RSS feeds
РусскийEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2022

 / 

January

←  →

Reviews of topical problems


Wavelets for the space-time structure analysis of physical fields

 a, b,  c, d, e,  a, f
a Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, ul. akad. Koroleva 1, Perm, 614013, Russian Federation
b Perm State National Research University, Bukireva st. 15, Perm', 614990, Russian Federation
c Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
d Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Kaluzhskoe shosse 4, Troitsk, Москва, 108840, Russian Federation
e Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
f Perm National Research Polytechnic University, Komsomol'skii prosp. 29, Perm, 614990, Russian Federation

Spectral analysis, based on the Fourier method, is a general tool in physics. Wavelets appeared as a natural generalization of classical spectral analysis to the case of complex nonstationary and spatially inhomogeneous systems, for which a comparison with an infinite sinusoid, which forms the basis of the Fourier method, has to be replaced by a comparison with a finite wave packet, which is known as a wavelet. In this review, the authors, based largely on their own experience of application wavelet analysis in astro- and geophysics, solar-terrestrial relations, as well as climatology, medical physics, and laboratory hydrodynamic experiments, demonstrate the possibilities and discuss the practical aspects of the application of the wavelet apparatus to the interpretation of signals and images of various physical natures.

Fulltext pdf (2.7 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2020.10.038859
Keywords: wavelets, spectral analysis, data processing for signals and images, solar and stellar activity, galactic magnetic fields, geophysics, medical physics
PACS: 47.27.er, 95.75.−z (all)
DOI: 10.3367/UFNe.2020.10.038859
URL: https://ufn.ru/en/articles/2022/1/d/
000788597000004
2-s2.0-85128540479
2022PhyU...65...62F
Citation: Frick P G, Sokoloff D D, Stepanov R A "Wavelets for the space-time structure analysis of physical fields" Phys. Usp. 65 62–89 (2022)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 8th, August 2020, revised: 20th, October 2020, 25th, October 2020

Оригинал: Фрик П Г, Соколов Д Д, Степанов Р А «Вейвлет-анализ пространственно-временной структуры физических полей» УФН 192 69–99 (2022); DOI: 10.3367/UFNr.2020.10.038859

References (113) ↓ Cited by (9) Similar articles (20)

  1. Yaglom A M Korrelyatsionnaya Teoriya Statsionarnykh Sluchainykh Funktsii s Primerami iz Meteorologii (L.: Gidrometeoizdat, 1981)
  2. Gabor D J. Inst. Electr. Eng. 93 429 (1945)
  3. Grossmann A, Morlet J SIAM J. Math. Anal. 15 723 (1984)
  4. Meyer Y Wavelets And Operators (Cambridge: Cambridge Univ. Press, 1992)
  5. Daubechies I Ten Lectures On Wavelets (Philadelphia, Pa.: Society for Industrial and Applied Mathematics, 1992)
  6. Holschneider M Wavelets: An Analysis Tool (New York: Oxford Univ. Press, 1995)
  7. Torresani B Continuous Wavelet Transform (Paris: Savoire, 1995)
  8. Mallat S A Wavelet Tour Of Signal Processing: The Sparse Way 3rd ed. (Amsterdam: Elsevier. Academic Press, 2009)
  9. Farge M Annu. Rev. Fluid Mech. 24 395 (1992)
  10. Astaf’eva N M Usp. Fiz. Nauk 166 1145 (1996); Astaf’eva N M Phys. Usp. 39 1085 (1996)
  11. 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)
  12. Pavlov A N, Anishchenko V S Usp. Fiz. Nauk 177 859 (2007); Pavlov A N, Anishchenko V S Phys. Usp. 50 819 (2007)
  13. Pavlov A N i dr Usp. Fiz. Nauk 182 905 (2012); Pavlov A N Phys. Usp. 55 845 (2012)
  14. Frick P, Zimin V Wavelets, Fractals And Fourier Transform (Inst. Of Math And Its Appl. Conf. Ser. No. 43, Eds M Farge, J Hunt, J Vassilicos) (Oxford: Clarendon Press, 1993) p. 265
  15. Frick P Astron. Astrophys. 328 670 (1997)
  16. Frick P Mon. Not. R. Astron. Soc. 491 5572 (2020)
  17. Bruijn de N G Inequalities: Proc. Of A Symp., Wright-Patterson Air Force Base (Ed. O Shisha) (New York: Academic Press, 1965) p. 57-71
  18. Frik P G Turbulentnost’: Podkhody i Modeli 2-e izd., ispr. i dop. (M. - Izhevsk: RKhD, 2010)
  19. Tikhonov A N, Arsenin V Ya Metody Resheniya Nekorrektnykh Zadach (M.: Nauka, 1986)
  20. Patrikeev I A, Stepanov R A, Frik P G Vychislitel’nye Metody Programmirovanie 6 35 (2005)
  21. Bloomfield P Fourier Analysis Of Time Series: An Introduction (New York: Wiley, 1976)
  22. Nesme-Ribes E Comptes Rendus B Acad. Sci. Paris 321 525 (1995)
  23. Torrence C, Webster P J J. Climate 12 2679 (1999)
  24. Guedes M R G, Pereira E S, Cecatto J R Astron. Astophys. 573 A64 (2015)
  25. Chavez M, Cazelles B Sci. Rep. 9 7389 (2019)
  26. Soon W Earth-Sci. Rev. 134 1 (2014)
  27. Velasco Herrera V M New Astron. 56 86 (2017)
  28. Frick P Astophys. J. 483 426 (1997)
  29. Frick P, Grossmann A, Tchamitchian P J. Math. Phys. 39 4091 (1998)
  30. Soon W Mon. Not. R. Aston. Soc. 483 2748 (2019)
  31. Monin A S Usp. Fiz. Nauk 132 123 (1980); Monin A S Sov. Phys. Usp. 23 594 (1980)
  32. Vitinskii Yu I, Kopetskii M, Kuklin G V Statistika Pyatnoobrazovatel’noi Deyatel’nosti Solntsa (M.: Nauka, 1986)
  33. Soon W W-H, Yaskell S H The Maunder Minimum And The Variable Sun-Earth Connection (River Edge, NJ: World Scientific, 2003)
  34. Ogurtsov M G Solar Phys. 211 371 (2002)
  35. Sokoloff D Sun Geosphere 12 20 (2017)
  36. Zolotova N V, Ponyavin D I Astrophys. J. 800 42 (2015)
  37. Usoskin I G Astron. Astrophys. 581 A95 (2015)
  38. Hoyt D V, Schatten K H Solar Phys. 179 189 (1998)
  39. Vaquero J M Solar Phys. 291 3061 (2016)
  40. Svalgaard L, Schatten K H Solar Phys. 291 2653 (2016)
  41. Chatzistergos T Astron. Astrophys. 602 A69 (2017)
  42. Svalgaard L p. 2020, Personal communication; Svalgaard L Sun-Climate Symp. 2020, Tucson, AZ
  43. Pipin V V, Sokoloff D D, Usoskin I G Astron. Astrophys. 542 A26 (2012)
  44. Kitchatinov L L, Mordvinov A V, Nepomnyashchikh A A Astron. Astrophys. 615 A38 (2018)
  45. Bazilevskaya G Space Sci. Rev. 186 359 (2014)
  46. Ruzmaikin A Usp. Fiz. Nauk 184 297 (2014); Ruzmaikin A Phys. Usp. 57 280 (2014)
  47. Sokolov D D, Stepanov R A, Frik P G Usp. Fiz. Nauk 184 313 (2014); Sokoloff D D, Stepanov R A, Frick P G Phys. Usp. 57 292 (2014)
  48. Plunian F, Sarson G R, Stepanov R Mon. Not. R. Astron Soc. 400 L47 (2009)
  49. Pipin V V, Kosovichev A G Astrophys. J. 867 145 (2018)
  50. Sych R A Solnechno-zemnaya Fizika 1 (2) 3 (2015)
  51. Sych R A, Nakariakov VM Solar Phys. 248 395 (2008)
  52. Sych R Astron. Astrophys. 539 23 (2012)
  53. Sych R Astron. Astrophys. 577 A43 (2015)
  54. Laclare F Astron. Astrophys. 125 200 (1983)
  55. Lanza A F Proc. Int. Astron. Union 5 (S264) 120 (2009)
  56. Goncharskii A V i dr Astron. Zhurn. 59 1146 (1982); Goncharskii A V Sov. Astron. 26 690 (1982)
  57. Miyake F, Usoskin I, Poluianov S (Eds) Extreme Solar Particle Storms (Bristol: IOP Publ., 2019)
  58. Frick P New Astron. 9 599 (2004)
  59. Baliunas S Mon. Not. R. Astron. Soc. 365 181 (2006)
  60. Baliunas S Solar Phys. 224 179 (2004)
  61. Sosnovtseva O V Phys. Rev. E 70 031915 (2004)
  62. Sosnovtseva O V Phys. Rev. Lett. 94 218103 (2005)
  63. Soon W, Frick P, Baliunas S Astrophys. J. 510 L135 (1999)
  64. Stepanov R Mon. Not. R. Astron. Soc. 495 3788 (2020)
  65. Katsova M M, Bondar’ N I, Livshits M A Astron. Zhurn. 92 596 (2015); Katsova M M, Bondar N I, Livshits M A Astron. Rep. 59 726 (2015)
  66. Stefani F Astron. Nachr. 341 600 (2020)
  67. Baliunas S Geophys. Res. Lett. 24 1351 (1997)
  68. Panovska S, Finlay C C, Hirt A M Earth Planet. Sci. Lett. 379 88 (2013)
  69. Galyagin D K i dr Dokl. Ross. Akad. Nauk 360 541 (1998); Galyagin D K Dokl. Earth Sci. 360 617 (1998)
  70. Sokolov D D, Shibalova A S Fiz. Zemli (5) 156 (2015); Sokoloff D D, Shibalova A S Izv. Phys. Solid Earth 51 764 (2015)
  71. Sokoloff D D, Shibalova A S Geomagn. Aeron. 58 888 (2018)
  72. Gruzdev A N, Bezverkhnii V A J. Atmos. Solar-Terr. Phys. 187 53 (2019)
  73. Zhao X H, Feng X S J. Atmos. Solar-Terr. Phys. 122 26 (2015)
  74. Burakov K S i dr Izv. RAN. Fizika Zemli 34 83 (1998); Burakov K S Izv. Phys. Solid Earth 34 773 (1998)
  75. Klausner V J. Atmos. Solar-Terr. Phys. 92 124 (2013)
  76. Klausner V J. Geophys. Res. Space Phys. 119 3077 (2014)
  77. Ginzburg V L Rasprostranenie Elektromagnitnykh Voln v Plazme (M.: Fizmatgiz, 1960); Per. na angl. yaz., Ginzburg V L Propagation Of Electromagnetic Waves In Plasma (New York: Gordon and Breach, 1961)
  78. Stepanov R A, Sokolov D D Usp. Fiz. Nauk 189 1285 (2019); Stepanov R A, Sokoloff D D Phys. Usp. 62 1208 (2019)
  79. Frick P Mon. Not. R. Astron. Soc. 318 925 (2000)
  80. Frick P Mon. Not. R. Astron. Soc. 327 1145 (2001)
  81. Edwards A L Multiple Regression And The Analysis Of Variance And Covariance (San Francisco, CA: W.H. Freeman, 1979)
  82. Tabatabaei F S Astron. Astrophys. 557 A129 (2013)
  83. Frick P Astron. Astrophys. 585 A21 (2016)
  84. Patrikeev I Astron. Astrophys. 458 441 (2006)
  85. Ossenkopf-Okada V, Stepanov R Astron. Astrophys. 621 A5 (2019)
  86. Kolesnichenko I Exp. Fluids 56 88 (2015)
  87. Khalilov R Phys. Rev. Fluid 3 043503 (2018)
  88. Vasiliev A Int. Commun. Heat Mass Transfer 108 104319 (2019)
  89. Noskov V Magnetohydrodynamics 55 149 (2019)
  90. Frick P Magnetohydrodynamics 51 267 (2015)
  91. Mikhailovich B, Shapiro A, Stepanov R Magnetohydrodynamics 52 125 (2016)
  92. Noskov V Phys. Rev. E 85 016303 (2012)
  93. Frick P Magnetohydrodynamics 38 143 (2002)
  94. Noskov V Phys. Fluids 21 045108 (2009)
  95. Frick P Phys. Rev. Lett. 105 184502 (2010)
  96. Ruzmaikin A A, Shukurov A M, Sokoloff D D Magnetic Fields Of Galaxies (Astrophysics And Space Science Library, Vol. 133) (Dordrecht: Kluwer Acad. Publ., 1988); Ruzmaikin A A, Sokolov D D, Shukurov A M Magnitnye Polya Galaktik (M.: Nauka, 1988)
  97. Brentjens M A, de Bruyn A G Astron. Astrophys. 441 1217 (2005)
  98. Burn B J Mon. Not. R. Astron. Soc. 133 67 (1966)
  99. Frick P Mon. Not. R. Astron. Soc. 401 L24 (2010)
  100. Frick P Mon. Not. R. Astron. Soc. 414 2540 (2011)
  101. Beck R Mon. Not. R. Astron. Soc. 543 A113 (2012)
  102. Sun X H Astron. J. 149 60 (2015)
  103. Beck R, Hoernes P Nature 379 47 (1996)
  104. Chupin A Astron. Nachr. 339 440 (2018)
  105. Sokoloff D Galaxies 6 (4) 121 (2018)
  106. Stepanov R Bioimpedance In Biomedical Applications And Research (Eds F Simini, P Bertemes-Filho) (Cham: Springer Intern. Publ., 2018) p. 257
  107. Podtaev S, Morozov M, Frick P Cardiovascular Eng. 8 185 (2008)
  108. Tankanag A V, Chemepic N K Biofizika 54 537 (2009); Tankanag A V, Chemeris N K Biophysics 54 375 (2009)
  109. Mizeva I J. Biomed. Opt. 20 037007 (2015)
  110. Frick P, Mizeva I, Podtaev S Biomed. Signal Process. Control 21 1 (2015)
  111. Martini R, Bagno A Clin. Hemorheol. Microcirc. 70 213 (2018)
  112. Dumler A A i dr Al’manakh Klinicheskoi Meditsiny 44 179 (2016)
  113. Stepanov R Biomed. Signal Process. Control 36 50 (2017)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions