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Uspekhi Fizicheskikh Nauk, 2007, Volume 177, Number 8, Pages 859–876
DOI: https://doi.org/10.3367/UFNr.0177.200708d.0859 (Mi ufn503) 		 
This article is cited in 119 scientific papers (total in 119 papers)

METHODOLOGICAL NOTES

Multifractal analysis of complex signals

A. N. Pavlov, V. S. Anishchenko

International Research Institute of Nonlinear Dynamics, N. G. Chernyshevskii Saratov State University
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DOI: https://doi.org/10.3367/UFNr.0177.200708d.0859
Abstract: This paper presents the foundations of the continuous wavelet-transform-based multifractal analysis theory and the information necessary for its practical application. It explains generalizations of a multifractal concept to irregular functions, better known as the method of wavelet transform modulus maxima; it investigates the benefits and limitations of this technique in the analysis of complex signals; and it discusses the efficiency of the multifractal formalism in the investigation of nonstationary processes and short signals. The paper also considers the effects of the loss of multifractality in the dynamics of various systems.
Received: May 3, 2006
Revised: March 25, 2007
English version:
Physics–Uspekhi, 2007, Volume 50, Issue 8, Pages 819–834
DOI: https://doi.org/10.1070/PU2007v050n08ABEH006116
Bibliographic databases:
Document Type: Article
PACS: 05.45.-a, 05.45.Pq, 05.45.Tp
Language: Russian
Citation: A. N. Pavlov, V. S. Anishchenko, “Multifractal analysis of complex signals”, UFN, 177:8 (2007), 859–876; Phys. Usp., 50:8 (2007), 819–834
Citation in format AMSBIB
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    • This publication is cited in the following 119 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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