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.

PACS: 05.45.−a, 05.45.Pq, 05.45.Tp (all) DOI: 10.1070/PU2007v050n08ABEH006116 URL: https://ufn.ru/en/articles/2007/8/c/ 000251514700003 2-s2.0-37049001827 2007PhyU...50..819P Citation: Pavlov A N, Anishchenko V S "Multifractal analysis of complex signals" Phys. Usp. 50 819–834 (2007) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI Multifractal analysis of complex signals AU Pavlov A N FAU Pavlov AN AU Anishchenko V S FAU Anishchenko VS DP 10 Aug, 2007 TA Phys. Usp. VI 50 IP 8 PG 819-834 RX 10.1070/PU2007v050n08ABEH006116 URL https://ufn.ru/en/articles/2007/8/c/ SO Phys. Usp. 2007 Aug 10;50(8):819-834 Оригинал: Павлов А Н, Анищенко В С «Мультифрактальный анализ сложных сигналов» УФН 177 859–876 (2007); DOI: 10.3367/UFNr.0177.200708d.0859