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JUCS
2006

Construction of Wavelets and Applications

13 years 3 months ago
Construction of Wavelets and Applications
: A sequence of increasing translation invariant subspaces can be defined by the Haar-system (or generally by wavelets). The orthogonal projection to the subspaces generates a decomposition (multiresolution) of a signal. Regarding the rate of convergence and the number of operations, this kind of decomposition is much more favorable then the conventional Fourier expansion. In this paper, starting from Haar-like systems we will introduce a new type of multiresolution. The transition to higher levels in this case, instead of dilation will be realized by a two-fold map. Starting from a convenient scaling function and two-fold map, we will introduce a large class of Haar-like systems. Besides others, the original Haar system and Haar-like systems of trigonometric polynomials, and rational functions can be constructed in this way. We will show that the restriction of Haar-like systems to an appropriate set can be identified by the original Haar-system. Haar-like rational functions are used ...
Ildikó László, Ferenc Schipp,
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JUCS
Authors Ildikó László, Ferenc Schipp, Samuel P. Kozaitis
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