вейвлеты

Necessary and Sufficient Condition for an Orthogonal Scaling Function on Vilenkin Groups

Authors: Berdnikov G. S.

There are several approaches to the problem of construction of an orthogonal MRA on Vilenkin groups, but all of them are reduced to the search of the so-called scaling function. In 2005 Yu. Farkov used the so-called “blocked sets” in order to find all possible band-limited scaling functions with compact support for each set of certain parameters and his conditions are necessary and sufficient. S. F. Lukomskii, Iu. S. Kruss and G. S.

On Applications of Wavelets in Digital Signal Processing

Authors: Rodionov E. A.

Discrete Wavelet transform associated with the Walsh functions was defined by Lang in 1998. The article describes an application of Lang’s transform and some its modifications in analysis of financial time series and for the compression of fractal data. It is shown that for the processing of certain signals the studied discrete wavelet transform has advantages over the discrete transforms Haar, Daubechies and the method of zone coding.