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Convex Optimization approach to signals with fast varying instantaneous frequency

Publication ,  Journal Article
Kowalski, M; Meynard, A; Wu, HT
Published in: Applied and Computational Harmonic Analysis
January 1, 2018

Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, which involves few properties an “ideal time-frequency representation” should satisfy, for example, the signal reconstruction and concentrative time-frequency representation. FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) is applied to achieve an efficient numerical approximation of the functional. We coin the algorithm as Time-frequency bY COnvex OptimizatioN (Tycoon). The numerical results confirm the potential of the Tycoon algorithm.

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Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

January 1, 2018

Volume

44

Issue

1

Start / End Page

89 / 122

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

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Kowalski, M., Meynard, A., & Wu, H. T. (2018). Convex Optimization approach to signals with fast varying instantaneous frequency. Applied and Computational Harmonic Analysis, 44(1), 89–122. https://doi.org/10.1016/j.acha.2016.03.008
Kowalski, M., A. Meynard, and H. T. Wu. “Convex Optimization approach to signals with fast varying instantaneous frequency.” Applied and Computational Harmonic Analysis 44, no. 1 (January 1, 2018): 89–122. https://doi.org/10.1016/j.acha.2016.03.008.
Kowalski M, Meynard A, Wu HT. Convex Optimization approach to signals with fast varying instantaneous frequency. Applied and Computational Harmonic Analysis. 2018 Jan 1;44(1):89–122.
Kowalski, M., et al. “Convex Optimization approach to signals with fast varying instantaneous frequency.” Applied and Computational Harmonic Analysis, vol. 44, no. 1, Jan. 2018, pp. 89–122. Scopus, doi:10.1016/j.acha.2016.03.008.
Kowalski M, Meynard A, Wu HT. Convex Optimization approach to signals with fast varying instantaneous frequency. Applied and Computational Harmonic Analysis. 2018 Jan 1;44(1):89–122.
Journal cover image

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

January 1, 2018

Volume

44

Issue

1

Start / End Page

89 / 122

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics