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An Analytical Expression for Empirical Mode Decomposition Based on B-Spline Interpolation

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Abstract

Although empirical mode decomposition (EMD) lacks a rigorous theoretical basis, it has attracted much attention for analyzing nonstationary signals adaptively. In this paper, the EMD method is investigated from a digital signal processing perspective. Based on an analysis of extrema sampling and B-spline interpolation, we show that the upper and lower envelopes of signals are formed by a succession of three basic operations: decimation of local extrema, interpolation, and filtering by a B-spline filter. We then show that some aliasing noise can be suppressed by the mean of the envelopes, though the extrema sampling is a sub-Nyquist sampling. For uniformly spaced extrema of signals, we derive a general analytical expression of intrinsic mode functions (IMFs) extracted by the EMD method from signals.

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Acknowledgement

The authors would like to thank Prof. Ran Tao for many helpful discussions.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin, China

    Yanli Yang & Changyun Miao

  2. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, China

    Yanli Yang & Jiahao Deng

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  1. Yanli Yang
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  2. Changyun Miao
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  3. Jiahao Deng
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Correspondence to Yanli Yang.

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Yang, Y., Miao, C. & Deng, J. An Analytical Expression for Empirical Mode Decomposition Based on B-Spline Interpolation. Circuits Syst Signal Process 32, 2899–2914 (2013). https://doi.org/10.1007/s00034-013-9592-5

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  • DOI: https://doi.org/10.1007/s00034-013-9592-5

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