Which Wavelet Best Reproduces the Fourier Power Spectrum?
MetadataShow full item record
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.
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
Showing items related by title, author, creator and subject.
Power spectral estimates using two-dimensional Morlet-fan wavelets with emphasis on the long wavelengths: jackknife errors, bandwidth resolution and orthogonality propertiesKirby, Jonathan; Swain, Christopher (2013)We present a method for estimating the errors on local and global wavelet power spectra using the jackknife approach to error estimation, and compare results with jackknifed multitaper (MT) spectrum estimates. We test the ...
Trott, Cathryn (2016)The Cosmic Dawn and Epoch of Reionization, during which collapsed structures produce the first ionizing photons and proceed to reionize the intergalactic medium, span a large range in redshift (z ~ 30-6) and time (tage ~ ...
The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling DataSoltanpour, A.; Nahavandchi, H.; Featherstone, Will (2006)The merging of a gravimetric quasigeoid model with GPS-levelling data using second-generation wavelets is considered so as to provide better transformation of GPS ellipsoidal heights to normal heights. Since GPS-levelling ...