Wavelets; Time-frequency analysis; Mode extraction; EMD; Time series analysis
Abstract :
[en] This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components that build amplitude modulated-frequency modulated signals. The essence of this technique relies on the successive extractions of the dominant ridges of wavelet-based time-frequency representations of the signal under consideration. Our tests on simulated examples indicate strong decomposition and reconstruction skills, trouble-free handling of crossing trajectories in the time-frequency plane, sharp performances in frequency detection in the case of mode-mixing problems, and a natural tolerance to noise. These results are compared with those obtained with empirical mode decomposition. We also show that WIME still gives meaningful results with real-life data, namely, the Oceanic Niño Index.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others Mathematics Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
Author, co-author :
Deliège, Adrien ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Extracting oscillating components from nonstationary time series: A wavelet-induced method
Publication date :
11 September 2017
Journal title :
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
ISSN :
1063-651X
eISSN :
1095-3787
Publisher :
American Physical Society, College Park, United States - Maryland
P. Flandrin, Time-Frequency/Time-Scale Analysis, Wavelet analysis and Its applications (Academic Press, London, 1999).
P. Flandrin, G. Rilling, and P. Goncalves, IEEE Signal Process. Lett. 11, 112 (2004). IESPEJ 1070-9908 10.1109/LSP.2003.821662
N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. London A 454, 903 (1998). 1364-5021 10.1098/rspa.1998.0193
G. Rilling, P. Flandrin, and P. Goncalves, in IEEE-EURASIP Workshop Nonlinear Signal Image Processing (NSIP) (2003).
I. Daubechies, J. Lu, and H.-T. Wu, J. Appl. Comput. Harmonic Anal. 30, 243 (2011). 1063-5203 10.1016/j.acha.2010.08.002
M. Costa, A. A. Priplata, L. Lipsitz, Z. Wu, N. Huang, A. Goldberger, and C.-K. Peng, Europhys. Lett. 77, 68008 (2007). EULEEJ 0295-5075 10.1209/0295-5075/77/68008
D. Cummings, R. Irizarry, N. Huang, T. Endy, A. Nisalak, K. Ungchusak, and D. Burke, Nature (London) 427, 344 (2004). NATUAS 0028-0836 10.1038/nature02225
Z. Wu and N. E. Huang, Adv. Adapt. Data Anal. 1, 1 (2009). 1793-5369 10.1142/S1793536909000047
N. Huang, M.-L. Wu, W. Qu, S. Long, S. Shen, and J. Zhang, Appl. Stochastic Models Bus. Indust. 19, 245 (2003). 1524-1904 10.1002/asmb.501
N. E. Huang and Z. Wu, Rev. Geophys. 46, RG2006 (R) (2008). REGEEP 8755-1209 10.1029/2007RG000228
J. Gilles, IEEE Trans. Signal Proc. 61, 3999 (2013). ITPRED 1053-587X 10.1109/TSP.2013.2265222
A. Arneodo, C. Vaillant, B. Audit, F. Argoul, Y. d'Aubenton Carafa, and C. Thermes, Phys. Rep. 498, 45 (2011). PRPLCM 0370-1573 10.1016/j.physrep.2010.10.001
G. Saracco, P. Guillemain, and R. Kronland-Martinet, IEEE Ultrasonics 2, 881 (1990). 10.1109/ULTSYM.1990.171490
U. Gebhardt and M. Hiete, Geol. Soc., London, Special Pub. 376, 177 (2013). GSSPDQ 0305-8719 10.1144/SP376.12
A. Deliège and S. Nicolay, Pure Appl. Geophys. 173, 2885 (2016). PAGYAV 0033-4553 10.1007/s00024-016-1339-3
A. Deliège and S. Nicolay, Pure Appl. Geophys. 174, 1815 (2017) 10.1007/s00024-017-1491-4.
C. Torrence and G. Compo, Bull. Am. Meteorol. Soc. 79, 61 (1998). BAMIAT 0003-0007 10.1175/1520-0477(1998)079%3C0061:APGTWA%3E2.0.CO;2
E. Gerasimova, B. Audit, S. G. Roux, A. Khalil, O. Gileva, F. Argoul, O. Naimark, and A. Arneodo, Front. Physiol. 5, 176 (2014). 1664-042X 10.3389/fphys.2014.00176
E. Gerasimova-Chechkina, B. Toner, Z. Marin, B. Audit, S. G. Roux, F. Argoul, A. Khalil, O. Gileva, O. Naimark, and A. Arneodo, Front. Physiol. 7, 336 (2016). 1664-042X 10.3389/fphys.2016.00336
I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992).
S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, San Diego, 1999).
S. Nicolay, Eur. Phys. J. B 80, 223 (2011). EPJBFY 1434-6028 10.1140/epjb/e2011-10756-3
S. Mallat, Trans. Am. Math. Soc. 315, 69 (1989). 10.1090/S0002-9947-1989-1008470-5
Y. Meyer and D. Salinger, Wavelets and Operators (Cambridge University Press, Cambridge, 1995), Vol. 1.
F. Auger and P. Flandrin, IEEE Trans. Signal Proc. 43, 1068 (1995). ITPRED 1053-587X 10.1109/78.382394
E. Chassande-Mottin, I. Daubechies, F. Auger, and P. Flandrin, IEEE Signal Process. Lett. 4, 293 (1997). IESPEJ 1070-9908 10.1109/97.633772
E. Chassande-Mottin, F. Auger, and P. Flandrin, Time-frequency/time-scale reassignment, in Wavelets and Signal Processing, edited by L. Debnath (Birkhäuser, Boston, 2003), pp. 233-267.
I. Daubechies and S. Maes, Wavelets in Medicine and Biology (CRC Press, New York, 1996), pp. 527-546.
M. E. Torres, M. A. Colominas, G. Schlotthauer, and P. Flandrin, in IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP) (IEEE, Piscataway, NJ, 2011).
A. G. Barnston, M. K. Tippett, M. L. L'Heureux, S. Li, and D. G. DeWitt, Bull. Am. Meteorol. Soc. 93, 631 (2012). BAMIAT 0003-0007 10.1175/BAMS-D-11-00111.1
D. Petrova, S. J. Koopman, J. Ballester, and X. Rodó, Climate Dyn. 48, 1249 (2017) 10.1007/s00382-016-3139-y.
R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Proc. 44, 998 (1996). ITPRED 1053-587X 10.1109/78.492555
S. Ventosa, C. Simon, M. Schimmel, J. J. Danobeitia, and A. Manuel, IEEE Trans. Signal Proc. 56, 2771 (2008). ITPRED 1053-587X 10.1109/TSP.2008.917029
P. Caraiani, PLoS ONE 7, 1 (2012). 1932-6203 10.1371/journal.pone.0040693
G. S. Welter and P. A. A. Esquef, Phys. Rev. E 87, 032916 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.87.032916
