Design of Two-channel Half-band Bank of Digital Filters using Optimization Methods

The paper deals with the optimization of the criterial function of a two-channel bank of digital filters with perfect reconstruction (PR) and with limiting conditions given by the required frequency processing of the input signal. The bank of digital filters has been derived from the basic low-pass filter with transfer function H0(z). This filter defines the initial impulse characteristic and, at the same time, determines the properties of the whole bank. The functionality and universality of the given approach of the optimum design are demonstrated on several typical examples. Genetic algorithms are used for the selection of correctly conditional initial optimization conditions. Two- and multi-channel banks of digital filters are used frequently, in particular in telecommunications in signal compression and its extraction from noise, in communication technology, in biomedicine, etc. These filter banks are often associated with the wavelet transform, which defines directly individual impulse characteristics of digital filters in the bank. Our approach is more general, with the optimization process being used to determine individual impulse characteristics of partial filters in the bank.