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A B-spline approach for empirical mode decompositions

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Abstract

We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments. We present numerical implementations of the B-spline algorithm for an earthquake signal and compare the numerical performance of this approach with that given by the standard empirical mode decomposition. Finally, we discuss several open mathematical problems related to the empirical mode decomposition.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, P.R. China

    Qiuhui Chen

  2. Laboratory for Hydrospheric Process/Oceans and Ice Branch, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, U.S.A.

    Norden Huang

  3. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, U.S.A.

    Sherman Riemenschneider

  4. Deparment of Mathematics, Syracuse University, Syracuse, NY 13244, U.S.A. and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Yuesheng Xu

Authors
  1. Qiuhui Chen
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  2. Norden Huang
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  3. Sherman Riemenschneider
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  4. Yuesheng Xu
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Additional information

Communicated by Achui Zhou

Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday with friendship and esteem

Mathematics subject classification (2000)

94A12.

Supported in part by National Aeronautics and Space Administration under grant NAG5-5364, and National Science Foundation under grants NSF0314742 and NSF0312113.

Yuesheng Xu: Corresponding author. Supported in part by Natural Science Foundation of China under grant 10371122.

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Chen, Q., Huang, N., Riemenschneider, S. et al. A B-spline approach for empirical mode decompositions. Adv Comput Math 24, 171–195 (2006). https://doi.org/10.1007/s10444-004-7614-3

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  • DOI: https://doi.org/10.1007/s10444-004-7614-3

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