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


For citation:

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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Russian
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Article
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519.6:577.359

Wavelet-analysis of chirps

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

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. 

Key words: 
Reference: 
  1. Gabor D. Theory of communication. J. Inst. Electr. Eng. London. 1946;93(3):429–457.
  2. Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5(1):82–87. DOI: 10.1063/1.166141.
  3. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Phys. Rev. E. 1994;49(2):1685–1689. DOI: 10.1103/physreve.49.1685.
  4. Grossmann A, Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape. S.I.A.M. J. Math. Anal. 1984;15(4):723–736. DOI: 10.1137/0515056.
  5. Meyer Y. Wavelets: Algorithms and Applications. Philadelphie: S.I.A.M.; 1993. 133 p.
  6. Mallat S. A Wavelet Tour of Signal Processing. Academic Press; 2008. 832 p.
  7. Koronovskii AA, Khramov AE. Continuous Wavelet Analysis in Applications to Problems of Nonlinear Dynamics. Saratov: «College»; 2002. 176 p. (in Russian).
  8. Astaf’eva NM. Wavelet analysis: basic theory and some applications. Phys. Usp. 1996;39(11):1085–1108. DOI: 10.1070/PU1996v039n11ABEH000177.
  9. Dremin IM, Ivanov OV, Nechitailo VA. Wavelets and their uses. Phys. Usp. 2001;44(5):447–478. DOI: 10.1070/PU2001v044n05ABEH000918.
  10. Muzy JF, Bacry E, Arneodo A. The multifractal formalism revisited with wavelets. Int. J. Bifurcat. Chaos. 1994;4(2):245–302. DOI: 10.1142/S0218127494000204.
  11. Pavlov AN, Anishchenko VS. Multifractal analysis of complex signals. Phys. Usp. 2007;50(8):819–834. DOI: 10.1070/PU2007v050n08ABEH006116.
  12. Dremin IM. Cumulant and factorial moments in perturbative gluodynamics. Phys. Lett. B. 1993;313(1–2):209–212. DOI: 10.1016/0370-2693(93)91214-8.
  13. Sosnovtseva OV, Pavlov AN, Brazhe NA, Brazhe AR, Erokhova LA, Maksimov GV, Mosekilde E. Interference microscopy under double-wavelet analysis: A new tool to studying cell dynamics. Phys. Rev. Lett. 2005;94(21):218103. DOI: 10.1103/physrevlett.94.218103.
  14. Marsh DJ, Sosnovtseva OV, Pavlov AN, Yip KP, Holstein-Rathlou NH. Frequency encoding in renal blood flow regulation. American Journal of Physiology. 2005;288(5):R1160–R1167. DOI: 10.1152/ajpregu.00540.2004.
  15. Pavlov AN, Makarov VA, Mosekilde E, Sosnovtseva OV. Application of wavelet-based tools to study the dynamics of biological processes. Briefings in Bioinformatics. 2006;7(4):375–389. DOI: 10.1093/bib/bbl041.
  16. Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation. Phys. Rev. E. 2004;70(3):031915. DOI: 10.1103/physreve.70.031915.
  17. Sosnovtseva OV, Pavlov AN, Mosekilde E, Holstein-Rathlou NH, Marsh DJ. Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics. Physiological Measurement. 2005;26(4):351–362. DOI: 10.1088/0967-3334/26/4/002.
  18. Wand H, Siu K, Ju K, Chon KH. A high resolution approach to estimating time-frequency spectra and their amplitudes. Annals of Biomedical Engineering. 2006;34(2):326–338. DOI: 10.1007/s10439-005-9035-y.
Received: 
05.11.2007
Accepted: 
12.02.2008
Published: 
31.12.2008
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