Abstract:
Two algorithms of evaluation of the continuous wavelet transform with the Morlet wavelet are presented. The first one is the solution of PDE with transformed signal, which plays a role of the initial value. The second allows to explore the influence of central frequency variation via the diffusion smoothing of the data modulated by the harmonic functions. These approaches are illustrated by the analysis of the chaotic oscillations of the coupled Roessler systems.
Citation:
E. B. Postnikov, “Wavelet transform with the Morlet wavelet: calculation methods based
on a solution of diffusion equations”, Computer Research and Modeling, 1:1 (2009), 5–12
\Bibitem{Pos09}
\by E.~B.~Postnikov
\paper Wavelet transform with the Morlet wavelet: calculation methods based
on a solution of diffusion equations
\jour Computer Research and Modeling
\yr 2009
\vol 1
\issue 1
\pages 5--12
\mathnet{http://mi.mathnet.ru/crm616}
\crossref{https://doi.org/10.20537/2076-7633-2009-1-1-5-12}
Linking options:
https://www.mathnet.ru/eng/crm616
https://www.mathnet.ru/eng/crm/v1/i1/p5
This publication is cited in the following 2 articles:
D. Yu. Vasil'ev, P. V. Velmovsky, “Analysis of Surface Air Temperature Characteristics over the Territory of Russia for 1930–2021”, Atmos Ocean Opt, 37:S1 (2024), S72
I M Dantsevich, M N Lyutikova, AY Novikov, S A Osmukha, “Analysis of a nonlinear system dynamics in the Morlet wavelet basis”, IOP Conf. Ser.: Mater. Sci. Eng., 873:1 (2020), 012035
Citation in format AMSBIB
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