Introducing libeemd: a program package for performing the ensemble empirical mode decomposition

Computational Statistics volume 31, pages545–557(2016)Cite this article

Abstract

The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the decomposition. We release our implementation, libeemd, with the aim of providing a user-friendly, fast, stable, well-documented and easily extensible EEMD library for anyone interested in using (E)EMD in the analysis of time series data. While written in C for numerical efficiency, our implementation includes interfaces to the Python and R languages, and interfaces to other languages are straightforward.

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Notes

  1. 1.

    In rare cases the finite precision of computer arithmetic can cause the number of zero crossings or extrema to get stuck oscillating between two consecutive numbers. To avoid an endless loop or extreme oversifting in this case our implementation relaxes the latter condition so that a case where only one of the numbers changes by 1 is still considered stable. This change does not affect the normal operation of EMD.

  2. 2.

    http://cran.r-project.org/web/packages/Rlibeemd/index.html.

  3. 3.

    https://github.com/helske/Rlibeemd.

  4. 4.

    http://perso.ens-lyon.fr/patrick.flandrin/emd.html.

  5. 5.

    http://ptsa.sourceforge.net.

  6. 6.

    https://bitbucket.org/luukko/libeemd.

  7. 7.

    http://www.physionet.org/cgi-bin/atm/ATM.

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Acknowledgments

This work was supported by the Finnish Cultural Foundation, the Emil Aaltonen Foundation, the Academy of Finland, and the European Community’s FP7 through the CRONOS project, Grant Agreement No. 280879. The authors wish to thank N. E. Huang for useful discussions.

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Affiliations

  1. Nanoscience Center, University of Jyväskylä, 40014, Jyväskylä, Finland

    P. J. J. Luukko

  2. Department of Mathematics and Statistics, University of Jyväskylä, 40014, Jyväskylä, Finland

    J. Helske

  3. Department of Physics, Tampere University of Technology, 33101, Tampere, Finland

    E. Räsänen

Authors
  1. P. J. J. Luukko
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  2. J. Helske
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  3. E. Räsänen
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Correspondence to P. J. J. Luukko.

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Luukko, P.J.J., Helske, J. & Räsänen, E. Introducing libeemd: a program package for performing the ensemble empirical mode decomposition. Comput Stat 31, 545–557 (2016). https://doi.org/10.1007/s00180-015-0603-9

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Keywords

  • Hilbert–Huang transform
  • Intrinsic mode function
  • Time series analysis
  • Adaptive data analysis
  • Noise-assisted data analysis
  • Detrending