Abstract
The problem of digital filtering of signals with localized disturbances is considered by the example of complex multicomponent and noisy processes detected in a seismic survey. The possibility to perform the time-and-frequency analysis of the corresponding signals with the use of wavelets and empirical modes is discussed. It is noted that decomposition of the signal into empirical modes is a promising instrument for studying the structure of experimental data, which extends the possibilities of studying the dynamics of systems with time-variable characteristics.
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References
A. Grossman and J. Morlet, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 15(4), 273 (1984).
I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992).
Y. Meyer, Wavelets: Algorithms and Applications (SIAM, Philadelphia, 1993).
Y. Meyer, Wavelets and Operators (Cambridge Univ. Press, Cambridge, 1993).
A. A. Koronovskii and A. E. Hramov, Continuous Wavelet Analysis and Its Applications (Fizmatlit, Moscow, 2003) [in Russian].
J. Morlet, G. Arens, I. Fourgeau, and D. Giard, Geophysics 47(2), 203 (1982).
S. G. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998).
P. S. Addison, The Illustrated Wavelet Transform Handbook: Applications in Science, Engineering, Medicine and Finance (IOP Publishing, Philadelphia, 2002).
Wavelets in Physics, Ed. by J. C. Berg (Cambridge Univ. Press, Cambridge, 1993).
Wavelets in Geophysics, Ed. by E. Foufoula-Georgiou and P. Kumar (Academic, New York, 1994).
A. Aldroubi and M. Unser, Wavelets in Medicine and Biology (CRC Press, Boca Raton, FL, 1996).
N. M. Astaf’eva, Usp. Fiz. Nauk 166, 1145 (1996).
V. G. Anfinogentov, A. A. Koronovskii, and A. E. Hramov, Izv. RAN, Ser. Fiz. 64, 2383 (2000).
A. A. Koronovskii, V. I. Ponomarenko, M. D. Prokhorov, and A. E. Hramov, Radiotekh. Elektron. (Moscow) 52, 581 (2007) [J. Commun. Technol. Electron. 52, 544 (2007)].
E. Sitnikova, A. E. Hramov, A. A. Koronovskii, and G. van Luijtelaar, J. Neurosci. Methods 180, 304 (2009).
A. E. Hramov, A. A. Koronovskii, V. I. Ponomarenko, and M. D. Prokhorov, Phys. Rev. E 75, 056207 (2007).
A. A. Koronovskii, V. I. Ponomarenko, M. D. Prokhorov, and A. E. Hramov, Zh. Tekh. Fiz. 77(9), 6 (2007) [Tech. Phys. 52, 1106 (2007)].
J. Bendat and A. Piersol, Random Data. Analysis and Measurement Procedures (Mir, Moscow, 1989; Wiley, New York, 1986).
N. E. Huang, Z. Shen, S. R. Long, et al., Proc. R. Soc. London, Ser. A 454(1971), 903 (1998).
E. P. S. Neto, M. A. Custaud, J. C. Cejka, et al., Meth. Inform. Med. 3(1), 60 (2004).
Z. Wu and N. E. Huang, Proc. Royal Soc. A 460(2046), 1597 (2004).
N. E. Huang, Z. Shen, and S. R. Long, Annual Rev. Fluid Mech. 31, 417 (1999).
P. Flandrin and P. Goncalvés, Int. J. Wavelets, Multiresolution Inform. Process. 2, 477 (2004).
A. E. Filatova, A. E. Artem’ev, A. A. Koronovskii, A. N. Pavlov, and A. E. Hramov, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din. 18(3), 3 (2010).
A. E. Filatova, A. A. Ovchinnikov, A. A. Koronovskii, and A. E. Hramov, Vestn. TGU, Ser. Estestv. Tekh. Nauki 15, 524 (2010).
I. M. Dremin, O. V. Ivanov, and V. A. Nechitailo, Usp. Fiz. Nauk 171, 465 (2001).
A. N. Pavlov, V. A. Makarov, E. Mosekilde, and O. V. Sosnovtseva, Briefings in Bioinformatics 7, 375 (2006).
O. V. Sosnovtseva, A. N. Pavlov, E. Mosekilde, K. P. Yip, N.-H. Holstein-Rathlou, and D. J. Marsh, Am. J. Physiol. Renal Physiol. 293, F1545 (2007).
C.-K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, Chaos 5(1), 82 (1995).
J. F. Muzy, E. Bacry, and A. Arneodo, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 245 (1994).
A. N. Pavlov and V. S. Anishchenko, Usp. Fiz. Nauk 177, 859 (2007).
P. Ch. Ivanov, L. A. Nunes Amaral, A. L. Goldberger, et al., Nature 399(6734), 461 (1999).
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Original Russian Text © A.N. Pavlov, A.E. Filatova, A.E. Hramov, 2011, published in Radiotekhnika i Elektronika, 2011, Vol. 56, No. 9, pp. 1099–1106.
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Pavlov, A.N., Filatova, A.E. & Hramov, A.E. Digital filtering and time-and-frequency analysis of nonstationary signals on the basis of wavelets and empirical modes. J. Commun. Technol. Electron. 56, 1098–1104 (2011). https://doi.org/10.1134/S1064226911080092
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DOI: https://doi.org/10.1134/S1064226911080092