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A B-spline approach for empirical mode decompositions
Authors:Qiuhui Chen  Norden Huang  Sherman Riemenschneider  Yuesheng Xu
Institution:(1) Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, P.R. China;(2) Laboratory for Hydrospheric Process/Oceans and Ice Branch, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, U.S.A.;(3) Department of Mathematics, West Virginia University, Morgantown, WV, 26506, U.S.A.;(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
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. 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.
Keywords:B-splines  nonlinear and nonstationary signals  empirical mode decompositions  Hilbert transforms
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