New natural selection process and chromosome encoding for the design of multiplierless lattice QMF using genetic algorithm

A new natural selection process and chromosome encoding for the design of signed power-of-two (SPT) coefficient lattice structure quadrature mirror filter (QMF) bank using a genetic algorithm (GA) is presented. In the design of filters using genetic algorithms, in general, genetic operations may render the SPT representation of a value noncanonical. In this paper, a new encoding scheme is introduced to encode the SPT values. In this new scheme, the canonical property of the SPT values is preserved under genetic operations. Additionally, a new feature which drastically improves the performance of the GA is introduced. The new feature is: the probability of mutation for each codon of a chromosome is weighted by the reciprocal of its effect. Owing to the new feature, the performance of our new GA outperforms conventional GA.