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Which Wavelet Best Reproduces the Fourier Power Spectrum?

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Authors
Kirby, Jonathan
Date
2005
Type
Journal Article

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Kirby, Jonathan. 2005. Which Wavelet Best Reproduces the Fourier Power Spectrum? Computers and Geosciences. 31 (7): pp. 846-864.
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Computers and Geosciences
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Department of Spatial Sciences
Faculty of Science and Engineering
WA School of Mines
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The link to the journal's home page is: "http://www.elsevier.com/wps/find/journaldescription.cws_home/622273/description#description" Copyright © 2005 Elsevier B.V. All rights reserved

NOTICE: this is the author’s version of a work that was accepted for publication in Computers and Geosciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Geosciences, [VOL31, ISSUE7, (2005)] http://dx.doi.org/10.1016/j.cageo.2005.01.014

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Abstract

The article compares the radially averaged Fourier power spectrum against the global wavelet power spectrum ('global scalogram') for seven continuous, two-dimensional wavelets: Derivative of Gaussian, Halo, Morlet, Paul, Perrier and Poisson wavelets, and a new wavelet based on a superposition of rotated Morlet wavelets, named the 'Fan' wavelet. This wavelet is complex, yet is able to give quasi-isotropic wavelet phase spectra. All seven wavelets were applied to synthetic and real data to test their ability to reproduce the Fourier spectrum: the Fan, Halo and Morlet wavelets reproduced this spectrum exactly; the Poisson wavelet performed very poorly. However, in tests of the space domain resolution of these wavelets with real and synthetic data, the Poisson wavelet gave by far the best results.