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Empirical Fourier Decomposition for Time-Domain Signal Decomposition

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Topics in Modal Analysis & Testing, Volume 8

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Abstract

Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM), have been developed based on Fourier theory. However, the EWT can suffer from a mode mixing problem for signals with closely spaced modes, and decomposition results by FDM can suffer from an inconsistency problem. An accurate adaptive signal decomposition method, called the empirical Fourier decomposition (EFD), is proposed to solve the problems in this work. The proposed EFD combines the uses of an improved Fourier spectrum segmentation technique and an ideal filter bank. The segmentation technique can solve the inconsistency problem by predefining the number of modes in a signal to be decomposed, and filter functions in the ideal filter bank have no transition phases, which can solve the mode mixing problem. A numerical investigation is conducted to study the accuracy of the EFD. It is shown that the EFD can yield an accurate and consistent decomposition result for a signal with closely spaced modes, compared with decomposition results by the EWT, FDM, variational mode decomposition, and empirical mode decomposition.

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Acknowledgements

The author Y.F. Xu is grateful for the financial support from the National Science Foundation through Grant No. CMMI-1762917. The authors gratefully acknowledge valuable discussions with and input from Dr. Gang Yu, Dr. Pushpendra Singh, Dr. Shiqian Chen, and Dr. Heng Li. They also thank people who share their contributions to the signal processing community.

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, P.R. China

    Wei Zhou

  2. Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH, USA

    Wei Zhou

  3. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, P.R. China

    Zhongren Feng

  4. School of Urban Construction, Wuchang Shouyi University, Wuhan, P.R. China

    Zhongren Feng

  5. Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH, USA

    Y. F. Xu

  6. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, P.R. China

    Xiongjiang Wang & Hao Lv

Authors
  1. Wei Zhou
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  2. Zhongren Feng
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  3. Y. F. Xu
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  4. Xiongjiang Wang
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  5. Hao Lv
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Corresponding author

Correspondence to Y. F. Xu .

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Editors and Affiliations

  1. Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA, USA

    Brandon J. Dilworth

  2. University of Cincinnati, Cincinnati, OH, USA

    Michael Mains

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Zhou, W., Feng, Z., Xu, Y.F., Wang, X., Lv, H. (2022). Empirical Fourier Decomposition for Time-Domain Signal Decomposition. In: Dilworth, B.J., Mains, M. (eds) Topics in Modal Analysis & Testing, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-75996-4_8

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  • DOI: https://doi.org/10.1007/978-3-030-75996-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-75995-7

  • Online ISBN: 978-3-030-75996-4

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