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).
Full text:
(downloads: 112)
Article type: 

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. 

Key words: 
  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.
Short text (in English):
(downloads: 34)