Wavelet spectra compared to Fourier spectra
- 1 March 1995
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 36 (3), 1506-1519
- https://doi.org/10.1063/1.531340
Abstract
The relation between Fourier spectra and spectra obtained from waveletanalysis is established. Small scale asymptotic analysis shows that the wavelet spectrum is meaningful only when the analyzingwavelet has enough vanishing moments. These results are related to regularity theorems in Besov spaces. For the analysis of infinitely regular signals, a new wavelet, with an infinite number of cancellations is proposed.Keywords
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