文章基本信息

标题：Construction of Wavelets and Applications
作者：Ildikó László ; Ferenc Schipp ; Samuel P. Kozaitis 等
期刊名称：Journal of Universal Computer Science
印刷版ISSN：0948-6968
出版年度：2006
卷号：12
期号：9
页码：1278-1291
出版社：Graz University of Technology and Know-Center
摘要：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 for the approximation of rational transfer functions which play an important role in signal processing [Bokor1 1998, Schipp01 2003, Bokor3 2003, Schipp 2002].