WAVELET-­ANALYSIS AND EXAMPLES OF ITS APPLICATIONS


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Pavlov A. N. WAVELET-­ANALYSIS AND EXAMPLES OF ITS APPLICATIONS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 5, pp. 99-111. DOI: https://doi.org/10.18500/0869-6632-2009-17-5-99-111


Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

DOI: 
10.18500/0869-6632-2009-17-5-99-111
Literature

1. Grossman A., Morlet J. Decomposition of Hardy functions into square intergable wavelets of constant shape // SIAM J. Math. Anal. 1984. Vol. 15. P. 723.

2. Daubechies I. Ten lectures on wavelets (Philadelphia: S.I.A.M., 1992).

3. Meyer Y. Wavelets: Algorithms and applications (Philadelphia: S.I.A.M., 1993).

4. Kaiser G. A friendly guide to wavelets (Boston: Birkhauser, 1994).  ̈

5. Астафьева Н.М. Вейвлет-анализ: основы теории и примеры применения // Успехи физических наук. 1996. T. 166, No 11. С. 1145.

6. Mallat S.G. A wavelet tour of signal processing (New York: Academic Press, 1998).

7. Короновский А.А., Храмов А.Е. Непрерывный вейвлетный анализ и его приложения. (М.: Физматлит, 2003).

8. Addison P.S. The illustrated wavelet transform handbook: applications in science, engineering, medicine and finance (Bristol, Philadelphia: IOP Publishing, 2002).

9. Vetterli M., Kovacevic J. Wavelets and subband coding (NJ: Prentice Hall, 1995).

10. Holstein-Rathlou N.-H., Leyssac P.P. TGF-mediated oscillations in the proximal intratubular pressure: Differences between spontaneously hypertensive rats and Wistar-Kyoto rats // Acta Physiol. Scand. 1986. Vol. 126. P. 333.

11. Marsh D.J., Sosnovtseva O.V., Pavlov A.N., Yip K.-P., Holstein-Rathlou N.-H. Frequency encoding in renal blood flow regulation // American Journal of Physiology (Regul. Integr. Comp. Physiol.). 2005. Vol. 288. P. R1160.

12. Sosnovtseva O.V., Pavlov A.N., Mosekilde E., Yip K.-P., Holstein-Rathlou N.-H., Marsh D.J. Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats // American Journal of Physiology (Renal Physiology). 2007. Vol. 293. P. F1545.

13. Moreno A., Garsia-Gonzalez V., Sanches-Jimenez A., Panetsos F. Principalis, oralis and interpolaris responses to whisker movements provoked by air jets in rats // NeuroReport. 2005. Vol. 16. P. 1569.

14. Pavlov A.N., Makarov V.A., Mosekilde E., Sosnovtseva O.V. Application of wavelet-based tools to study the dynamics of biological processes // Briefings in Bioinformatics. 2006. Vol. 7. P. 375.

15. Carvell G.E., Simons D.J. Task- and subject-related differences in sensorimotor behavior during active touch // Somat. Mot. Res. 1995. Vol. 12. P. 11.

16. Garabedian C.E., Jones S.R., Merzenich M.M., Dale A., Moore C.I. Band-pass response properties of rat SI neurons // J. Neurophysiology. 2003. Vol. 90. P. 1379.

17. Павлов А.Н. Детектирование информационных сигналов на основе реконструкции динамических систем и дискретного вейвлет-преобразования // Известия вузов. Прикладная нелинейная динамика. 2008. Т. 16, No 6. С. 3.

18. Kocarev L., Halle K.S., Eckert K., Chua L.O., Parlitz U. Experimental demonstration of secure communications via chaotic synchronization // Int. J. Bifurcation and Chaos. 1992. Vol. 2. P. 709.

19. Cuomo K.M., Oppenheim A.V., Strogatz S.H. Synchronization of Lorenz-based chaotic circuits with application to communications // IEEE Trans. Circuits Syst. 1993. Vol. 40. P. 626.

20. Parlitz U., Kocarev L. Multichannel communication using autosynchronization // Int. J. Bifurcation and Chaos. 1996. Vol. 6. P. 581.

21. Дмитриев А.С., Панас А.И. Динамический хаос. Новые носители информации для систем связи (М: Физматлит, 2002).

22. Короновский А.А., Москаленко О.И., Попов П.В., Храмов А.Е. Способ скрытой передачи информации, основанный на явлении обобщенной синхронизации // Известия РАН. Серия физическая. 2008. Т. 72, No 1. C. 143.

23. Anishchenko V.S., Pavlov A.N. Global reconstruction in application to multichannel communication // Phys. Rev. E. 1998. Vol. 57. P. 2455.

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BibTeX

@article{Павлов -IzvVUZ_AND-17-5-99,
author = {A. N. Pavlov},
title = {WAVELET-­ANALYSIS AND EXAMPLES OF ITS APPLICATIONS},
year = {2009},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {17},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/wavelet-analysis-and-examples-of-its-applications},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2009-17-5-99-111},pages = {99--111},issn = {0869-6632},
keywords = {time series analysis,wavelet­transform,nonstationary processes.},
abstract = {Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal. }}