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Iterative filtering as a direct method for the decomposition of nonstationary signals. (English) Zbl 1459.94031

Summary: The Iterative Filtering method is a technique developed recently for the decomposition and analysis of nonstationary and nonlinear signals. In this work, we propose two alternative formulations of the original algorithm which allows to transform the iterative filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65T50 Numerical methods for discrete and fast Fourier transforms
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93E11 Filtering in stochastic control theory

References:

[1] Balocchi, R.; Menicucci, D.; Santarcangelo, E.; Sebastiani, L.; Gemignani, A.; Ghelarducci, B.; Varanini, M., Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition, Chaos Solitons & Fractals, 20, 171-177 (2004) · Zbl 1071.92014 · doi:10.1016/S0960-0779(03)00441-7
[2] Bertello, I.; Piersanti, M.; Candidi, M.; Diego, P.; Ubertini, P., Electromagnetic field observations by the DEMETER satellite in connection with the, L’Aquila earthquake, Annales Geophysicae, 36, 2018, 1483-1493 (2009)
[3] Blanco-Velasco, M.; Weng, B.; Barner, KE, ECG signal denoising and baseline wander correction based on the empirical mode decomposition, Comput. Biol Med., 38, 1-13 (2008) · doi:10.1016/j.compbiomed.2007.06.003
[4] Chen, X.; Zhang, X.; Church, JA; Watson, CS; King, MA; Monselesan, D.; Legresy, B.; Harig, C., The increasing rate of global mean sea-level rise during 1993-2014, Nat. Clim. Change, 7, 492-495 (2017) · doi:10.1038/nclimate3325
[5] Cicone, A.: Nonstationary signal decomposition for dummies, Advances in mathematical methods and high performance computing, Advances in Mechanics and Mathematics 41, Chapter 3 Springer Nature (2019) · Zbl 1442.62208
[6] Cicone, A.: Multivariate fast iterative filtering for the decomposition of nonstationary signals, submitted. arXiv:1902.04860 · Zbl 1442.94019
[7] Cicone, A., Dell’Acqua, P.: Study of boundary conditions in the iterative filtering method for the decomposition of nonstationary signals. Journal of Computational and Applied Mathematics (2019)
[8] Cicone, A.; Garoni, C.; Serra-Capizzano, S., Spectral and convergence analysis of the Discrete ALIf method, Linear Algebra Appl., 580, 62-95 (2019) · Zbl 1477.94025 · doi:10.1016/j.laa.2019.06.021
[9] Cicone, A.; Liu, J.; Zhou, H., Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, Appl. Comput. Harmon. Anal., 41, 384-411 (2016) · Zbl 1360.94068 · doi:10.1016/j.acha.2016.03.001
[10] Cicone, A.; Liu, J.; Zhou, H., Hyperspectral chemical plume detection algorithms based on multidimensional iterative filtering decomposition, Phil. Trans. R. Soc. A:, Math. Phys. Eng. Sci., 374, 2016, 0196 (2015)
[11] Cicone, A., Wu, H.-T.: How nonlinear-type time-frequency analysis can help in sensing instantaneous heart rate and instantaneous respiratory rate from photoplethysmography in a reliable way, Front. Physiol. 8, Article Number 701 (2017)
[12] Cicone, A.; Zhou, H., Multidimensional iterative filtering method for the decomposition of high-dimensional non-stationary signals, Numer. Math. Theory Methods Appl., 10, 278-298 (2017) · Zbl 1389.62141 · doi:10.4208/nmtma.2017.s05
[13] Cicone, A., Zhou, H.: Numerical analysis for iterative filtering with new efficient implementations based on FFT, preprint. arXiv:1802.01359(2018)
[14] Coughlin, KT; Tung, K., 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method, Adv. Space Res., 34, 323-329 (2004) · doi:10.1016/j.asr.2003.02.045
[15] Echeverria, JC; Crowe, JA; Woolfson, MS; Hayes-Gill, BR, Application of empirical mode decomposition to heart rate variability analysis, Med. Biol. Eng. Comput., 39, 471-479 (2001) · doi:10.1007/BF02345370
[16] Elsner, J. B., Tsonis, A. A.: Singular spectrum analysis: a new tool in time series analysis, Springer Science & Business Media (2013)
[17] Golyandina, N., Zhigljavsky, A.: Singular Spectrum Analysis for time series, Springer Science & Business Media (2013) · Zbl 1276.62053
[18] Gregoriou, GG; Gotts, SJ; Zhou, H.; Desimone, R., High-frequency, long-range coupling between prefrontal and visual cortex during attention, Science, 324, 1207-1210 (2009) · doi:10.1126/science.1171402
[19] Groth, A.; Ghil, M., Monte Carlo singular spectrum analysis (SSA) revisited: detecting oscillator clusters in multivariate datasets, J. Climate, 28, 7873-7893 (2015) · doi:10.1175/JCLI-D-15-0100.1
[20] Gubler, DJ, Cities spawn epidemic dengue viruses, Nat. Med., 10, 129-130 (2004) · doi:10.1038/nm0204-129
[21] Hassani, H., Singular spectrum analysis: methodology and comparison, J. Data Sci., 5, 239-257 (2007)
[22] Huang, NE; Shen, Z.; Long, SR; Wu, MC; Shih, HH; Zheng, Q.; Yen, NC; Tung, CC; Liu, HH, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. London. Ser. A: Math. Phys. Eng. Sci., 454, 903 (1998) · Zbl 0945.62093 · doi:10.1098/rspa.1998.0193
[23] Huang, N. E., Wu, Z.: A review on Hilbert-Huang transform: method and its applications to geophysical studies, Reviews of geophysics 46 (2008)
[24] Ji, F.; Wu, Z.; Huang, J.; Chassignet, EP, Evolution of land surface air temperature trend, Nat. Clim. Change, 4, 462-466 (2014) · doi:10.1038/nclimate2223
[25] Lei, Y.; Lin, J.; He, Z.; Zuo, MJ, A review on empirical mode decomposition in fault diagnosis of rotating machinery, Mech. Syst. Signal Proc., 35, 108-126 (2013) · doi:10.1016/j.ymssp.2012.09.015
[26] Liang, H.; Lin, Q.; Chen, JDZ, Application of the empirical mode decomposition to the analysis of esophageal manometric data in gastroesophageal reflux disease, IEEE Trans. Biomed. Eng., 52, 1692-1701 (2005) · doi:10.1109/TBME.2005.855719
[27] Lin, L.; Wang, Y.; Zhou, H., Iterative filtering as an alternative algorithm for empirical mode decomposition, Adv Adaptive Data Anal., 1, 543-560 (2009) · doi:10.1142/S179353690900028X
[28] Loh, C.; Wu, T.; Huang, NE, Application of the empirical mode decomposition-Hilbert spectrum method to identify near-fault ground-motion characteristics and structural responses, Bull. Seismol. Soc. Am., 91, 1339-1357 (2001) · doi:10.1785/0120000715
[29] Materassi, M.; Piersanti, M.; Consolini, G.; Diego, P.; D’Angelo, G.; Bertello, I.; Cicone, A., Stepping into the Equatorward Boundary of the Auroral Oval: preliminary results of multi scale statistical analysis, Annals of Geophysics, 61, 55 (2019) · doi:10.4401/ag-7801
[30] Mijovic, B.; De Vos, M.; Gligorijevic, I.; Taelman, J.; Van Huffel, S., Source separation from single-channel recordings by combining empirical mode decomposition and independent component analysis, IEEE Trans. Biomed. Eng., 57, 2188-2196 (2010) · doi:10.1109/TBME.2010.2051440
[31] Nunes, JC; Bouaoune, Y.; Delechelle, E.; Niang, O.; Bunel, P., Image analysis by bidimensional empirical mode decomposition, Imag. Vis. Comput., 21, 1019-1026 (2003) · doi:10.1016/S0262-8856(03)00094-5
[32] Nunes, JC; Guyot, S.; Deléchelle, E., Texture analysis based on local analysis of the bidimensional empirical mode decomposition, Mach. Vis. Appl., 16, 177-188 (2005) · doi:10.1007/s00138-004-0170-5
[33] Pachori, R. B.: Discrimination between ictal and seizure-free EEG signals using empirical mode decomposition, Research Letters in Signal Processing 2008 (2008)
[34] Piersanti, M.; Materassi, M.; Cicone, A.; Spogli, L.; Zhou, H.; Ezquer, RG, Adaptive local iterative filtering: a promising technique for the analysis of non-stationary signals, Journal of Geophysical Research - Space Physics, 123, 1031-1046 (2018) · doi:10.1002/2017JA024153
[35] Varadarajan, N.; Nagarajaiah, S., Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/Hilbert transform, J. Eng. Mech., 130, 451-458 (2004) · doi:10.1061/(ASCE)0733-9399(2004)130:4(451)
[36] Vautard, R.; Ghil, M., Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D: Nonlinear Phenomena, 35, 395-424 (1989) · Zbl 0709.62628 · doi:10.1016/0167-2789(89)90077-8
[37] Vautard, R.; Yiou, P.; Ghil, M., Singular-spectrum analysis: a toolkit for short, noisy chaotic signals, Physica D: Nonlinear Phenomena, 58, 95-126 (1992) · doi:10.1016/0167-2789(92)90103-T
[38] Sfarra, S.; Cicone, A.; Yousefi, B.; Ibarra-Castanedo, C.; Perillia, S.; Maldaguef, X., Improving the detection of thermal bridges in buildings via on-site infrared thermography: the potentialities of innovative mathematical tools, Energy and Buildings, 182, 159-171 (2019) · doi:10.1016/j.enbuild.2018.10.017
[39] Wu, Z., Huang, N. E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method Advances in adaptive data analysis 1, 1-41 (2009)
[40] Zhang, X.; Lai, KK; Wang, S., A new approach for crude oil price analysis based on empirical mode decomposition, Energy Econ., 30, 905-918 (2008) · doi:10.1016/j.eneco.2007.02.012
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