RSS feeds
РусскийEnglish
Issue 4, 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

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 (96) Similar articles (16)

  1. Mandelbrot B B The Fractal Geometry Of Nature (San Francisco: W.H. Freeman, 1982)
  2. Halsey T C et al. Phys. Rev. A 33 1141 (1986)
  3. Tel T Z. Naturforsh. A 43 1154 (1988)
  4. Feder E Fraktaly (M.: Mir, 1991)
  5. Shreder M Fraktaly, Khaos, Stepennye Zakony: Miniatyury iz Beskonechnogo Raya (Izhevsk: RKhD, 2001)
  6. Paitgen Kh-O, Rikhter P-Kh Krasota Fraktalov (M.: Mir, 1993)
  7. Family F, Vicsek T Dynamics Of Fractal Surfaces (Singapore: World Scientific, 1991)
  8. Zel’dovich Ya B, Sokolov D D Usp. Fiz. Nauk 146 493 (1985); Zel’dovich Ya B, Sokolov D D Sov. Phys. Usp. 28 608 (1985)
  9. Sokolov I M Usp. Fiz. Nauk 150 221 (1986); Sokolov I M Sov. Phys. Usp. 29 924 (1986)
  10. Zosimov V V, Lyamshev L M Usp. Fiz. Nauk 165 361 (1995); Zosimov V V, Lyamshev L M Phys. Usp. 38 347 (1995)
  11. Vainshtein S I et al. Phys. Rev. E 50 1823 (1994)
  12. Eisenberg E et al. Phys. Rev. E 47 2333 (1993)
  13. Dräger J, Bunde A Phys. Rev. E 54 4596 (1996)
  14. Arneodo A, Decoster N, Roux S G Phys. Rev. Lett. 83 1255 (1999)
  15. Chhabra A B et al. Phys. Rev. A 40 5284 (1989)
  16. Benzi R et al. J. Phys. A 17 3521 (1984)
  17. Badii R, Broggi G Phys. Lett. A 131 339 (1988)
  18. Feigenbaum M J J. Stat. Phys. 46 919 (1987)
  19. Jensen M H, Kadanoff L P, Procaccia I Phys. Rev. A 36 1409 (1987)
  20. Mandelbrot B B Fractals And Multifractals: Noise, Turbulence And Galaxies (New York: Springer-Verlag, 1989)
  21. Strait B J, Dewey T G Phys. Rev. E 52 6588 (1995)
  22. Glazier J A et al. Phys. Rev. E 51 2665 (1995)
  23. Hentschel H G E Phys. Rev. E 50 243 (1994)
  24. Wiklund K O, Elgin J N Phys. Rev. E 54 1111 (1996)
  25. Pavlov A N et al. Physica A 300 310 (2001)
  26. Pavlov A N et al. Physica A 316 233 (2002)
  27. Frish U, Parisi G in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (Proc. of the Intern. School of Physics "Enrico Fermi", Course 88, Eds M Ghil, R Benzi, G Parisi) (Amsterdam: North-Holland, 1985) p. 71
  28. Barabási A-L, Vicsek T Phys. Rev. A 44 2730 (1991)
  29. Gagne Y, Hopfinger E, Frisch U In New Trends In Nonlinear Dynamics And Pattern-Forming Phenomena: The Geometry Of Nonequilibrium (NATO ASI Series. Ser. B, Vol. 237, Eds P Coullet, P Huerre) (New York: Plenum Press, 1990) p. 315
  30. Muzy J F, Bacry E, Arneodo A Phys. Rev. Lett. 67 3515 (1991)
  31. Muzy J F, Bacry E, Arneodo A Phys. Rev. E 47 875 (1993)
  32. Grossmann A, Morlet J SIAM J. Math. Anal. 15 723 (1984)
  33. Meyer Y Wavelets: Algorithms And Applications (Philadelpha, Pa.: Society for Industrial and Applied Mathematics, 1993)
  34. Meyer Y Wavelets And Operators (Cambridge: Cambridge Univ. Press, 1992)
  35. Daubechies I Ten Lectures On Wavelets (Philadelpha, Pa.: Society for Industrial and Applied Mathematics, 1992)
  36. Chui C K An Introduction To Wavelets (Boston: Academic Press, 1992)
  37. Mallat S A Wavelet Tour Of Signal Processing (San Diego: Academic Press, 1998)
  38. Astaf’eva N M Usp. Fiz. Nauk 166 1145 (1996); Astaf’eva N M Phys. Usp. 39 1085 (1996)
  39. Dremin I M, Ivanov O V, Nechitailo V A Usp. Fiz. Nauk 171 465 (2001); Dremin I M, Ivanov O V, Nechitailo V A Phys. Usp. 44 447 (2001)
  40. Koronovskii A A, Khramov A E Nepreryvnyi Veivletnyi Analiz i Ego Prilozheniya (M.: Fizmatlit, 2003)
  41. Sosnovtseva O V et al. Phys. Rev. Lett. 94 218103 (2005)
  42. Pavlov A N et al. Brief. Bioinform. 7 375 (2006)
  43. Ivanov P Ch et al. Nature 399 461 (1999)
  44. Arneodo A et al. Physica A 249 439 (1998)
  45. Stanley H E et al. Physica A 270 309 (1999)
  46. Nunes Amaral L A et al. Phys. Rev. Lett. 86 6026 (2001)
  47. Ivanov P Ch et al. Chaos 11 641 (2001)
  48. Marrone A et al. Phys. Rev. E 60 1088 (1999)
  49. Thurner S, Feurstein M C, Teich M C Phys. Rev. Lett. 80 1544 (1998)
  50. Gabor D J. IEE (London) 93 429 (1946)
  51. Vainshtein L A, Vakman D E Razdelenie Chastot v Teorii Kolebanii i Voln (M.: Nauka, 1983)
  52. Peng C-K et al. Chaos 5 82 (1995)
  53. Peng C-K et al. Phys. Rev. E 49 1685 (1994)
  54. Hausdorff F Math. Ann. 79 157 (1918)
  55. Besicovitch A S Math. Ann. 110 321 (1935)
  56. Falconer K J The Geometry Of Fractal Sets (Cambridge: Cambridge Univ. Press, 1985)
  57. Farmer J D, Ott E, Yorke J A Physica D 7 153 (1983)
  58. Muzy J F, Bacry E, Arneodo A Int. J. Bifurcat. Chaos 4 245 (1994)
  59. Bozhokin S V, Parshin D A Fraktaly i Mul’tifraktaly (Izhevsk: RKhD, 2001)
  60. Grassberger P Phys. Lett. A 97 227 (1983)
  61. Grassberger P, Procaccia I Physica D 9 189 (1983)
  62. Hentschel H G E, Procaccia I Physica D 8 435 (1983)
  63. Grassberger P, Procaccia I Phys. Rev. Lett. 50 346 (1983)
  64. Bowen R Equilibrium States And The Ergodic Theory Of Anosov Diffeomorphisms (Lecture Notes in Mathematics, Vol. 470) (Berlin: Springer-Verlag, 1975)
  65. Collet P, Lebowiz J L, Porzio A J. Stat. Phys. 47 609 (1987)
  66. Afraimovich V, Zaslavsky G M Phys. Rev. E 55 5418 (1997)
  67. Postnov D E et al. Chaos 9 227 (1999)
  68. Pavlov A N, Sosnovtseva O V, Mosekilde E Chaos, Solitons Fractals 16 801 (2003)
  69. Benzi R, Sutera A, Vulpiani A J. Phys. A 14 L453 (1981)
  70. Nicolis C, Nicolis G Tellus 33 225 (1981)
  71. Anishchenko V S i dr. Usp. Fiz. Nauk 169 7 (1999); Anishchenko V S et al. Phys. Usp. 42 7 (1999)
  72. Silchenko A, Hu C-K Phys. Rev. E 63 041105 (2001)
  73. Anishchenko V S et al. Nonlinear Dynamics Of Chaotic And Stochastic Systems (Berlin: Springer, 2002)
  74. Anishchenko V S i dr. Nelineinye Effekty v Khaoticheskikh i Stokhasticheskikh Sistemakh (Izhevsk: RKhD, 2003)
  75. Pavlov A N, Ziganshin A R, Klimova O A Chaos, Solitons Fractals 24 57 (2005)
  76. Jaffard S, Meyer Y Mem. Am. Math. Soc. 123 587 (1996)
  77. Veneziano D, Moglen G E, Bras R L Phys. Rev. E 52 1387 (1995)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions