Wavelet
Spectra compared to Fourier Spectra
Valerie Perrier,
Thierry Philipovitch and Claude Basdevant
The relation between Fourier spectra and spectra obtained from wavelet
analysis is established. Small scale asymptotic analysis shows that the
wavelet spectrum is meaningful only when the analysing wavelet has enough
vanishing moments. We relate these results to regularity theorems in Besov
spaces. For the analysis of infinitly regular signals, a new wavelet, with
infinit number of cancellations is proposed.
J. Math. Phys. 36(3), pp.1506-1519 (1995).
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