A novel genetic algorithm for the design of a signed power-of-two coefficient quadrature mirror filter lattice filter bank.
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.
scientific article; zbMATH DE number 1885799