References

The bibliography lists the published work on the decomposition methods and their analysis. The methods guide explains the component definitions and connects them to the operations available in xemd. The function reference specifies the numerical conventions, arguments and outputs of the implementation.

The introduction develops EMD, VMD and Hilbert analysis through the examples. Validation and interpretation distinguishes reconstruction, numerical diagnostics and evidence about physical components; seismic records applies those distinctions to record grouping, selection and reconstruction.

Bibliography

Cicone, Antonio, Jingfang Liu, and Haomin Zhou. 2015. “Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency Analysis.” Version 3. https://arxiv.org/abs/1411.6051v3.

Cicone, Antonio, and Haomin Zhou. 2018. “Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT.” Version 2. https://arxiv.org/abs/1802.01359v2.

Colominas, Marcelo A., Gastón Schlotthauer, and María E. Torres. 2014. “Improved Complete Ensemble EMD: A Suitable Tool for Biomedical Signal Processing.” Biomedical Signal Processing and Control 14: 19–29. https://doi.org/10.1016/j.bspc.2014.06.009.

Daubechies, Ingrid, Jianfeng Lu, and Hau-Tieng Wu. 2009. “Synchrosqueezed Wavelet Transforms: A Tool for Empirical Mode Decomposition.” Version 1. https://arxiv.org/html/0912.2437v1.

Deering, Ryan, and James F. Kaiser. 2005. “The Use of a Masking Signal to Improve Empirical Mode Decomposition.” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 4: 485–88.

Dragomiretskiy, Konstantin, and Dominique Zosso. 2014. “Variational Mode Decomposition.” IEEE Transactions on Signal Processing 62 (3): 531–44. https://doi.org/10.1109/TSP.2013.2288675.

Fabus, Marco S., Andrew J. Quinn, Catherine E. Warnaby, and Mark W. Woolrich. 2021. “Automatic Decomposition of Electrophysiological Data into Distinct Nonsinusoidal Oscillatory Modes.” Journal of Neurophysiology 126 (5): 1670–84. https://doi.org/10.1152/jn.00315.2021.

Gilles, Jérôme. 2013. “Empirical Wavelet Transform.” Version 1. https://arxiv.org/html/2410.23534v1.

Huang, Norden E., Zheng Shen, Steven R. Long, et al. 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 454: 903–95. https://doi.org/10.1098/rspa.1998.0193.

Nazari, Mojtaba, and Sayed Mahmoud Sakhaei. 2020. “Successive Variational Mode Decomposition.” Signal Processing, ahead of print. https://doi.org/10.1016/j.sigpro.2020.107610.

Rehman, Naveed ur, and Hania Aftab. 2019. “Multivariate Variational Mode Decomposition.” Version 1. https://arxiv.org/abs/1907.04509v1.

Rehman, Naveed ur, and Danilo P. Mandic. 2011. “Filter Bank Property of Multivariate Empirical Mode Decomposition.” IEEE Transactions on Signal Processing 59 (5): 2421–26. https://doi.org/10.1109/TSP.2011.2106779.

Rehman, N., and D. P. Mandic. 2010. “Multivariate Empirical Mode Decomposition.” Proceedings of the Royal Society A 466: 1291–302. https://doi.org/10.1098/rspa.2009.0502.

Rilling, Gabriel, Patrick Flandrin, Paulo Gonçalves, and Jonathan M. Lilly. 2007. “Bivariate Empirical Mode Decomposition.” IEEE Signal Processing Letters 14: 936–39.

Rilling, Gabriel, Patrick Flandrin, and Paulo Gonçalvès. 2003. “On Empirical Mode Decomposition and Its Algorithms.” IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (Grado, Italy). https://perso.ens-lyon.fr/patrick.flandrin/NSIP03.pdf.

Smith, Jonathan S. 2005. “The Local Mean Decomposition and Its Application to EEG Perception Data.” Journal of the Royal Society Interface 2 (5): 443–54. https://doi.org/10.1098/rsif.2005.0058.

Torres, María E., Marcelo A. Colominas, Gastón Schlotthauer, and Patrick Flandrin. 2011. “A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise.” 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4144–47. https://doi.org/10.1109/ICASSP.2011.5947265.

Wu, Zhaohua, and Norden E. Huang. 2009. “Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method.” Advances in Adaptive Data Analysis 1 (1): 1–41. https://doi.org/10.1142/S1793536909000047.

Yeh, Jia-Rong, Jiann-Shing Shieh, and Norden E. Huang. 2010. “Complementary Ensemble Empirical Mode Decomposition: A Novel Noise Enhanced Data Analysis Method.” Advances in Adaptive Data Analysis 2 (2): 135–56. https://doi.org/10.1142/S1793536910000422.