RSS feeds
ÐóññêèéEnglish
Issue 2, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2007

 / 

August

←  →

Methodological notes


Multifractal analysis of complex signals

,
International Research Institute of Nonlinear Dynamics, Department of Physics, N.G. Chernyshevskii; Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russian Federation

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.

Fulltext pdf (552 KB)
Fulltext is also available at DOI: 10.1070/PU2007v050n08ABEH006116
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

Îðèãèíàë: Ïàâëîâ À Í, Àíèùåíêî Â Ñ «Ìóëüòèôðàêòàëüíûé àíàëèç ñëîæíûõ ñèãíàëîâ» ÓÔÍ 177 859–876 (2007); DOI: 10.3367/UFNr.0177.200708d.0859

References (77) Cited by (106) ↓ Similar articles (16)

  1. Tadić B Phys. Rev. B 113 (10) (2026)
  2. Akhmetkhanov R S J. Mach. Manuf. Reliab. 54 (8) 916 (2025)
  3. Tadić B, Dankulov M M, Melnik R Chaos, Solitons & Fractals 201 117261 (2025)
  4. Mijatović S, Spasojević D et al CMES 142 (2) 1021 (2025)
  5. Akhmetkhanov R S Inorg Mater 60 (4) 502 (2024)
  6. Tadić B, Shapoval A, Shnirman M Phys. Rev. E 110 (5) (2024)
  7. Kumar V, Wasnik Sh, Sarangi S Nonlinear Dyn 112 (18) 15771 (2024)
  8. Akhmetkhanov R S Zavod. Lab., Diagn. Mater. 90 (3) 62 (2024)
  9. BÜYÜKTAŞ SELİN, KARAÇOR DENİZ Fractals 32 (05) (2024)
  10. Liu K, Zhang Zh et al Geoenergy Science And Engineering 239 212978 (2024)
  11. Meshalkin V P, Butusov O B i dr Teoretičeskie Osnovy Himičeskoj Tehnologii 57 (3) 284 (2023)
  12. Tadić B, Mitrović D M, Melnik R Chaos, Solitons & Fractals 171 113459 (2023)
  13. Sahoo S, Tadić B et al Phys. Rev. E 108 (3) (2023)
  14. Meshalkin V P, Butusov O B et al Theor Found Chem Eng 57 (3) 265 (2023)
  15. Dubnov Yu A, Popkov A Yu, Darkhovsky B S Autom Remote Control 84 (4) 337 (2023)
  16. Mitrović D M, Tadić B, Melnik R Dynamics 3 (4) 764 (2023)
  17. Miśkiewicz Ja, Burdach Z et al Membranes 13 (4) 406 (2023)
  18. Dick O E Neurosci Behav Physi (2023)
  19. Dick O E Biofizika 68 (1) 179 (2023) [Dick O E BIOPHYSICS 68 (1) 146 (2023)]
  20. Makarevich N A Polym. Sci. Ser. A 64 (2) 128 (2022)
  21. Mijatović S, Graovac S et al Physica E: Low-dimensional Systems And Nanostructures 142 115319 (2022)
  22. Saha P, Sarkar D Biosystems 218 104711 (2022)
  23. Frick P G, Sokoloff D D, Stepanov R A Phys.-Usp. 65 (1) 62 (2022)
  24. Tadić B Dynamics 2 (4) 449 (2022)
  25. Lyubushin A Front. Earth Sci. 10 (2022)
  26. Tadić B, Chutani M, Gupte N Chaos, Solitons & Fractals 160 112201 (2022)
  27. Darkhovsky B S Matematicheskie Zametki 111 (4) 620 (2022)
  28. Dmitriev A, Lebedev A et al Complexity 2022 (1) (2022)
  29. Darkhovsky B S Math Notes 111 (3-4) 628 (2022)
  30. Akhmetkhanov R S J. Mach. Manuf. Reliab. 51 (8) 845 (2022)
  31. Runnova A, Selskii A et al Chaos: An Interdisciplinary Journal of Nonlinear Science 31 (9) (2021)
  32. Dik O E BIOPHYSICS 66 (3) 508 (2021)
  33. Akhmetkhanov R S, Shul’zhenko A A J. Mach. Manuf. Reliab. 50 (4) 370 (2021)
  34. Piryatinska A, Darkhovsky B Entropy 23 (12) 1626 (2021)
  35. Kovalchuk V I, Svechnikova O S, Bulavin L A Ukr. J. Phys. 66 (10) 879 (2021)
  36. Akhmetkhanov R S, Akhmetkhanov R S i dr Problemy bezopasnosti i chrezvychainykh situatsii (2) 18 (2021)
  37. Pavlov A N, Pavlova O N et al Chaos: An Interdisciplinary Journal of Nonlinear Science 31 (4) (2021)
  38. Tadić B, Melnik R Dynamics 1 (2) 181 (2021)
  39. Chin C H, Abdullah S et al Soft Comput 25 (8) 6469 (2021)
  40. Lyubushin A Pure Appl. Geophys. 177 (10) 4677 (2020)
  41. Chin C H, Abdullah S et al Measurement 158 107697 (2020)
  42. Akhmetkhanov R S, Shul’zhenko A A J. Mach. Manuf. Reliab. 49 (7) 633 (2020)
  43. Butenko P N, Gilyarov V L et al Tech. Phys. 65 (2) 205 (2020)
  44. Hilarov V L Tech. Phys. 65 (3) 485 (2020)
  45. Tadić B, Gupte N EPL 132 (6) 60008 (2020)
  46. Lyubushin A Pure Appl. Geophys. 177 (2) 621 (2020)
  47. Semenistaya T V, Plugotarenko N K Surf. Engin. Appl.Electrochem. 56 (3) 311 (2020)
  48. Tan J, Xie Ju et al Geofluids 2020 1 (2020)
  49. Tadić B, Mijatović S et al Sci Rep 9 (1) (2019)
  50. Akhmetkhanov R S, Akhmenkhanov R S Problemy bezopasnosti i chrezvychainykh situatsii (5) 20 (2019)
  51. Tadić B Physica A: Statistical Mechanics And Its Applications 493 330 (2018)
  52. Maslovskaya A G, Barabash T K J. Phys.: Conf. Ser. 973 012038 (2018)
  53. Akhmetkhanov R S J. Mach. Manuf. Reliab. 47 (3) 235 (2018)
  54. Lavrova D, Poltavtseva M, Shtyrkina A 2018 IEEE Industrial Cyber-Physical Systems (ICPS), (2018) p. 818
  55. Maksimenko V A, Pavlov A et al Nonlinear Dyn 91 (4) 2803 (2018)
  56. Lavrova D, Poltavtseva M et al SHS Web Of Conf. 44 00051 (2018)
  57. Bondarenko A N, Bondarenko M A et al BIOPHYSICS 62 (5) 796 (2017)
  58. Osypenko K S, Zhuikov V Ya Mìkrosist. Elektron. Akust. 22 (5) 13 (2017)
  59. Cabrera-Brito L, Rodriguez G et al Journal of Atmospheric and Oceanic Technology 34 (4) 817 (2017)
  60. Kuvayskova Yu E Procedia Engineering 201 767 (2017)
  61. Tadić B, Dankulov M M, Melnik R Phys. Rev. E 96 (3) (2017)
  62. Rusanova I A Samara Journal Of Science 6 (4) 246 (2017)
  63. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 13 (2) 169 (2016)
  64. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 5 (2016) p. 179
  65. Yasin A S, Pavlov A N, Hramov A E J. Commun. Technol. Electron. 61 (2) 145 (2016)
  66. Pavlov A N, Abdurashitov A S et al Physica A: Statistical Mechanics And Its Applications 442 149 (2016)
  67. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 13 (2) 178 (2016)
  68. Pavlov A N, Semyachkina-Glushkovskaya O V et al Chaos, Solitons & Fractals 91 210 (2016)
  69. Tadić B J. Stat. Mech. 2016 (6) 063305 (2016)
  70. Dick O E, Nozdrachev A D Hum Physiol 42 (3) 271 (2016)
  71. Pavlov A N, Semyachkina-Glushkovskaya O V et al Chaos, Solitons & Fractals 77 6 (2015)
  72. Pavlov A N, Pavlova O N Tech. Phys. Lett. 41 (8) 762 (2015)
  73. Orozco-Duque A, Novak D et al Physiol. Meas. 36 (11) 2269 (2015)
  74. de Godoy Stênico Jeferson Wilian, Ling L L J Supercomput 71 (5) 1712 (2015)
  75. Pavlov A N, Abdurashitov A S et al J. Innov. Opt. Health Sci. 08 (05) 1550041 (2015)
  76. Pavlov A N, Pavlova O N, Shikhalov G M Tech. Phys. Lett. 41 (11) 1110 (2015)
  77. Mukhametzyanov I Z, Maiski R A, Yantudin M N OGBUS (5) 446 (2015)
  78. Shtremel’ M A Russ. Metall. 2015 (10) 771 (2015)
  79. Sukhov V M, Rudoy V M Colloid J 76 (1) 85 (2014)
  80. de Godoy Je, Ling L Simulation Technologies in Networking and Communications (2014) p. 149
  81. Pavlov A N, Semyachkina-Glushkovskaya O V et al Physiol. Meas. 35 (10) 1983 (2014)
  82. PAVLOV ALEXEY N, NAZIMOV ALEXEY I et al J. Innov. Opt. Health Sci. 07 (01) 1350055 (2014)
  83. Lyubushin A A Nat Hazards 70 (1) 471 (2014)
  84. Lyubushin A A Izv., Phys. Solid Earth 49 (1) 9 (2013)
  85. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 10 (6) 481 (2013)
  86. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 10 (6) 491 (2013)
  87. Vybornov F I, Rakhlin A V Open Astronomy 22 (1) (2013)
  88. Novikov D V, Elyashevich G K et al Phys. Solid State 55 (2) 443 (2013)
  89. ROCHA FLÁVIO GERALDO COELHO, VIEIRA FLÁVIO HENRIQUE TELES Int. J. Wavelets Multiresolut Inf. Process. 11 (03) 1350026 (2013)
  90. Pavlov A N, Semyachkina-Glushkovskaya O V et al Eur. Phys. J. Spec. Top. 222 (10) 2705 (2013)
  91. Stakhovsky I R Izv., Phys. Solid Earth 48 (11-12) 829 (2012)
  92. Golovko A A, Salakhutdinova I I Astron. Rep. 56 (6) 410 (2012)
  93. Lyubushin A NS 04 (08) 659 (2012)
  94. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 9 (6-7) 552 (2012)
  95. Nazimov A I, Pavlov A N J. Commun. Technol. Electron. 57 (7) 702 (2012)
  96. Vieira F H T, Rocha F G C, dos Santos J A Computer Communications 35 (2) 263 (2012)
  97. Gelashvili D B, Solntsev L A, Iudin D I Biol Bull Rev 2 (2) 124 (2012)
  98. Maslovskaya A G, Barabash T K J. Synch. Investig. 6 (1) 37 (2012)
  99. Rybakov A S, Vedin V Yu Aut. Conrol Comp. Sci. 45 (3) 162 (2011)
  100. Pavlov A N, Filatova A E, Hramov A E J. Commun. Technol. Electron. 56 (9) 1098 (2011)
  101. Dedovich T G, Tokarev M V Phys. Part. Nuclei Lett. 8 (6) 521 (2011)
  102. Hilarov V L, Varkentin M S et al Phys. Solid State 52 (7) 1404 (2010)
  103. PAVLOV ALEXEY N, PAVLOVA OLGA N et al Fluct. Noise Lett. 09 (03) 259 (2010)
  104. Dolgonosov B M Ecological Modelling 221 (13-14) 1702 (2010)
  105. Aleskerov F K, Kakhramanov S Sh Inorg Mater 45 (9) 975 (2009)
  106. Pavlov A N, Pavlova O N Tech. Phys. Lett. 34 (4) 306 (2008)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions