Nonstationary Signal Decomposition for Dummies
- 826 Downloads
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.
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.
- 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
- 5.Cicone, A., Zhou, H.: Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT. Submitted. ArXiv 1802.01359Google Scholar
- 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.Cohen, L.: Time–frequency Analysis. Prentice Hall (1995)Google Scholar
- 10.Daubechies, I.: Ten lectures on wavelets. SIAM (1992)Google Scholar
- 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
- 13.Flandrin, P.: Time–frequency/time–scale analysis. Academic press (1998)Google Scholar
- 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
- 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.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
- 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