Abstract.
We propose a wavelet-based method for analyzing non-stationary data. The idea, inspired by the empirical mode decomposition, is to decompose a data set into a finite number of components, well separated in the time-frequency plane, plus a residue, such that each component has a zero mean and is associated to one frequency only. When applied to climatic data, this method gives interesting results.
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References
M. Mudelsee, Climate Time Series Analysis: Classical Statistical and Bootstrap Methods (Springer, Dordrecht, 2010)
M.B. Priestley, Spectral Analysis and Time Series (Academic Press, London, 1981), Vols. I and II
E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University Press, 1948)
P. Goupillaud, A. Grossman, J. Morlet, Geoexploration 23, 85 (1984)
R. Kronland-Martinet, J. Morlet, A. Grossmann, Int. J. Pattern Recogn. Artific. Intellig. 1, 273 (1987)
N.E. Huang et al., Proc. Roy. Soc. London A 454, 903 (1998)
G. Rilling, P. Flandrin, IEEE transactions on signal processing 56, 85 (2008)
I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphie, 1992)
S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, New-York, 1999)
B. Torresani, Analyse Continue par Ondelettes (CNRS Éditions, Paris, 1995)
E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, Phys. Rev. Lett. 64, 745 (1990)
A. Arneodo, B. Audit, N. Decoster, J.-F. Muzy, C. Vaillant, The Science of Disaster, edited by A. Bunde, H.J. Schellnhuber (Springer, Berlin, 2002), pp. 27–102
Wavelets and their Applications, edited by M.B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, L. Raphael (Jones and Bartlett, Boston, 1992)
M.B. Priestley, J. Time Ser. Anal. 17, 85 (1996)
S. Nicolay, Analyse de séquences ADN par la transformée en ondelettes, Ph.D. thesis, University of Liège, 2009
S. Nicolay, G. Mabille, X. Fettweis, M. Erpicum, Clim. Dyn. 33, 1117 (2006)
S.L. Hahn, Hilbert transforms in signal processing (Artech House, Boston, 1996)
D.B. Percival, A.T. Walden, Spectral analysis for physical applications (Cambridge University Press, Cambridge, 1993)
J. Hansen, R. Ruedy, J. Glascoe, M. Sato, J. Geophys. Res. 104, 30997 (1999)
W. Rudloff, World-climates (Wissenschaftliche Verlagsgesellschaft mbH, 1981)
I. Matyasovszky, Theor. Appl. Climatol. 101, 281 (2010)
M. Paluš, D. Novotná, Nonlinear Proc. Geophys., 13, 287 (2006)
K. Levenberg, Quart. Appl. Math. 2, 164 (1944)
G. Mabille, S. Nicolay, Eur. Phys. J. Special Topics 174, 135 (2009)
S. Nicolay, G. Mabille, X. Fettweis, M. Erpicum, Nonlinear Processes Geophysics 17, 269 (2010)
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Nicolay, S. A wavelet-based mode decomposition. Eur. Phys. J. B 80, 223–232 (2011). https://doi.org/10.1140/epjb/e2011-10756-3
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DOI: https://doi.org/10.1140/epjb/e2011-10756-3