Citing the EMD Package#


If this package has significantly contributed to your work, please include the following citation:

Andrew J. Quinn, Vitor Lopes-dos-Santos, David Dupret, Anna Christina Nobre & Mark W. Woolrich (2021)
EMD: Empirical Mode Decomposition and Hilbert-Huang Spectral Analyses in Python
Journal of Open Source Software 10.21105/joss.02977
@article{Quinn2021_joss,
  doi = {10.21105/joss.02977},
  url = {https://doi.org/10.21105/joss.02977},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {59},
  pages = {2977},
  author = {Quinn, Andrew J. and Lopes-dos-Santos, Vitor and Dupret, David and Nobre, Anna C. and Woolrich, Mark W.},
  title = {EMD: Empirical Mode Decomposition and Hilbert-Huang Spectral Analyses in Python},
  journal = {Journal of Open Source Software}
}

The Empirical Mode Decomposition and Hilbert-Huang Spectrum were initially developed by Norden Huang and colleagues in 1998. This paper is the main reference for the motivation, theory and initial practice of EMD.

Norden E. Huang, Zheng Shen, Steven R. Long, Manli C. Wu, Hsing H. Shih, Quanan Zheng, Nai-Chyuan Yen, Chi Chao Tung & Henry H. Liu (1998)
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 10.1098/rspa.1998.0193
@article{Huang1998,
  doi = {10.1098/rspa.1998.0193},
  url = {https://doi.org/10.1098/rspa.1998.0193},
  year = {1998},
  month = mar,
  publisher = {The Royal Society},
  volume = {454},
  number = {1971},
  pages = {903--995},
  author = {Norden E. Huang and Zheng Shen and Steven R. Long and Manli C. Wu and Hsing H. Shih and Quanan Zheng and Nai-Chyuan Yen and Chi Chao Tung and Henry H. Liu},
  title = {The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis},
  journal = {Proceedings of the Royal Society of London. Series A: Mathematical,  Physical and Engineering Sciences}
}

Reference Library#

Depending on the analysis in question, you may also consider citing one or more of the following papers. The function docstrings in the EMD toolbox contains many citations and references for each method. Here we include a range of the most relevant papers, grouped by topic.


EMD, sifting and the Hilbert-Huang Transform#

Norden E. Huang, Zheng Shen, Steven R. Long, Manli C. Wu, Hsing H. Shih, Quanan Zheng, Nai-Chyuan Yen, Chi Chao Tung & Henry H. Liu (1998)
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 10.1098/rspa.1998.0193

Further EMD Theory#

P. Flandrin, G. Rilling & P. Goncalves (2004)
Empirical Mode Decomposition as a Filter Bank
IEEE} Signal Processing Letters 10.1109/lsp.2003.821662
G. Rilling & P. Flandrin (2008)
One or Two Frequencies? The Empirical Mode Decomposition Answers
IEEE} Transactions on Signal Processing 10.1109/tsp.2007.906771

Ensemble Sift#

Zhaohua Wu & Norden E. Huang (2009)
Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method
Advances in Adaptive Data Analysis 10.1142/s1793536909000047
Maria E. Torres, Marcelo A. Colominas, Gaston Schlotthauer & Patrick Flandrin (2011)
A complete ensemble empirical mode decomposition with adaptive noise
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 10.1109/icassp.2011.5947265

Masked Sift#

Ryan Deering & James F. Kaiser (2005)
The Use of a Masking Signal to Improve Empirical Mode Decomposition
2005 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 10.1109/icassp.2005.1416051
Feng-Fang Tsai, Shou-Zen Fan, Yi-Shiuan Lin, Norden E. Huang & Jia-Rong Yeh (2016)
Investigating Power Density and the Degree of Nonlinearity in Intrinsic Components of Anesthesia EEG by the Hilbert-Huang Transform: An Example Using Ketamine and Alfentanil
PLOS-ONE 10.1371/journal.pone.0168108
Marco S. Fabus, Andrew J. Quinn, Catherine E. Warnaby & Mark W. Woolrich (2021)
Automatic decomposition of electrophysiological data into distinct nonsinusoidal oscillatory modes
Journal of Neurophysiology 10.1152/jn.00315.2021

Instantaneous Frequency#

Norden E. Huang, Zhaohua Wu, Steven R. Long, Kenneth C. Arnold, Xianyao Chen & Karin Blank (2009)
On Instantaneous Frequency
Advances in Adaptive Data Analysis 10.1142/s1793536909000096

Cycle Analysis and Waveform Shape#

Quinn, Andrew J., Lopes-dos-Santos, VĂ­tor, Huang, Norden, Liang, Wei-Kuang, Juan, Chi-Hung, Yeh, Jia-Rong, Nobre, Anna C., Dupret, David, Woolrich & Mark W. (2021)
Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics
Journal of Neurophysiology 10.1152/jn.00201.2021
Marco S. Fabus, Mark W. Woolrich, Catherine W. Warnaby & Andrew J. Quinn (2022)
Understanding Harmonic Structures Through Instantaneous Frequency
IEEE} Open Journal of Signal Processing 10.1109/ojsp.2022.3198012

Holospectrum#

Norden E. Huang, Kun Hu, Albert C. C. Yang, Hsing-Chih Chang, Deng Jia, Wei-Kuang Liang, Jia Rong Yeh, Chu-Lan Kao, Chi-Hung Juan, Chung Kang Peng, Johanna H. Meijer, Yung-Hung Wang, Steven R. Long & Zhauhua Wu (2016)
On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 10.1098/rsta.2015.0206