A Genetic Search Algorithm for Linear-Phase Filter Banks

Abstract

A genetic algorithm is presented for searching optimization parameters in the factorization matrices in linear-phase filter banks. The genetic algorithm is combined with the simplex algorithm to accelerate the design process. The newly algorithm alleviates the problem of being trapped in local minimums, as the initial parameters are selected by the genetic algorithm. Less human interactions are required in the design of filter banks, especially when impulse responses are long. The experimental results show that the proposed algorithm is robust in the optimization of the filter coefficients. Design results of filter banks with 8 channels are included. Introduction Filter banks have drawn increasing attentions lately in image processing and biomedical engineering [1]-[5]. Wavelets and filter banks have also been used in power systems in electrical engineering. A method of power quality disturbances hierarchical identification which combines conversion, wavelet transform energy distribution and fuzzy nearness was proposed in [6]. An implementation for analyzing real time current and voltage signal harmonics for non-linear loads using wavelet transform based on virtual instrument concept was demonstrated in [7]. In [8], an adaptive wavelet filter banks and neural network (AWNN) based technique for low-order dominant harmonics estimation was described. An extensive review of applications of wavelets and filter banks in the measurement and analysis of harmonic distortion in power systems was given in [9]. In this paper, the design of analysis and synthesis filters in filter banks with FIR responses and linear-phase property is revisited by using genetic algorithm. In the design of filter banks, the number of parameters increases with filter length and number ( M ) of channels. Local minimums hinder the optimization programs from searching further especially when the number of design parameters becomes very large. The proposed approach is efficient as it combines genetic search with simplex optimization to mitigate the problem of local minimums. The initial parameters of simplex optimization are selected by the genetic algorithm. The experimental results show the proposed algorithm converges fast, and less human interactions are required in the design process. Multirate Filter Banks Fig. 1 shows analysis/synthesis systems in a filter bank, where analysis and synthesis filters are denoted as ( ) k H z , 0 1 k M ≤ ≤ − and ( ) k F z , 0 1 k M ≤ ≤ − , respectively. The expression for the reconstructed signal ˆ ( ) X z is of the form [1].