ISSN:
1572-9044
Keywords:
Analytic wavelet
;
non-stationary wavelet
;
radial function
;
shift-invariant space
;
time-frequency window
;
Littlewood-Paley identity
;
41A15
;
41A30
;
42C15
;
65D15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of “projection”, such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of ℝ s is large. Thus projecting a functionf onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02124736
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