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Nonstationary Signal Decomposition for Dummies

  • Antonio CiconeEmail author
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

Abstract

How can I decompose a nonstationary signal? What are the advantages of using the most recent methods available in the literature versus using classical methods like (short time) Fourier transform or wavelet transform? This paper tries to address these and other questions providing the reader with a brief and self-contained survey on what and how to tackle the decomposition of nonstationary signals.

Notes

Acknowledgements

The author’s research was supported by Istituto Nazionale di Alta Matematica (INdAM) “INdAM Fellowships in Mathematics and/or Applications cofunded by Marie Curie Actions,” PCOFUND-GA-2009-245492 INdAM-COFUND Marie Sklodowska Curie Integration Grants.

The author is deeply grateful to Haomin Zhou, a great researcher and a wonderful person. He contributed substantially to this work and to the author career with many suggestions and pieces of advice he gave to the author over the years.

References

  1. 1.
    Auger, F., Flandrin, P., Lin, Y. T., McLaughlin, S., Meignen, S. , Oberlin, T., Wu, H.-T.: Time–frequency reassignment and synchrosqueezing: An overview. IEEE Signal Processing Magazine, 30, 32–41 (2013)CrossRefGoogle Scholar
  2. 2.
    Bracewell, R. N., Bracewell, R. N.: The Fourier transform and its applications, McGraw-Hill, New York (1986)zbMATHGoogle Scholar
  3. 3.
    Cicone, A., Dell’Acqua, P.: Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signals. Preprint. ArXiv 1811.07610Google Scholar
  4. 4.
    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).  https://doi.org/10.4208/nmtma.2017.s05 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cicone, A., Zhou, H.: Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT. Submitted. ArXiv 1802.01359Google Scholar
  6. 6.
    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). https://doi.org/10.1016/j.acha.2016.03.001 MathSciNetCrossRefGoogle Scholar
  7. 7.
    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, 20150196 (2016).  https://doi.org/10.1098/rsta.2015.0196 CrossRefGoogle Scholar
  8. 8.
    Cicone, A., Garoni, C., Serra-Capizzano, S.: Spectral and convergence analysis of the Discrete ALIF method. Submitted. http://www.it.uu.se/research/publications/reports/2017-018/
  9. 9.
    Cohen, L.: Time–frequency Analysis. Prentice Hall (1995)Google Scholar
  10. 10.
    Daubechies, I.: Ten lectures on wavelets. SIAM (1992)Google Scholar
  11. 11.
    Daubechies, I., Maes, S.: A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models. Wavelets in Medicine and Biology, 527–546 (1996).Google Scholar
  12. 12.
    Daubechies, I., Lu, J., Wu, H.-T.: Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal., 30, 243–261 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Flandrin, P.: Time–frequency/time–scale analysis. Academic press (1998)Google Scholar
  14. 14.
    Flandrin, P., Chassande-Mottin, E., Auger, F.: Uncertainty and spectrogram geometry. Signal Processing Conference (EUSIPCO), 2012 Proceedings of the 20th European, 794–798 (2012)Google Scholar
  15. 15.
    Gross, R. S.: Combinations of Earth-orientation measurements: SPACE97, COMB97, and POLE97. Journal of Geodesy, 73, 627–637 (2000)CrossRefGoogle Scholar
  16. 16.
    Höpfner, J.: Seasonal variations in length of day and atmospheric angular momentum. Geophys. J. Int., 135, 407–437 (1998). https://doi.org/10.1046/j.1365-246X.1998.00648.x CrossRefGoogle Scholar
  17. 17.
    Hou, T.Y. , Shi, Z.: Adaptive data analysis via sparse time-frequency representation. Adv. in Adap. Data Anal., 3, 1–28 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Hou, T.Y., Yan, M.P., Wu, Z.: A variant of the EMD method for multi–scale data. Adv. in Adap. Data Anal., 1, 483–516 (2009)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Huang, N. E., Wu, Z.: A review on Hilbert–Huang transform: Method and its applications to geophysical studies. Reviews of Geophysics, 46 (2008)Google Scholar
  20. 20.
    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. A: Math. Phys. Eng. Sci., 454, 903–995 (1998)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Huang,, N. E., Wu, M. L., Long, S. R., Shen, S. S., Qu, W. D., Gloersen, P., Fan, K. L.: A confidence limit for the position empirical mode decomposition and Hilbert spectral analysis. Proc. R. Soc. London, Ser. A, 459, 2317–2345 (2003)zbMATHGoogle Scholar
  22. 22.
    Lin, L., Wang, Y., Zhou, H.: Iterative filtering as an alternative algorithm for empirical mode decomposition. Adv. Adapt. Data Anal., 1, 543–560 (2009)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Petit, J. R., Jouzel, J., Raynaud, D., Barkov, N. I., Barnola, J. M., Basile, I., Bender, M., Chappellaz, J., Davis, M., Delaygue, G. et al.: Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 399, 429–436 (1999). https://doi.org/10.1038/20859.CrossRefGoogle Scholar
  24. 24.
    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. https://doi.org/10.1002/2017JA024153 Google Scholar
  25. 25.
    Saltzman, E. S., Petit, J. R., Basile, I., Leruyuet, A., Raynaud, D., Lorius, C., Jouzel, J., Stievenard, M., Lipenkov, V. Y., Barkov, N. I., et al.: Four climate cycles in Vostok ice core. Nature, 387, 359–360 (1997). https://doi.org/10.1038/387359a0.CrossRefGoogle Scholar
  26. 26.
    Wu Z., Huang, N. E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv. Adapt. Data Anal., 1, 1–41 (2009)CrossRefGoogle Scholar
  27. 27.
    Wu, Z. , Huang, N. E., Chen, X.: The Multi-Dimensional Ensemble Empirical Mode Decomposition Method. Advances in Adaptive Data Analysis, 1, 339–372 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Istituto Nazionale di Alta Matematica, Città UniversitariaRomeItaly
  2. 2.Department of Information Engineering, Computer Science and MathematicsUniversità degli Studi dell’AquilaL’AquilaItaly
  3. 3.Gran Sasso Science InstituteL’AquilaItaly

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