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Continuous Wavelet Transform with Arbitrary Scales and O(N) Complexity

A. Muñoz Barrutia, R. Ertlé, M. Unser

Signal Processing, vol 82, no. 5, pp. 749-757, May 2002.


Summary

The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that the computational cost is independent of the scale value. Its complexity is of the same order as that of the fastest published methods, without being restricted to dyadic or integer scales. The method reduces to the filtering of an auxiliary (pre-integrated) signal with an expanded mask that acts as a kind of modified ‘à trous’ filter.The algorithm is well-suited for a parallel implementation.

Résumé

La transformée continue en ondelettes (Continuous Wavelet Transform, CWT) est un outil de traitement de signal que l'on utilise volontiers pour analyser des signaux non-stationnaires. Nous proposons ici une nouvelle méthode de calcul de CWT, basée sur les B-splines, valide à toute échelle. Une propriété intéressante de l'algorithme est que son coût de calcul est indépendant de l'échelle. Son ordre de complexité est identique à celui des méthodes les plus rapides de la littérature, sans restriction à des échelles entières ou dyadiques. La méthode se résume à filtrer un signal auxiliaire (préalablement intégré) par un masque étendu, qui agit à la façon d'un filtre ‘à trous’ modifié. L'algorithme se prête facilement à une implémentation parallèle.

Zusammenfassung

Auf dem Gebiet der Signalverarbeitung ist die stetige Wavelet Transformation (CWT) eine weit verbreitete Methode zur Analyse nicht stationärer Signale. Wir schlagen eine B-spline basierte Methode vor, die die Berechnung der CWT auf einer beliebigen Skala ermöglicht. Ein Vorteil dieser Methode besteht darin, daß der Aufwand für die Berechnung unabhängig von der Skala ist. Der Berechnungsaufwand ist von gleicher Ordnung wie derjenige der schnellsten Methoden, die bisher veröffentlicht wurden. Die Methode ist nicht beschränkt auf dyadische oder ganzzahlige Skalen. Die Berechnungsmethode entspricht der Filterung eines vorher integrierten Hilfssignals mit einer erweiterten Maske, die als eine Art ‘à trous’ Filter dient. Der Algorithmus eignet sich sehr gut für eine parallel Implementation.

@ARTICLE(http://bigwww.epfl.ch/publications/munoz0202.html,
AUTHOR="Mu{\~{n}}oz Barrutia, A. and Ertl{\'{e}}, R. and Unser, M.",
TITLE="Continuous Wavelet Transform with Arbitrary Scales and
	{$\mathcal{O}(N)$} Complexity",
JOURNAL="Signal Processing",
YEAR="2002",
volume="82",
number="5",
pages="749--757",
month="May",
note="")

© 2002 Elsevier. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Elsevier. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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