A Novel Genetic Algorithm for the Design of a Signed Power-of-Two Coefficient Quadrature Mirror Filter Lattice Filter Bank

Abstract

A novel genetic algorithm (GA) for the design of a canonical signed power-of-two (SPT) coefficient lattice structure quadrature mirror filter bank is presented in this paper. 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, two new features that drastically improve the performance of our GA are introduced. (1) An additional level of natural selection is introduced to simulate the effect of natural selection when sperm cells compete to fertilize an ovule; this dramatically improves the offspring survival rate. A conventional GA is analogous to intracytoplasmic sperm injection and has an extremely low offspring survival rate, resulting in very slow convergence. (2) The probability of mutation for each codon of a chromosome is weighted by the reciprocal of its effect. Because of these new features, the performance of our new GA outperforms conventional GAs.