×

Wavelet spectra compared to Fourier spectra. (English) Zbl 0833.42020

Authors’ abstract: “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”.
Reviewer: K.Seip (Trondheim)

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] DOI: 10.1137/0515056 · Zbl 0578.42007 · doi:10.1137/0515056
[2] DOI: 10.1017/S0022112091003786 · Zbl 0749.76033 · doi:10.1017/S0022112091003786
[3] DOI: 10.1146/annurev.fl.24.010192.002143 · doi:10.1146/annurev.fl.24.010192.002143
[4] DOI: 10.1016/0167-2789(94)90263-1 · Zbl 1194.76081 · doi:10.1016/0167-2789(94)90263-1
[5] DOI: 10.1007/BF01232261 · Zbl 0741.26004 · doi:10.1007/BF01232261
[6] Jaffard S., C. R. Acad. Sci. Paris, Série I 308 pp 79– (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.