Which Wavelet Best Reproduces the Fourier Power Spectrum?
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 superposit...
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| Format: | Journal Article |
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Pergamon
2005
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| Online Access: | http://hdl.handle.net/20.500.11937/22577 |
| _version_ | 1848750909084925952 |
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| author | Kirby, Jonathan |
| author_facet | Kirby, Jonathan |
| author_sort | Kirby, Jonathan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T07:44:19Z |
| format | Journal Article |
| id | curtin-20.500.11937-22577 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:44:19Z |
| publishDate | 2005 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-225772019-02-19T05:35:00Z Which Wavelet Best Reproduces the Fourier Power Spectrum? Kirby, Jonathan Isotropic wavelets Continuous wavelet transform Fourier transform 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. 2005 Journal Article http://hdl.handle.net/20.500.11937/22577 10.1016/j.cageo.2005.01.014 Pergamon fulltext |
| spellingShingle | Isotropic wavelets Continuous wavelet transform Fourier transform Kirby, Jonathan Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title | Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title_full | Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title_fullStr | Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title_full_unstemmed | Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title_short | Which Wavelet Best Reproduces the Fourier Power Spectrum? |
| title_sort | which wavelet best reproduces the fourier power spectrum? |
| topic | Isotropic wavelets Continuous wavelet transform Fourier transform |
| url | http://hdl.handle.net/20.500.11937/22577 |