RSS feeds
ÐóññêèéEnglish
Issue 11, 2024
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 (101) ↓ Similar articles (16)

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