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Uspekhi Fizicheskikh Nauk, 2001, Volume 171, Number 5, Pages 465–501
DOI: https://doi.org/10.3367/UFNr.0171.200105a.0465
(Mi ufn1876)
 

This article is cited in 240 scientific papers (total in 240 papers)

REVIEWS OF TOPICAL PROBLEMS

Wavelets and their uses

I. M. Dremin, O. V. Ivanov, V. A. Nechitailo

P. N. Lebedev Physical Institute, Russian Academy of Sciences
References:
Abstract: This review paper is intended to give a useful guide for those who want to apply the discrete wavelet transform in practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to the corresponding literature. The multiresolution analysis and fast wavelet transform have become a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for the achievement of a goal. Analysis of various functions with the help of wavelets allows one to reveal fractal structures, singularities etc. The wavelet transform of operator expressions helps solve some equations. In practical applications one often deals with the discretized functions, and the problem of stability of the wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves to a few examples only. The authors would be grateful for any comments which would move us closer to the goal proclaimed in the first phrase of the abstract.
Received: December 13, 2000
English version:
Physics–Uspekhi, 2001, Volume 44, Issue 5, Pages 447–478
DOI: https://doi.org/10.1070/PU2001v044n05ABEH000918
Bibliographic databases:
Document Type: Article
PACS: 02.60.-x, 02.70.-c, 05.40.-a, 87.57.-s
Language: Russian


Citation: I. M. Dremin, O. V. Ivanov, V. A. Nechitailo, “Wavelets and their uses”, UFN, 171:5 (2001), 465–501; Phys. Usp., 44:5 (2001), 447–478
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  • This publication is cited in the following 240 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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