Wavelets: Mathematics and applications

The notion of wavelets is defined. It is briefly described what wavelets are, 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 what specific features of signals (functions) can be revealed by this analysis, but cannot 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.