Advances in Computational Mathematics

, Volume 24, Issue 1–4, pp 171–195 | Cite as

A B-spline approach for empirical mode decompositions

  • Qiuhui Chen
  • Norden Huang
  • Sherman Riemenschneider
  • Yuesheng Xu
Article

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.

Keywords

B-splines nonlinear and nonstationary signals empirical mode decompositions Hilbert transforms 

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Copyright information

© Springer 2006

Authors and Affiliations

  • Qiuhui Chen
    • 1
  • Norden Huang
    • 2
  • Sherman Riemenschneider
    • 3
  • Yuesheng Xu
    • 4
  1. 1.Faculty of Mathematics and Computer ScienceHubei UniversityWuhanP.R. China
  2. 2.Laboratory for Hydrospheric Process/Oceans and Ice BranchNASA Goddard Space Flight CenterGreenbeltU.S.A.
  3. 3.Department of MathematicsWest Virginia UniversityMorgantownU.S.A.
  4. 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 SciencesBeijingP.R. China

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