Banco de filtros Wavelets com fator de escala maior que dois

Abstract

The traditional wavelet analysis is equivalent to a filter bank, formed by a low-pass and a high-pass filter, in which the frequency resolution changes by one octave between two subsequent stages. In some applications, mainly in the one that inspired this work, i.e. modeling of the peripheral human auditory system, the frequency resolution of one octave is fairly poor (in human audition the frequency resolution is approximately of 1/3 of an octave) to attain a good representation of auditory phenomena. In the present work, it was chosen to particionate the subspaces using a scale factor greater then two and more than one wavelet, so that it is possible to achieve a better frequency resolution for certain bands. This change in the scale factor leads to the need to design new wavelets suited to the scale factor in use. In order to achieve this objective, a generalization of the wavelet construction proposed by Ingrid Daubechies, adapted to the situation in which the scale factor is not two anymore, is carried out. The results achieved show how to design the scale function and determine a property that the filter bank coefficients must satisfy in order to obtain a perfect reconstruction analysis filter bank. It is shown analytically and numerically that certain results achieved are indeed solutions. Nevertheless, it is still necessary to determine how to design the wavelet functions satisfying the imposed restriction and using the scale function desired.