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A two-level method for sparse time-frequency representation of multiscale data

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Abstract

Based on the recently developed data-driven time-frequency analysis (Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function (IMF) and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent. We also present a method to reduce the end effects.

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Acknowledgements

This work was supported by National Science Foundation of USA (Grants Nos. DMS-1318377 and DMS-1613861) and National Natural Science Foundation of China (Grant Nos. 11371220, 11671005, 11371173, 11301222 and 11526096).

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Authors and Affiliations

  1. Department of Mathematics, Jinan University, Guangzhou, 510632, China

    ChunGuang Liu

  2. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

    ZuoQiang Shi

  3. Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125, USA

    Thomas Yizhao Hou

Authors
  1. ChunGuang Liu
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  2. ZuoQiang Shi
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  3. Thomas Yizhao Hou
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Corresponding author

Correspondence to Thomas Yizhao Hou.

Additional information

Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday

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Liu, C., Shi, Z. & Hou, T.Y. A two-level method for sparse time-frequency representation of multiscale data. Sci. China Math. 60, 1733–1752 (2017). https://doi.org/10.1007/s11425-016-9088-9

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  • DOI: https://doi.org/10.1007/s11425-016-9088-9

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