A Hilbert-space approach to the complete investigation of Vaidyanathan's procedure applied to the design of unitary filterbanks for the generation of orthogonal wavelet bases
Peter Steffen, Wolfgang Brandhuber · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
The decomposition of signals using the classical Daubechies wavelets can equivalently be described as a decomposition using a two channel filterbank with the scaling function corresponding to the low pass and the mother wavelet to the high pass channel. This classical two channel approach was extended to also comprise filterbanks with more than two channels, corresponding to one scaling function and two or more mother wavelets.1 Although these newly found wavelets fitted in very well with the theory of the existing Daubechies wavelets, the frequency selectivity of the corresponding filterbank was in general not satisfying. We presented a new method2 to improve the selectivity of the corresponding filterbank by introducing additional elementary building blocks in the design process, leaving the low pass filter and the polynomial degree of the 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 be achieved but also what possibilities there are to modify the design and what patterns they adhere to. Furthermore we introduce a figure of merit of the total filterbank and its individual filters and show the improvements to the design process.