Wavelet spectra compared to Fourier spectra
Valérie Perrier, Thierry Philipovitch, Claude Basdevant · Journal of Mathematical Physics · 1995
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 analyzing wavelet 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.