[en] We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “classic” wavelet-based decomposition and the empirical mode decomposition (EMD). We compare the reconstruction skills and the period detection ability of the method with the well-established EMD on toys examples and the ENSO climate index. It appears that the EWMD accurately decomposes and reconstructs a given signal (with the same efficiency as the EMD), it is better at detecting prescribed periods and is less sensitive to noise. This work provides the first version of the EWMD. Even though there is still room for improvement, it turns out that preliminary results are highly promising.
Disciplines :
Mathématiques
Auteur, co-auteur :
Deliège, Adrien ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Langue du document :
Anglais
Titre :
A New Wavelet-Based Mode Decomposition for Oscillating Signals and Comparison with the Empirical Mode Decomposition
Date de publication/diffusion :
avril 2016
Nom de la manifestation :
13th International Conference on Information Technology : New Generations
Nicolay, S.: A wavelet-based mode decomposition. European Physical Journal B 80, 223–232 (2011)
Arneodo, A., Audit, B., Decoster, N., Muzy, J.F., Vaillant, C.: Wavelet based multifractal formalism: applications to DNA sequences, satellite images of the cloud structure, and stock market data. In: The Science of Disasters: Climate Disruptions. Heart Attacks, and Market Crashes, pp. 27–102. Springer, Berlin (2002)
Daubechies, I.: Ten lectures on Wavelets. SIAM (1992)
Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press (1999)
Gilles, J.: Empirical wavelet transform. IEEE Transactions on Signal Processing 61(16), 3999–4010 (2013)
Flandrin, P., Rilling, G., Goncalves, P.: Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters 11(2), 112–114 (2004)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society of London A 454, 903–995 (1998)
Rilling, G., Flandrin, P., Goncalves, P.: On empirical mode decomposition and its algorithms. In: IEEE-EURASIP Workshop Nonlinear Signal Image Processing (NSIP) (2003)
Wu, Z., Huang, N.E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptative Data Analysis 1, 1–41 (2009)
Torres, M.E., Colominas, M.A., Schlotthauer, G., Flandrin, P.: A complete ensemble empirical mode decomposition with adaptive noise. In: IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP) (2011)
Ashok, K., Behera, S., Rao, S., Weng, H., Yamagata, T.: El niño modoki and its possible teleconnection. Journal of Geophysical Research 112(10.1029) (2007)
Glantz, M.: Currents of Change: Impacts of ElNiño and La Niña on climate society. Cambridge University Press (2001)
Hsiang, S., Meng, K., Cane, M.: Civil conflicts are associated with the global climate. Nature 476(7361), 438–441 (2011)
Yeh, S., Kug, J., Dewitte, B., Kwon, M., Kirtman, B., Jin, F.: El niño in a changing climate. Nature 461(7263), 511–514 (2009)
Moron, V., Vautard, R., Ghil, M.: Trends, interdecadal and interannual oscillations in global sea-surface temperatures. Climate Dynamics 14(7), 545–569 (1998)
Nicolay, S., Mabille, G., Fettweis, X., Erpicum, M.: 30 and 43months period cycles found in air temperature time series using the morlet wavelet method. Climate dynamics 33(7), 1117–1129 (2009)
