A Hilbert-Space Approach to the Complete Investigation ofVaidyanathan's Procedure Applied to the Design of Unitary Filterbanks for the Generation of Orthogonal Wavelet Bases

摘要

The decomposition of signals using the classical Daubechies wavelets can equivalently be described as a decom-position using a two channel filterbank with the scaling function corresponding to the low pass arid the motherwavelet to the high pass channel. This classical two channel approach was extended to also comprise filterbanks with more than two chan-nels, corresponding to one scaling function and two or more mother wavelets.' Although these newly foundwavelets fitted in very well with the theory of the existing Daubechies wavelets, the frequency selectivity of thecorresponding filterbank was in general not satisfying. We presented a new method to improve the selectivity of the corresponding filterbank by introducing addi-tional elementary building blocks in the design process, leaving the low pass filter and the polynomial degree ofthe impulse responses of the other filters of the filterbank untouched. In this paper we take the new method one step further and not only show how the improvement could beachieved but also what possibilities there are to modify the design and what patterns they adhere to. Furthermorewe introduce a figure of merit of the total filterbank and its individual filters and show the improvements to thedesign process.