research-article

Parametrization of compactly supported orthonormal wavelets

Authors:

H. Zou,

A.H. TewfikAuthors Info & Claims

IEEE Transactions on Signal Processing, Volume 41, Issue 3

Pages 1428 - 1431

https://doi.org/10.1109/78.205749

Published: 01 March 1993 Publication History

Abstract

The parametrization of two-channel reconstruction quadrature mirror filter banks is extended to obtain a single characterization of discrete orthonormal wavelets. In particular, it is shown that discrete orthonormal wavelets of support less than 2 N -1, where N is an even integer, are parametrized by N -1 real parameters, each taking values in (0, 2ý). A parametrization of discrete orthonormal wavelets with a number of vanishing moments greater than one is also given

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Singhai PKumar AAteek AAnsari ISingh GLee H(2023)ECG Signal Compression Based on Optimization of Wavelet Parameters and Threshold Levels Using Evolutionary TechniquesCircuits, Systems, and Signal Processing10.1007/s00034-022-02280-442:6(3509-3537)Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s00034-022-02280-4
Herrera-Alcántara OGonzález-Mendoza M(2018)Inverse formulas of parameterized orthogonal waveletsComputing10.1007/s00607-018-0585-x100:7(715-739)Online publication date: 1-Jul-2018
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Hämmerle-Uhl JPschernig EUhl APuech WChaumont MDittmann JCampisi P(2013)Non-invertible and revocable iris templates using key-dependent wavelet transformsProceedings of the first ACM workshop on Information hiding and multimedia security10.1145/2482513.2482532(105-110)Online publication date: 17-Jun-2013
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A characterization of compactly supported orthonormal wavelets
Abstract
In order to construct a compactly supported wavelet family inL ₂ with the help of the so-called (N stage) dilation equation, one has to impose some well-known constraints on its coefficients. To make the family an orthonormal basis ofL ₂, an ...

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cover image IEEE Transactions on Signal Processing

IEEE Transactions on Signal Processing Volume 41, Issue 3

March 1993

482 pages

ISSN:1053-587X

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IEEE Press

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Published: 01 March 1993

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Singhai PKumar AAteek AAnsari ISingh GLee H(2023)ECG Signal Compression Based on Optimization of Wavelet Parameters and Threshold Levels Using Evolutionary TechniquesCircuits, Systems, and Signal Processing10.1007/s00034-022-02280-442:6(3509-3537)Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s00034-022-02280-4
Herrera-Alcántara OGonzález-Mendoza M(2018)Inverse formulas of parameterized orthogonal waveletsComputing10.1007/s00607-018-0585-x100:7(715-739)Online publication date: 1-Jul-2018
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Hämmerle-Uhl JPschernig EUhl APuech WChaumont MDittmann JCampisi P(2013)Non-invertible and revocable iris templates using key-dependent wavelet transformsProceedings of the first ACM workshop on Information hiding and multimedia security10.1145/2482513.2482532(105-110)Online publication date: 17-Jun-2013
https://dl.acm.org/doi/10.1145/2482513.2482532
Abo-Zahhad MAl-Ajlouni AAhmed SSchilling R(2013)A new algorithm for the compression of ECG signals based on mother wavelet parameterization and best-threshold levels selectionDigital Signal Processing10.1016/j.dsp.2012.11.00523:3(1002-1011)Online publication date: 1-May-2013
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Herrera Alcántara OGonzález Mendoza M(2011)Optimization of parameterized compactly supported orthogonal wavelets for data compressionProceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II10.1007/978-3-642-25330-0_45(510-521)Online publication date: 26-Nov-2011
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Alcántara O(2010)On the best evolutionary wavelet based filter to compress a specific signalProceedings of the 9th Mexican international conference on Artificial intelligence conference on Advances in soft computing: Part II10.5555/1927099.1927138(394-405)Online publication date: 8-Nov-2010
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Brachtl MUhl ADietl WDittmann JFridrich J(2004)Key-dependency for a wavelet-based blind watermarking algorithmProceedings of the 2004 workshop on Multimedia and security10.1145/1022431.1022462(175-179)Online publication date: 20-Sep-2004
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Shark LYu C(2003)Design of optimal shift-invariant orthonormal wavelet filter banks via genetic algorithmSignal Processing10.1016/j.sigpro.2003.07.00183:12(2579-2591)Online publication date: 1-Dec-2003
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Dietl WMeerwald PUhl A(2003)Protection of wavelet-based watermarking systems using filter parametrizationSignal Processing10.1016/S0165-1684(03)00170-183:10(2095-2116)Online publication date: 1-Oct-2003
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Strauss DSteidl G(2002)Hybrid wavelet-support vector classification of waveformsJournal of Computational and Applied Mathematics10.1016/S0377-0427(02)00557-5148:2(375-400)Online publication date: 15-Nov-2002
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Construction of Biorthogonal Compactly Supported Vector-Valued Wavelets

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