ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Anisimov A. A., Pavlova O. N., Tupicyn A. N., Pavlov A. N. Wavelet-analysis of chirps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 5, pp. 3-11. DOI: 10.18500/0869-6632-2008-16-5-3-11

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Wavelet-analysis of chirps

Anisimov Aleksej Aleksandrovich, Saratov State University
Pavlova Olga Nikolaevna, Saratov State University
Tupicyn Anatolij Nikolaevich, Saratov State University
Pavlov Aleksej Nikolaevich, Saratov State University

The paper discusses the possibilities of studying of rhythmic processes with linearly changed frequencies («chirps») based on the wavelet-analysis. Limitations of the continuous wavelet-transformation in the analysis of superpositions of signals with linear frequency modulation are formulated. Effects of the interference and the modulation of rhythmic processes are considered. 

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  1. Gabor D. Theory of communication // J. Inst. Electr. Eng. London. 1946. Vol. 93. P. 429.
  2. Peng C.-K., Havlin S., Stanley H.E., Goldberger A.L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series // Chaos. 1995. Vol. 5. P. 82.
  3. Peng C.-K., Buldyrev S.V., Havlin S., Simons M., Stanley H.E., Goldberger A.L. Mosaic organization of DNA nucleotides // Phys. Rev. E. 1994. Vol. 49. P. 1685.
  4. Grossmann A., Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape // S.I.A.M. J. Math. Anal. 1984. Vol. 15. P. 723.
  5. Meyer Y. Wavelets: Algorithms and Applications. Philadelphie: S.I.A.M., 1993.
  6. Малла С. Вэйвлеты в обработке сигналов. М.: Мир, 2005.
  7. Короновский А.А., Храмов А.Е. Непрерывный вейвлетный анализ в приложениях к задачам нелинейной динамики. Саратов: ГосУНЦ «Колледж», 2002.
  8. Астафьева Н.М. Вейвлет-анализ: основы теории и примеры применения // Успехи физических наук. 1996. T. 166. С. 1145.
  9. Дремин И.М., Иванов О.В., Нечитайло В.А. Вейвлеты и их применение // Успехи физических наук. 2001. T. 171. С. 465.
  10. Muzy J.F., Bacry E., Arneodo A. The multifractal formalism revisited with wavelets // Int. J. Bifurcation Chaos. 1994. Vol. 4. P. 245.
  11. Павлов А.Н., Анищенко В.С. Мультифрактальный анализ сложных сигналов // Успехи физических наук. 2007. Т. 177. С. 859.
  12. Dremin I.M. Cumulant and factorial moments in perturbative gluodynamics // Phys. Lett. B. 1993. Vol. 313. P. 209.
  13. Sosnovtseva O.V., Pavlov A.N., Brazhe N.A., Brazhe A.R., Erokhova L.A., Maksimov G.V., Mosekilde E. Interference microscopy under double-wavelet analysis: A new tool to studying cell dynamics // Physical Review Letters. 2005. Vol. 94. P. 218103.
  14. 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. 2005. Vol. 288. P. R1160.
  15. 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(4). P. 375.
  16. Sosnovtseva O.V., Pavlov A.N., Mosekilde E., Holstein-Rathlou N.-H., Marsh D.J. Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation // Phys. Rev. E. 2004. Vol. 70. P. 031915.
  17. Sosnovtseva O.V., Pavlov A.N., Mosekilde E., Holstein-Rathlou N.-H., Marsh D.J. Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics // Physiological Measurement. 2005. Vol. 26. P. 351.
  18. Wand H., Siu K., Ju K., Chon K.H. A high resolution approach to estimating time-frequency spectra and their amplitudes // Annals of Biomedical Engineering. 2006. Vol. 34. P. 326.
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