Name: On the regularity of wavelets
Creator: Hans Volkmer
Keywords: dilation equation, regularity index, Fourier transform, scaling functions, 0202 electrical engineering, electronic engineering, information engineering, Nontrigonometric harmonic analysis involving wavelets and other special systems, 02 engineering and technology, 0101 mathematics, wavelets, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1992Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Information Theory, volume 38, pages 872-876 (issn: 0018-9448, eissn: 1557-9654,

Authors: Hans Volkmer;

doi: 10.1109/18.119743

On the regularity of wavelets

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Abstract

Summary: The regularity index \(\alpha_ N\) of the scaling functions \(_ N\phi\), \(N=2,3,\dots\), of multiresolution analysis introduced by \textit{I. Daubechies} [Commun. Pure Appl. Math. 41, No. 7, 901-996 (1988; Zbl 0644.42026)] is investigated. It is shown that \(0.51<\alpha_ 2<0.53\) and \[ \lim_{N\to\infty}\alpha_ N/N=1-(\log 3)/(2 \log 2) \] .

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Keywords

dilation equation, regularity index, Fourier transform, scaling functions, Nontrigonometric harmonic analysis involving wavelets and other special systems, wavelets, multiresolution analysis

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