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Iterative filtering as a direct method for the decomposition of nonstationary signals

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Abstract

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.

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Notes

  1. Matlab code available at https://dept.atmos.ucla.edu/tcd/ssa-tutorial-matlab

  2. www.cicone.com

  3. LOD dataset is maintained by the The International Earth Rotation and Reference Systems Service and it can be downloaded from http://hpiers.obspm.fr/eoppc/eop/eopc04/eopc04.62-now. A guide describing how the dataset has been generated can be downloaded from http://hpiers.obspm.fr/eoppc/eop/eopc04/C04.guide.pdf

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)

    Article  Google Scholar 

  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)

    Google Scholar 

  3. Blanco-Velasco, M., Weng, B., Barner, K. E.: ECG signal denoising and baseline wander correction based on the empirical mode decomposition. Comput. Biol Med. 38, 1–13 (2008)

    Article  Google Scholar 

  4. Chen, X., Zhang, X., Church, J. A., Watson, C. S., King, M. A., 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)

    Article  Google Scholar 

  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)

  6. Cicone, A.: Multivariate fast iterative filtering for the decomposition of nonstationary signals, submitted. arXiv:1902.04860

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  13. Cicone, A., Zhou, H.: Numerical analysis for iterative filtering with new efficient implementations based on FFT, preprint. arXiv:1802.01359(2018)

  14. Coughlin, K. T., Tung, K.: 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Adv. Space Res. 34, 323–329 (2004)

    Article  Google Scholar 

  15. Echeverria, J. C., Crowe, J. A., Woolfson, M. S., Hayes-Gill, B. R.: Application of empirical mode decomposition to heart rate variability analysis. Med. Biol. Eng. Comput. 39, 471–479 (2001)

    Article  Google Scholar 

  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)

  18. Gregoriou, G. G., Gotts, S. J., Zhou, H., Desimone, R.: High-frequency, long-range coupling between prefrontal and visual cortex during attention. Science 324, 1207–1210 (2009)

    Article  Google Scholar 

  19. Groth, A., Ghil, M.: Monte Carlo singular spectrum analysis (SSA) revisited: detecting oscillator clusters in multivariate datasets. J. Climate 28, 7873–7893 (2015)

    Article  Google Scholar 

  20. Gubler, D. J.: Cities spawn epidemic dengue viruses. Nat. Med. 10, 129–130 (2004)

    Article  Google Scholar 

  21. Hassani, H.: Singular spectrum analysis: methodology and comparison. J. Data Sci. 5, 239–257 (2007)

    Google Scholar 

  22. 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 non-stationary time series analysis. Proc. R. Soc. London. Ser. A: Math. Phys. Eng. Sci. 454, 903 (1998)

    Article  MathSciNet  Google Scholar 

  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, E. P.: Evolution of land surface air temperature trend. Nat. Clim. Change 4, 462–466 (2014)

    Article  Google Scholar 

  25. Lei, Y., Lin, J., He, Z., Zuo, M. J.: A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech. Syst. Signal Proc. 35, 108–126 (2013)

    Article  Google Scholar 

  26. Liang, H., Lin, Q., Chen, J. D. Z.: 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  28. Loh, C., Wu, T., Huang, N. E.: 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  31. Nunes, J. C., Bouaoune, Y., Delechelle, E., Niang, O., Bunel, P.: Image analysis by bidimensional empirical mode decomposition. Imag. Vis. Comput. 21, 1019–1026 (2003)

    Article  Google Scholar 

  32. Nunes, J. C., Guyot, S., Deléchelle, E.: Texture analysis based on local analysis of the bidimensional empirical mode decomposition. Mach. Vis. Appl. 16, 177–188 (2005)

    Article  Google Scholar 

  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, R. G.: Adaptive local iterative filtering: a promising technique for the analysis of non-stationary signals. Journal of Geophysical Research – Space Physics 123, 1031–1046 (2018)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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, K. K., Wang, S.: A new approach for crude oil price analysis based on empirical mode decomposition. Energy Econ. 30, 905–918 (2008)

    Article  Google Scholar 

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Acknowledgments

The author want to thank Haomin Zhou for all the interesting conversations they had and all the suggestions he gave to him. He is indeed a great researcher and a great person.

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Authors and Affiliations

  1. Istituto Nazionale di Alta Matematica, P.le Aldo Moro 5, 00185, Roma, Italy

    Antonio Cicone

  2. DISIM, Università degli Studi dell’Aquila, via Vetoio n.1, 67100, L’Aquila, Italy

    Antonio Cicone

  3. Gran Sasso Science Institute, Via Michele Jacobucci, 2, 67100, L’Aquila, Italy

    Antonio Cicone

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Correspondence to Antonio Cicone.

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Cicone, A. Iterative filtering as a direct method for the decomposition of nonstationary signals. Numer Algor 85, 811–827 (2020). https://doi.org/10.1007/s11075-019-00838-z

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