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The Synchrosqueezing transform for instantaneous spectral analysis

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Excursions in Harmonic Analysis, Volume 4

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the recovery of the signal. This article presents an overview of the theory and stability properties of Synchrosqueezing, as well as applications of the technique to topics in cardiology, climate science, and economics.

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Notes

  1. 1.

    Such signals are often called “nonstationary” in these domains, although this terminology is not related to its meaning for random processes.

  2. 2.

    We present a slightly different formulation of the transform than [14] that is more comparable with the approach in [7].

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Author information

Authors and Affiliations

  1. MITRE Corporation, 7515 Colshire Drive, McLean, VA, 22102, USA

    Gaurav Thakur

Authors
  1. Gaurav Thakur
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Corresponding author

Correspondence to Gaurav Thakur .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Norbert Wiener Center University of Maryland, College Park, Maryland, USA

    Radu Balan

  2. Department of Mathematics, Norbert Wiener Center University of Maryland, College Park, Maryland, USA

    Matthew Begué

  3. Department of Mathematics, Norbert Wiener Center University of Maryland, College Park, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, Norbert Wiener Center University of Maryland, College Park, Maryland, USA

    Wojciech Czaja

  5. Department of Mathematics, Norbert Wiener Center University of Maryland, College Park, Maryland, USA

    Kasso A. Okoudjou

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Thakur, G. (2015). The Synchrosqueezing transform for instantaneous spectral analysis. In: Balan, R., Begué, M., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 4. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-20188-7_15

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