RSS-ленты
РусскийEnglish
Выпуск 9, 2026
Том год страница
Выпуски Авторы PACS Подписчикам Для авторов

Выпуски

 / 

2001

 / 

май

←  →

Обзоры актуальных проблем


Вейвлеты и их использование

, ,
Физический институт им. П.Н. Лебедева РАН, Ленинский проспект 53, Москва, 119991, Российская Федерация

Цель этого обзора состоит в том, чтобы дать полезное пособие тем, кто собирается применять дискретное вейвлет-преобразование в практических расчетах. Введено понятие вейвлетов и кратко описано их использование в практических вычислениях и различных приложениях без строгих доказательств математических утверждений, ссылки на которые приведены в цитируемой литературе. Многомасштабный анализ и быстрое вейвлет-преобразование стали практически синонимом дискретного вейвлет-преобразования. Правильный выбор вейвлета и использование нестандартного матричного умножения оказываются зачастую весьма существенными для решения поставленной задачи. Анализ различных функций с помощью вейвлетов позволяет выявить фрактальные свойства, особенности функции и т.п. Вейвлет-преобразование операторных выражений помогает в решении некоторых уравнений. В практических приложениях приходится часто иметь дело с дискретными наборами чисел, и тогда возникает проблема устойчивости вейвлет-преобразования и соответствующих численных алгоритмов. После обсуждения всех этих вопросов мы переходим к практическим применениям вейвлет-анализа. Они столь многочисленны, что нам приходится ограничить себя несколькими примерами. Мы будем благодарны всем за конкретные предложения, которые позволили бы приблизиться к цели, сформулированной в первой фразе аннотации.

Текст pdf (863 Кб)
English fulltext is available at DOI: 10.1070/PU2001v044n05ABEH000918
PACS: 02.60.−x, 02.70.−c, 05.40.−a, 87.57.−s (все)
DOI: 10.3367/UFNr.0171.200105a.0465
URL: https://ufn.ru/ru/articles/2001/5/a/
000170938900001
Цитата: Дремин И М, Иванов О В, Нечитайло В А "Вейвлеты и их использование" УФН 171 465–501 (2001)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

English citation: Dremin I M, Ivanov O V, Nechitailo V A “Wavelets and their uses” Phys. Usp. 44 447–478 (2001); DOI: 10.1070/PU2001v044n05ABEH000918

Список литературы (92) Статьи, ссылающиеся на эту (182) ↓ Похожие статьи (20)

  1. Kriukova M O, Khamidullin R K Lecture Notes in Networks and Systems Vol. Integrated Approaches to Systems Engineering, Intelligent Technology, and Innovation in Space ExplorationModernization of the Polynomial Series Method for Modal Test Data Processing1632 Chapter 35 (2026) p. 407
  2. Trubacheev B, Levina A Communications in Computer and Information Science Vol. Intelligent SystemsTraining Neural Networks on Color-Space Reduced Images and Using Wavelet Transforms to Reduce Training Losses2604 Chapter 5 (2026) p. 59
  3. Liu G, Ji Z et al Water 18 (2) 154 (2026)
  4. Rayal A, Prajapati M et al Franklin Open 15 100571 (2026)
  5. Gavrikov A P, Beilekchi D V, Kolpakov A A 2026 International Russian Smart Industry Conference (SmartIndustryCon), (2026) p. 548
  6. Burda E A, Bogomolov D E et al td (329) 18 (2025)
  7. Bondarenko V I, Rekhviashvili S S, Chukhovskii F N Crystallogr. Rep. 70 (4) 523 (2025)
  8. Goshvarpour A, Goshvarpour A Cogn Comput 17 (1) (2025)
  9. Grishentsev A Yu, Korovkin N V, Ostrovskii D P jour 25 (4) 789 (2025)
  10. Nagappanavar S N, Y V et al Z Angew Math Mech 105 (8) (2025)
  11. null P, Singh I AJAM 13 (6) 419 (2025)
  12. Bernalte Sánchez Pedro, Segovia Ramírez Isaac et al Structural Health Monitoring 24 (5) 2762 (2025)
  13. Nagappanavar S N, Kondethimmanahalli R R Int. J. Appl. Comput. Math 11 (2) (2025)
  14. Uchendu N, Muggleton Je M, White P R Mechanical Systems and Signal Processing 221 111727 (2024)
  15. Bondarenko V I, Rekhviashvili S S, Chukhovskii F N Crystallogr. Rep. 69 (5) 629 (2024)
  16. Gorbunov S A, Volkov A E et al Успехи физических наук 194 (08) 826 (2024) [Gorbunov S A, Volkov A E et al Phys. Usp. 67 (08) 779 (2024)]
  17. Bondarenko V I, Rekhviashvili S S, Chukhovskii F N Kristallografiâ 69 (5) 755 (2024)
  18. Makhov V E, Shirobokov V V, Emelyanov A V td (309) 42 (2024)
  19. Aleksanyan G, Gorbatenko N et al BIO Web Conf. 84 03001 (2024)
  20. Kolpakov A A, Beilekchi D V 2024 International Russian Automation Conference (RusAutoCon), (2024) p. 685
  21. Mamedova N A, Bortsov A S Autom. Doc. Math. Linguist. 58 (6) 401 (2024)
  22. Dick O E Neurosci Behav Physi (2023)
  23. Kulikova L I, Makhortykh S A Pattern Recognit. Image Anal. 33 (4) 1273 (2023)
  24. Motiwala Z, Sandholu A S et al iScience 26 (7) 107031 (2023)
  25. Zadiraka V, Luts L, Shvidchenko I Theory of integrals computing from fast oscillating functions (2023)
  26. Khatua P, Ray K Ch Circuits Syst Signal Process 42 (12) 7297 (2023)
  27. Subba N, Haldar P K Eur. Phys. J. Plus 138 (12) (2023)
  28. Dosko S I, Sheptunov S A et al 2023 International Conference on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS), (2023) p. 115
  29. Kolpakov A A, Beilekchi D V, Proskuryakov A Yu 2023 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), (2023) p. 1102
  30. Cooray S, Takeuchi T T et al Publications of the Astronomical Society of Japan 75 (Supplement_1) S85 (2023)
  31. Sinevich A A, Chernyshov A A et al Geomagn. Aeron. 63 (6) 747 (2023)
  32. Sinitsyn I N Pattern Recognit. Image Anal. 33 (4) 862 (2023)
  33. Khan M A, Haque A et al e-Prime - Advances in Electrical Engineering, Electronics and Energy 3 100093 (2023)
  34. Anyutin A P, Khodykina T M et al IJERPH 19 (22) 14714 (2022)
  35. Abanin O I EJSI (1 (121)) (2022)
  36. Frick P G, Sokoloff D D, Stepanov R A Phys.-Usp. 65 (1) 62 (2022)
  37. Zamorano M, Gómez Garcia María Jesus, Castejón Cristina Journal of Vibration and Control 28 (21-22) 3152 (2022)
  38. Saberivahidaval M, Ranjbar A et al Braz J Phys 52 (3) (2022)
  39. Khatua P, Ray K Ch Circuits Syst Signal Process 41 (11) 6462 (2022)
  40. Teoh L, Ihalage A A et al PLoS ONE 17 (6) e0268962 (2022)
  41. Khatua P, Ray K Ch J Sign Process Syst 94 (12) 1381 (2022)
  42. Pan P, Mandal R K et al International Transactions on Electrical Energy Systems 2022 1 (2022)
  43. Belov A A, Kolpakov A A, Proskuryakov A Yu 2022 International Russian Automation Conference (RusAutoCon), (2022) p. 252
  44. Arts L P A, van den B E L Nat Comput Sci 2 (1) 47 (2022)
  45. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series in Synergetics Chapter 2 (2021) p. 15
  46. Singh R, Bhushan B Advances in Intelligent Systems and Computing Vol. Computational Methods and Data EngineeringFault Classification Using Support Vectors for Unmanned Helicopters1227 Chapter 28 (2021) p. 369
  47. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series in Synergetics Chapter 1 (2021) p. 1
  48. Hramov A E, Maksimenko V A, Pisarchik A N Physics Reports 918 1 (2021)
  49. Anisimov S V, Shikhova N M, Kleimenova N G Geomagn. Aeron. 61 (2) 180 (2021)
  50. Bibikova E A, Kundikova N D et al Computer Optics 45 (5) (2021)
  51. Guliyeva F WSEAS TRANSACTIONS ON MATHEMATICS 19 50 (2020)
  52. Bidyuk P, Manuilenko R, Pantyeyev R 2020 IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC), (2020) p. 1
  53. Guliyeva F A J. Phys.: Conf. Ser. 1564 012018 (2020)
  54. Strelkovskaya I, Solovskaya I et al 2020 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), (2020) p. 1
  55. Zadiraka V K, Luts L V, Shvidchenko I V Cybernetics and Computer Technologies (4) 47 (2020)
  56. Méneroux Y, Le Guilcher A et al Int J Data Sci Anal 10 (1) 101 (2020)
  57. Chugunin D V, Chernyshov A A et al Geomagn. Aeron. 60 (5) 538 (2020)
  58. Sinitsyn I N, Sinitsyn V I et al Autom Remote Control 81 (11) 2046 (2020)
  59. Tielieha V V, Lysiuk I R, Khyzhniak T A Mìkrosist. elektron. akust. 24 (3) 51 (2019)
  60. Abanin O I, Soloviev S V EJSI (6 (90)) (2019)
  61. Belov A A, A Yu P 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2019) p. 1
  62. Smirnov V M, Filatov V N 2019 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF), (2019) p. 1
  63. Grishina D S, Pavlov A N et al Tech. Phys. Lett. 45 (8) 820 (2019)
  64. Strelkovskaya I, Solovskaya I et al 2019 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo), (2019) p. 1
  65. Belov A A 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2019) p. 1
  66. Khristenko L A, Stepanov Ju I et al Practical and Theoretical Aspects of Geological Interpretation of Gravitational, Magnetic and Electric Fields Springer Proceedings in Earth and Environmental Sciences Chapter 36 (2019) p. 313
  67. Kalyakulina A I, Yusipov I I et al Radiophys Quantum El 61 (8-9) 689 (2019)
  68. Belov A A, Kropotov Y A 2018 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2018) p. 1
  69. Bagmanov V Kh, Potapov A A et al J. Commun. Technol. Electron. 63 (10) 1163 (2018)
  70. Proskuryakov A Yu, Kropotov Yu A 2018 3rd Russian-Pacific Conference on Computer Technology and Applications (RPC), (2018) p. 1
  71. Kropotov Y A, Proskuryakov A Y, Belov A A 2018 Moscow Workshop on Electronic and Networking Technologies (MWENT), (2018) p. 1
  72. Belov A A, Proskuryakov A Y 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE), (2018) p. 391
  73. Кропотов Ю, Kropotov Yu и др Bulletin of Bryansk state technical university 2018 (8) 67 (2018)
  74. Yamnenko Yu S, Levchenko V V, Niemchinova K S Mìkrosist. elektron. akust. 23 (3) 42 (2018)
  75. Pavlova O N, Pavlov A N Tech. Phys. Lett. 44 (7) 640 (2018)
  76. Hololobova O O, Havrilyuk V I STP (1(67)) 7 (2017)
  77. Proskuryakov A Y, Kropotov Y A Procedia Engineering 201 789 (2017)
  78. Yasin A S, Pavlov A N, Hramov A E J. Commun. Technol. Electron. 62 (3) 236 (2017)
  79. Кропотов Ю, Kropotov Yu и др Bulletin of Bryansk state technical university 2017 (4) 65 (2017)
  80. Efremov V I, Parfinenko L D, Solov’ev A A Geomagn. Aeron. 57 (8) 1045 (2017)
  81. Zelinsky N R, Kleimenova N G, Gromova L I Geomagn. Aeron. 57 (5) 559 (2017)
  82. Proskuryakov A Y 2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), (2017) p. 1
  83. Yaseen A S, Pavlova O N, Pavlov A N Tech. Phys. Lett. 43 (7) 641 (2017)
  84. Simankina T, Romanovich M et al MATEC Web of Conferences 53 01054 (2016)
  85. Yasin A S, Pavlov A N, Hramov A E J. Commun. Technol. Electron. 61 (2) 145 (2016)
  86. Tapiador F J, Behrangi A et al JGR Atmospheres 121 (5) 2161 (2016)
  87. Kartashevskiy I 2016 Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S&T), (2016) p. 11
  88. Yasin A S, Pavlova O N, Pavlov A N Tech. Phys. Lett. 42 (8) 865 (2016)
  89. Ismailov M, Guliyeva F, Nasibov Yu Journal of Function Spaces 2016 1 (2016)
  90. Chugai O N, Abashin S L et al Inorg Mater 51 (10) 972 (2015)
  91. Ivanov V V, Bondar T N Geomagn. Aeron. 55 (3) 389 (2015)
  92. Bilalov B, Guliyeva F Complex Anal. Oper. Theory 9 (7) 1609 (2015)
  93. Yaseen A S, Pavlov A N Tech. Phys. Lett. 41 (7) 680 (2015)
  94. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series in Synergetics Chapter 1 (2015) p. 1
  95. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series in Synergetics Chapter 2 (2015) p. 15
  96. Lyamets Yu Ya, Voronov P I, Romanov Yu V Therm. Eng. 61 (14) 1015 (2014)
  97. Pavlov A N, Semyachkina-Glushkovskaya O V et al Physiol. Meas. 35 (10) 1983 (2014)
  98. Efimov A I, Lukanina L A et al J. Commun. Technol. Electron. 58 (5) 429 (2013)
  99. Uspenskii Yu A, Ivanov O V et al Bull. Lebedev Phys. Inst. 40 (5) 132 (2013)
  100. Suleimanov B A, Dyshin O A Applied Mathematics and Computation 219 (12) 7036 (2013)
  101. Pavlov A N, Hramov A E et al Успехи физических наук 182 (9) 905 (2012)
  102. Ivanov V V, Bondar’ T N Geomagn. Aeron. 52 (5) 664 (2012)
  103. Efimov A I, Lukanina L A et al J. Commun. Technol. Electron. 56 (12) 1407 (2011)
  104. Pavlov A N, Filatova A E, Hramov A E J. Commun. Technol. Electron. 56 (9) 1098 (2011)
  105. Kirillov A, Kirillova O, Kirillov S 2011 3rd International Conference on Advanced Computer Control, (2011) p. 138
  106. Dremin I M, Eyyubova G Kh et al Indian J Phys 85 (1) 39 (2011)
  107. Sazhina O S, Sazhin M V Moscow Univ. Phys. 66 (6) 588 (2011)
  108. Sazhina O S, Sazhin M V J. Exp. Theor. Phys. 113 (5) 798 (2011)
  109. Skorbun A D, Ogorodnikov B I Russ. Meteorol. Hydrol. 35 (8) 536 (2010)
  110. PAVLOV A N, PAVLOVA O N et al Fluct. Noise Lett. 09 (03) 259 (2010)
  111. But A V, Mygal V P, Phomin A S Semiconductors 43 (5) 581 (2009)
  112. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. and Math. Phys. 49 (9) 1554 (2009)
  113. Abraamyan Kh U, Friesen A V et al Phys. Rev. C 80 (3) (2009)
  114. Makhortih S A, Semechkin R A Bull Exp Biol Med 147 (4) 493 (2009)
  115. Angelov I, Vachev B et al Nucl. Phys. At. Energy 9 (1) 46 (2008)
  116. Ivanov V V, Bondar’ T N Geomagn. Aeron. 48 (5) 680 (2008)
  117. Korotkikh V L, Eyyubova G Kh Moscow Univ. Phys. 63 (1) 20 (2008)
  118. Fedorets I D, Ratkevich S S Phys. Atom. Nuclei 71 (8) 1325 (2008)
  119. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. and Math. Phys. 48 (2) 251 (2008)
  120. Dolgal A S, Simanov A A Dokl. Earth Sc. 418 (1) 118 (2008)
  121. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. and Math. Phys. 48 (12) 2194 (2008)
  122. Dremin I M, Leonidov A V Bull. Lebedev Phys. Inst. 35 (1) 1 (2008)
  123. Dremin I M, Eyyubova G Kh et al J. Phys. G: Nucl. Part. Phys. 35 (9) 095106 (2008)
  124. Ardagna C A, Bernardoni E et al 2008 2nd IEEE International Conference on Digital Ecosystems and Technologies, (2008) p. 274
  125. Bolmont J, Jacholkowska A et al ApJ 676 (1) 532 (2008)
  126. Jones B J T Lecture Notes in Physics Vol. Data Analysis in CosmologyThe Sea of Wavelets665 Chapter 1 (2008) p. 3
  127. Novikov L V Instrum Exp Tech 50 (1) 61 (2007)
  128. Zakharov V I, Zienko A S Moscow Univ. Phys. 62 (2) 108 (2007)
  129. Kolodyazhny V M, Rvachov V A Cybern Syst Anal 43 (6) 893 (2007)
  130. Bityutskaya L A, Distler V V et al Phys. Solid State 49 (7) 1382 (2007)
  131. Lagutkin V N, Radchenko Yu V J. Commun. Technol. Electron. 52 (1) 28 (2007)
  132. Павлов А Н, Анищенко В С Uspekhi Fizicheskikh Nauk 177 (8) 859 (2007)
  133. Hennen B, Rotariu I, Steinbuch M 2007 American Control Conference, (2007) p. 570
  134. Ovchinnikov P E, Semin Yu A Radiophys Quantum Electron 50 (4) 317 (2007)
  135. Ryabinkov A I, Kaminker A D, Varshalovich D A Monthly Notices of the Royal Astronomical Society 376 (4) 1838 (2007)
  136. Novikov L V J. Commun. Technol. Electron. 51 (11) 1261 (2006)
  137. Mygal V P, Phomin A S Tech. Phys. Lett. 32 (6) 484 (2006)
  138. Novikov L V J. Commun. Technol. Electron. 51 (6) 663 (2006)
  139. Zakharov Yu P, Antonov V M et al Plasma Phys. Rep. 32 (3) 183 (2006)
  140. Sharov S A, Dolenko S A, Persiantsev I G Pattern Recognit. Image Anal. 16 (1) 65 (2006)
  141. Sharov S A, Orlov Yu V, Persiantsev I G Pattern Recognit. Image Anal. 16 (1) 68 (2006)
  142. Kharintsev S S, Galimullin D Z et al Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 65 (2) 292 (2006)
  143. Oshurko V B Tech. Phys. Lett. 32 (8) 691 (2006)
  144. Sidorenko A V, Solonovich N A J. Commun. Technol. Electron. 51 (4) 446 (2006)
  145. Balashov Yu A, Glaznev V N Geochem. Int. 44 (2) 109 (2006)
  146. Visheratin K N, Kamenogradskii N E et al Izv. Atmos. Ocean. Phys. 42 (2) 184 (2006)
  147. Voloshin V I, Korchinskii V M Kosmìčna nauka ì tehnologìâ 12 (5-6) 15 (2006)
  148. Dremin I M Nuclear Physics A 767 233 (2006)
  149. Distler V V, Bityutskaya L A et al Dokl. Earth Sc. 407 (1) 335 (2006)
  150. Kravchenko V F, Lazorenko O V et al Dokl. Math. 74 (2) 767 (2006)
  151. EFIMOV V G Nondestructive Testing and Evaluation 21 (1) 27 (2006)
  152. Kharintsev S S, Kamalova D I et al Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 61 (1-2) 149 (2005)
  153. Истомин И А, Istomin I A и др ТМФ 142 (1) 148 (2005)
  154. Lazorenko O V, Lazorenko S V, Chernogor L F Kosmìčna nauka ì tehnologìâ 11 (5-6) 22 (2005)
  155. Ivanov L M, Mel’nichenko O V Phys Oceanogr 15 (2) 92 (2005)
  156. Dremin I M Phys. Atom. Nuclei 68 (3) 508 (2005)
  157. Rushchitsky J J, Cattani C, Terletskaya E V Int Appl Mech 41 (4) 374 (2005)
  158. Istomin I A, Kotlyarov O L, Loskutov A Yu Theor Math Phys 142 (1) 128 (2005)
  159. Amosov G G, Man?ko V I Theor Math Phys 142 (2) 306 (2005)
  160. Chesnokov Yu V, Chizhikov V I Measurement Techniques 47 (4) 417 (2004)
  161. Voloshin V I, Korchinskii V M, Negoda A A Kosmìčna nauka ì tehnologìâ 10 (5-6) 178 (2004)
  162. Dremin I M Phys. Atom. Nuclei 67 (1) 41 (2004)
  163. Voloshin V I, Bushuev Y I et al Kosmìčna nauka ì tehnologìâ 10 (5-6) 187 (2004)
  164. Abramochkin E G, Volostnikov V G Uspekhi Fizicheskikh Nauk 174 (12) 1273 (2004)
  165. Chukalina M V, Dubrovskii Yu V, Funke H Low Temperature Physics 30 (11) 930 (2004)
  166. Fedorov M V, Chuev G N et al Phys. Rev. E 70 (5) (2004)
  167. Grafova I B, Grafov B M Russian Journal of Electrochemistry 39 (2) 130 (2003)
  168. Svistkov A L, Evlampieva S E Journal of Applied Mechanics and Technical Physics 44 (5) 727 (2003)
  169. Belozerova T S, Frick P G, Henner V K Phys. Atom. Nuclei 66 (7) 1269 (2003)
  170. Borisenko N A, Fertman A D Instruments and Experimental Techniques 46 (2) 164 (2003)
  171. Rotanova N M, Bondar T N, Kovalevskaya E V Russ. J. Earth Sci. 5 (5) 375 (2003)
  172. Ivanov A A, Krasil’nikov A D, Pravdin M I Jetp Lett. 78 (11) 695 (2003)
  173. Ivanov O, Nechitailo V, Dremin I Handbook of Scaling Methods in Aquatic Ecology (2003) p. 279
  174. Ellis J, Mavromatos N E et al A&A 402 (2) 409 (2003)
  175. Dremin I M, Furletov V I et al Control Engineering Practice 10 (6) 599 (2002)
  176. Dremin I M Uspekhi Fizicheskikh Nauk 172 (5) 551 (2002)
  177. Perov D V, Rinkevich A B Russian Journal of Nondestructive Testing 38 (4) 288 (2002)
  178. Perov D V, Rinkevich A B, Smorodinskii Ya G Russian Journal of Nondestructive Testing 38 (12) 869 (2002)
  179. Ippolitov I I, Kabanov M V, Loginov S V Russian Physics Journal 45 (11) 1086 (2002)
  180. Medvinskii A B, Petrovskii S V et al Uspekhi Fizicheskikh Nauk 172 (1) 31 (2002)
  181. Dremin I M Surveys in High Energy Physics 16 (3-4) 141 (2001)
  182. Man’ko M A Journal of Russian Laser Research 22 (6) 505 (2001)
© Успехи физических наук, 1918–2026
Электронная почта: ufn@ufn.ru Телефоны и адреса редакции О журнале Пользовательское соглашение