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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)
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Оригинал: Павлов А Н, Анищенко В С «Мультифрактальный анализ сложных сигналов» УФН 177 859–876 (2007); DOI: 10.3367/UFNr.0177.200708d.0859

References (77) Cited by (106) ↓ Similar articles (20)

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