×

Empirical mode decomposition with shape-preserving spline interpolation. (English) Zbl 1458.94134

Summary: Empirical mode decomposition (EMD) is a popular, novel, user-friendly algorithm to decompose a given signal into its constituting components, utilizing spline interpolation. In this paper, we equip EMD with a shape-preserving interpolation scheme based on quadratic B-splines. Using numerical experiments, we show that our scheme, which we coin Geometric EMD, or GEMD, outperforms the original EMD, both qualitatively and quantitatively.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
41A05 Interpolation in approximation theory
41A15 Spline approximation
65D07 Numerical computation using splines

Software:

PhysioToolkit
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Huang, N.; Shen, Z.; Long, S.; Wu, M.; Shih, H.; Zheng, Q., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc R Soc Lond Ser A Math Phys Eng Sci, 454, 1971, 903-995 (1998) · Zbl 0945.62093
[2] Huang, N.; Wu, Z., A review on Hilbert-Huang transform: Method and its applications to geophysical studies, Rev Geophys, 46, 2 (2008)
[3] Han, J.; van der Baan, M., Empirical mode decomposition for seismic time-frequency analysis, Geophysics, 78, 2, O9-O19 (2013)
[4] Lei, Y.; Lin, J.; He, Z.; Zuo, M., A review on empirical mode decomposition in fault diagnosis of rotating machinery, Mech Syst Signal Process, 35, 1-2, 108-126 (2013)
[5] Martis, R.; Acharya, U.; Tan, J.; Petznick, A.; Yanti, R.; Chua, C., Application of empirical mode decomposition (EMD) for automated detection of epilepsy using EEG signals, Int J Neural Syst, 22, 06, Article 1250027 pp. (2012)
[6] Zhang, X.; Lai, K.; Wang, S.-Y., A new approach for crude oil price analysis based on empirical mode decomposition, Energy Econ, 30, 3, 905-918 (2008)
[7] Wu, Z.; Huang, N., Ensemble empirical mode decomposition: a noise-assisted data analysis method, Adv Adapt Data Anal, 1, 01, 1-41 (2009)
[8] Chui, C.; van der Walt, M., Signal analysis via instantaneous frequency estimation of signal components, Int J Geomath, 1-42 (2015) · Zbl 1322.94028
[9] Li, Y.; Xu, M.; Wei, Y.; Huang, W., An improvement EMD method based on the optimized rational Hermite interpolation approach and its application to gear fault diagnosis, Measurement, 63, 330-345 (2015)
[10] Fan, Z.-P.; Zhang, G.-L., The research of improved envelope algorithm of EMD, Comput Simul, 27, 6, 126-129 (2010)
[11] Cicone, A.; Liu, J.; Zhou, H., Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, Appl Comput Harmon Anal, 41, 2, 384-411 (2016) · Zbl 1360.94068
[12] Li, L.; Cai, H.; Jiang, Q.; Ji, H., An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis, Mech Syst Signal Process, 121, 791-809 (2019)
[13] Schumaker, L., On shape preserving quadratic spline interpolation, SIAM J Numer Anal, 20, 4, 854-864 (1983) · Zbl 0521.65009
[14] Chui, C. K., Wavelets: A mathematical tool for signal analysis (1997), Society for Industrial and Applied Mathematics · Zbl 0903.94007
[15] Xu, Y.; Luo, M.; Li, T.; Song, G., ECG signal de-noising and baseline wander correction based on CEEMDAN and wavelet threshold, Sensors, 17, 12, 2754 (2017)
[16] Pan, N.; Mang, V.; Un, M., Accurate removal of baseline wander in ECG using empirical mode decomposition, (2007 Joint meeting of the 6th international symposium on noninvasive functional source imaging of the brain and heart and the international conference on functional biomedical imaging (2007), IEEE), 177-180
[17] Blanco-Velasco, M.; Weng, B.; Barner, K., ECG signal denoising and baseline wander correction based on the empirical mode decomposition, Comput Biol Med, 38, 1, 1-13 (2008)
[18] Moody, G.; Mark, R., The impact of the MIT-BIH arrhythmia database, IEEE Eng Med Biol Mag, 20, 3, 45-50 (2001)
[19] Goldberger, A.; Amaral, L.; Glass, L.; Hausdorff, J.; Ivanov, P.; Mark, R., PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals, Circulation, 101, 23, e215-e220 (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.