Technical Physics

, Volume 63, Issue 12, pp 1711–1717 | Cite as

Comparison of the Wavelet and Gabor Transforms in the Spectral Analysis of Nonstationary Signals

  • S. V. BozhokinEmail author
  • I. M. Sokolov


Two approaches to the analysis of nonstationary random processes (short-time Fourier transform and continuous wavelet transform) are compared. The comparison is based on the study of several model signals with known time–frequency characteristics. The application of the approaches is also analyzed in the study of spectral dynamics of fluorescence of cold atomic clouds excited by pulsed radiation. It is shown that the two approaches make it possible to reveal the main specific features of the signals under study. However, the continuous wavelet transform has several advantages, since the optimal conditions for the analysis using the short-time Fourier transform are reached if additional calculations aimed at determination of the optimal width of the window are performed.



  1. 1.
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).CrossRefGoogle Scholar
  2. 2.
    S. Mallat, A Wavelet Tour of Signal Processing, 3rd ed. (Academic, New York, 2008).zbMATHGoogle Scholar
  3. 3.
    V. P. Dvorkovich and A. V. Dvorkovich, Metrological Assurance for Video Information Systems (Tekhnosfera, 2015).Google Scholar
  4. 4.
    C. K. Chui, An Introduction to Wavelets (Academic, New York, 1992).zbMATHGoogle Scholar
  5. 5.
    N. K. Smolentsev, An Introduction to Wavelet Theory. Wavelets in Mathlab (DMK Press, Moscow, 2008).Google Scholar
  6. 6.
    R. K. R. Yarlagadda, Analog and Digital Signals and Systems (Springer, 2010).CrossRefzbMATHGoogle Scholar
  7. 7.
    C. K. Chui and Q. Jiang, Applied Mathematics. Data Compression. Spectral Methods, Fourier Analysis, Wavelets and Applications (Atlantis, 2013).Google Scholar
  8. 8.
    D. A. Andreev, S. V. Bozhokin, I. D. Venevtsev, and K. T. Zhunusov, Tech. Phys. 59, 1428 (2014).CrossRefGoogle Scholar
  9. 9.
    A. E. Hramov, A. A. Koronovskii, V. A. Makarov, A. N. Pavlov, and E. Sitnikova, Wavelets in Neuroscience (Springer, 2015).CrossRefzbMATHGoogle Scholar
  10. 10.
    P. S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance, 2nd ed. (CRC Press, 2017).zbMATHGoogle Scholar
  11. 11.
    C. Blatter, Wavelets—Eine Einführung (Vieweg & Sohn, 1998).Google Scholar
  12. 12.
    V. P. D’yakonov, Wavelets from Theory to Practice (Solon-R, Moscow, 2002).Google Scholar
  13. 13.
    S. V. Bozhokin, Tech. Phys. 57, 900 (2012).CrossRefGoogle Scholar
  14. 14.
    S. V. Bozhokin, S. V. Zharko, N. V. Larionov, A. N. Lit-vinov, and I. M. Sokolov, Tech. Phys. 62, 837 (2017).CrossRefGoogle Scholar
  15. 15.
    M. K. Kiymik, I. Güler, A. Dizibüyük, and M. Akin, Comput. Biol. Med. 35, 603 (2005).CrossRefGoogle Scholar
  16. 16.
    M. Akin, J. Med. Syst. 26, 241 (2002).CrossRefGoogle Scholar
  17. 17.
    E. Sitnikova, A. E. Hramov, A. A. Koronovsky, and G. Luijtelaar, J. Neurosci. Methods 180, 304 (2009).CrossRefGoogle Scholar
  18. 18.
    E. D. Ryan, J. T. Cramer, A. D. Egan, M. J. Hartman, and T. J. Herda, J. Electromyogr. Kinesiol. 18, 54 (2008).CrossRefGoogle Scholar
  19. 19.
    M. R. Canal, J. Med. Syst. 34, 91 (2010).CrossRefGoogle Scholar
  20. 20.
    L. Coppola, Q. Liu, S. Buso, D. Boroyevich, and A. Bell, IEEE Trans. Ind. Electron. 55, 880 (2008).CrossRefGoogle Scholar
  21. 21.
    S. H. Cho, G. Jang, and S. H. Kwon, IEEE Trans. Power Delivery 25, 494 (2010).CrossRefGoogle Scholar
  22. 22.
    S. Dass, M. S. Holi, and K. S. Rajan, Int. J. Eng. Res. Technol. 2, 636 (2013).CrossRefGoogle Scholar
  23. 23.
    E. D. Ubeyli and I. Guler, Comput. Biol. Med. 34, 345 (2004).CrossRefGoogle Scholar
  24. 24.
    L. Cnockaert, P. F. Migeotte, L. Daubigny, G. K. Prisk, F. Grenez, and R. C. Sa, IEEE Trans. Biomed. Eng. 55, 1640 (2008).CrossRefGoogle Scholar
  25. 25.
    T. M. E. Nijsen, R. M. Aarts, P. J. M. Cluitmans, and P. A. M. Griep, IEEE Trans. Inf. Technol. Biomed. 14, 1197 (2010).CrossRefGoogle Scholar
  26. 26.
    E. Shokrollahi, G. Zargar, and M. A. Riahi, Int. J. Sci. Emerging Technol. 5, 291 (2013).Google Scholar
  27. 27.
    Yi Hu and P. C. Loisou, IEEE Trans. Audio, Speech Lang. Process. 16, 229 (2008).CrossRefGoogle Scholar
  28. 28.
    J. Benesty, J. Chen, and Y. Huang, IEEE Trans. Audio, Speech Lang. Process. 16, 757 (2008).CrossRefGoogle Scholar
  29. 29.
    F. Jaskolski, C. Mulle, and O. Manzoni, J. Neurosci. Methods 146, 42 (2005).CrossRefGoogle Scholar
  30. 30.
    G. Labeyrie, E. Vaujour, C. A. Muller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, Phys. Rev. Lett. 91, 223904 (2003).ADSCrossRefGoogle Scholar
  31. 31.
    S. Balik, R. G. Olave, C. I. Sukenik, M. D. Havey, V. M. Datsyuk, I. M. Sokolov, and D. V. Kupriyanov, Phys. Rev. A 72, 051402 (2005).ADSCrossRefGoogle Scholar
  32. 32.
    S. Balik, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, Phys. Rev. A 79, 033418 (2009).ADSCrossRefGoogle Scholar
  33. 33.
    S. Balik, A. L. Win, M. D. Havey, I. M. Sokolov, and D. V. Kupriyanov, Phys. Rev. A 87, 053817 (2013).ADSCrossRefGoogle Scholar
  34. 34.
    J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, Phys. Rev. Lett. 113, 133602 (2014).ADSCrossRefGoogle Scholar
  35. 35.
    M. O. Araujo, I. Kresic, R. Kaiser, and W. Guerin, Phys. Rev. Lett. 117, 073002 (2016).ADSCrossRefGoogle Scholar
  36. 36.
    S. J. Roof, K. J. Kemp, M. D. Havey, and I. M. Sokolov, Phys. Rev. Lett. 117, 073003 (2016).ADSCrossRefGoogle Scholar
  37. 37.
    W. Guerin, M. O. Araujo, and R. Kaiser, Phys. Rev. Lett. 116, 083601 (2016).ADSCrossRefGoogle Scholar
  38. 38.
    I. M. Sokolov, J. Exp. Theor. Phys. 125, 384 (2017).ADSCrossRefGoogle Scholar
  39. 39.
    S. V. Bozhokin and I. M. Sokolov, Opt. Spectrosc. 123, 858 (2017).ADSCrossRefGoogle Scholar
  40. 40.
    Ya. A. Fofanov, A. S. Kuraptsev, I. M. Sokolov, and M. D. Havey, Phys. Rev. A 87, 063839 (2013).ADSCrossRefGoogle Scholar
  41. 41.
    I. M. Sokolov, A. S. Kuraptsev, D. V. Kupriyanov, M. D. Havey, and S. Balik, J. Mod. Opt. 60, 50 (2013).ADSCrossRefGoogle Scholar
  42. 42.
    V. V. Grubov, E. Sitnikova, A. N. Pavlov, A. A. Koronovskii, and A. E. Hramov, Phys. A 486, 206 (2017).CrossRefGoogle Scholar
  43. 43.
    U. V. Borodina and R. R. Aliev, Neurocomputing 121, 551 (2013).CrossRefGoogle Scholar
  44. 44.
    A. Bijaoui, in Wavelets in Physics, Ed. by J. C. van den Berg (Cambridge Univ. Press, 1999), p. 77.Google Scholar
  45. 45.
    J. W. Baker, Bull. Seismol. Soc. Am. 97, 1486 (2007).CrossRefGoogle Scholar
  46. 46.
    Y. Deng, Z. Wu, L. Chai, C. Wang, K. Yamane, R. Morita, M. Yamashita, and Z. Zhan, Opt. Express 13, 2120 (2005).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia

Personalised recommendations