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On convergence of wavelet packet expansions

โœ Scribed by Morten Nielsen


Publisher
Springer
Year
2002
Tongue
English
Weight
659 KB
Volume
18
Category
Article
ISSN
1573-8175

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๐Ÿ“œ SIMILAR VOLUMES


Walsh-Type Wavelet Packet Expansions
โœ Morten Nielsen ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 168 KB

We consider a family of basic nonstationary wavelet packets generated using the Haar filters except for a finite number of scales where we allow the use of arbitrary filters. Such a system, which we call a system of Walsh-type wavelet packets, can be considered as a smooth generalization of the Wals

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The expansion of a distribution or function in regular orthogonal wavelets is considered. The expansion of a function is shown to converge uniformly on compact subsets of intervals of continuity. The expansion of a distribution is shown to converge pointwise to the value of the distribution where it

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We consider the approximation of a fractional Brownian motion by a wavelet series expansion at resolution 2 -l . The approximation error is measured in the integrated mean squared sense over finite intervals and we obtain its expansion as a sum of terms with increasing rates of convergence. The depe

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โœ Morten Nielsen; Ding-Xuan Zhou ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 155 KB

We study the mean size of wavelet packets in L p . An exact formula for the mean size is given in terms of the p-norm joint spectral radius. This will be a corollary of an asymptotic formula for the L p norms on the subdivision trees. Then the stability and Schauder basis property of wavelet packets

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It is shown that a Gibbs phenomenon occurs in the wavelet expansion of a function with a jump discontinuity at 0 for a wide class of wavelets. Additional results are provided on the asymptotic behavior of the Gibbs splines and on methods to remove the Gibbs phenomenon.