A hybrid genetic algorithm for the design of FIR filters with SPoT coefficients

Abstract

An efficient way to reduce complexities and power in the implementation of digital finite impulse response (FIR) filters is to design the filters with coefficients restricted to the sum of signed powers-of-two (SPoT) terms. The design of SPoT-based FIR filters can be formulated as a non-linear optimization problem. Premature convergence and unacceptable computational cost are the major difficulties when conventional optimization algorithms are utilized in SpoT-based FIR filter design. To address the problem, a hybrid genetic algorithm (GST) is proposed in this paper. The hybrid scheme is formed by integrating the main features of an adaptive genetic algorithm (AGA), simulated annealing (SA) and tabu search algorithms. AGA with varying population size and varying probabilities of genetic operations is used as the basis of the hybrid algorithm. SA comes to the picture when it is indicated that AGA may get stuck in a local optimum. The use of SA is to help AGA escape from local optima and prevent premature convergence. The concept of tabu is introduced to increase convergence speed by reducing search space according to the properties of filters coefficients. It is shown by means of examples that the normalized peak ripples of filters can be largely reduced with the help of the proposed algorithm. Compared with other genetic algorithm, GST achieves not only the improved solution quality but also the considerable reduction of computational effort.