A novel genetic algorithm for the design of a signed power-of-two coefficient quadrature mirror filter lattice filter bank.
type: Item
instance of: scholarly article
title: A novel genetic algorithm for the design of a signed power-of-two coefficient quadrature mirror filter lattice filter bank.
zbMATH Open document ID: 1042.93059
author: Yong Ching Lim
author: Ya Jun Yu
published in: Circuits, Systems, and Signal Processing
publication date: 2003-06-23T00:00:00Z
review text: Quadrature mirror filters (QMF) are used widely in speech and image signal processing. Its subclass denoted by perfect reconstruction (PRQMF) is of particular importance. A well-known realization is the so-called lattice PRQFM. The principal merit of this last subclass lies in the fact that its PR property is preseved under a severe coefficient quantization. Owing to this property a design method for finding the coefficients in the signed power two (SPT) space was introduced. The feature of this method is the fact that the representation of a number \(J\) reads as follows: \[ J=\sum^{L-1}_{i=-S} s(i)2^i,\;s(i)=\{-1,0,1\}, \;-S\leq L-1, \] whence the denomination multiplication free (MF). Such a representation is said to be canonical if \(s(i)s(i+1)=0\), \(\forall i\). Several design techniques were found to obtain the optimum quantized. It is worth pointing out that the design method with SPTMF is algorithmic, i.e. step by step, i.e. there is no closed formula giving the optimum. In the last years, genetic algorithms (GA) were asked to perform the SPTMF of LPRQMF. The present paper brings some important contributions to the formulated task. First, the standard GA was modified so that the standard representation SPTMF be preserved at each step. Secondly, new stages were introduced in the GA so that the new design provides better results that those given when using standard GA. We think the present paper brings a remarkable contribution in the area of filter design using GA.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 68T05
zbMATH DE Number: 1885799
zbMATH Keywords: adaptive filtering
zbMATH Keywords: learning
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
full work available at URL: s00034-004-7043-z
OpenAlex ID: W1992781220
DOI: 10.1007/S00034-004-7043-Z
description: scientific article; zbMATH DE number 1885799