, what the second optimization level (by Differential Evolution (DE) algorithm) needs to do is no more than searching for the optimum transition point which incurs only minimal complexity . Owning to the combination between the cyclic-shift synthesis and DE algorithm, unlike the regular evolutionary computing schemes, our hybrid design is more attractive due to its narrowed search space and higher convergence speed . Numerical results also show that the proposed design is superior to the conventional DE design in both filter performance and design efficiency, and it is comparable to the Remez design.