WAVELETS: MATHEMATICS AND APPLICATIONS 论文

摘要

The notion of wavelets is defined. It is briefly described what are wavelets, how to use them, when we do need them, why they are preferred and where they have been applied. Then one proceeds to the multiresolution analysis and fast wavelet transform as a standard procedure for dealing with discrete wavelets. It is shown which specific features of signals (functions) can be revealed by this analysis, but can not be found by other methods (e.g., by the Fourier expansion). Finally, some examples of practical application are given. Rigorous proofs of mathematical statements are omitted, and the reader is referred to the corresponding literature. 1