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An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm

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  • Li, Hongyi
  • Qin, Xuyao
  • Zhao, Di
  • Chen, Jiaxin
  • Wang, Pidong

Abstract

Empirical mode decomposition (EMD) is a new method presented recently for analyzing nonlinear and non-stationary signals. Its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions (IMFs) based on the local characteristics of the signal in time domain. The key step of EMD is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively, and then calculate the mean values of upper and lower envelopes. Based on the cubic trigonometric B-spline interpolation algorithm, a new improved method for EMD is proposed named CTB-EMD in this paper. In this method, the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric B-splines curve. Thus, the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided, and then the decomposition of the signal is more accurate and effect. Through numerical experiments, we compare the effect of this method with other methods on decomposing simulation signals and real signals. Experimental results show that this method can decompose signals more effectively and accurately.

Suggested Citation

  • Li, Hongyi & Qin, Xuyao & Zhao, Di & Chen, Jiaxin & Wang, Pidong, 2018. "An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 406-419.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:406-419
    DOI: 10.1016/j.amc.2018.02.039
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    References listed on IDEAS

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    1. Zhao, Di & Li, Hongyi, 2015. "On the computation of inverses and determinants of a kind of special matrices," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 721-726.
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    Cited by:

    1. Li, Hongyi & Wang, Chaojie & Zhao, Di, 2020. "Preconditioning for PDE-constrained optimization with total variation regularization," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Hu, Gang & Bo, Cuicui & Wei, Guo & Qin, Xinqiang, 2020. "Shape-adjustable generalized Bézier surfaces: Construction and it is geometric continuity conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    3. Ze Shi & Hongyi Li & Di Zhao & Chengwei Pan, 2023. "Research on Relation Classification Tasks Based on Cybersecurity Text," Mathematics, MDPI, vol. 11(12), pages 1-16, June.

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