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

doi:10.1117/12.783086

25 April 2008 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

Author Affiliations +

Proceedings Volume 7000, Optical and Digital Image Processing; 70000D (2008) https://doi.org/10.1117/12.783086
Event: SPIE Photonics Europe, 2008, Strasbourg, France

Abstract

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.

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Peter Steffen and Wolfgang Brandhuber "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", Proc. SPIE 7000, Optical and Digital Image Processing, 70000D (25 April 2008); https://doi.org/10.1117/12.783086

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