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 ...

• Type: Journal
• Year: 2006
• Where: JUCS
• Authors: Ildikó László, Ferenc Schipp, Samuel P. Kozaitis
• Keywords: Haar-like Systems, JUCS 2006, Translation Invariant Subspaces, Two-fold Map