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Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis

Publication ,  Journal Article
Lin, CY; Su, L; Wu, HT
Published in: Journal of Fourier Analysis and Applications
April 1, 2018

We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.

Duke Scholars

Published In

Journal of Fourier Analysis and Applications

DOI

ISSN

1069-5869

Publication Date

April 1, 2018

Volume

24

Issue

2

Start / End Page

451 / 505

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Lin, C. Y., Su, L., & Wu, H. T. (2018). Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis. Journal of Fourier Analysis and Applications, 24(2), 451–505. https://doi.org/10.1007/s00041-017-9523-0
Lin, C. Y., L. Su, and H. T. Wu. “Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis.” Journal of Fourier Analysis and Applications 24, no. 2 (April 1, 2018): 451–505. https://doi.org/10.1007/s00041-017-9523-0.
Lin CY, Su L, Wu HT. Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis. Journal of Fourier Analysis and Applications. 2018 Apr 1;24(2):451–505.
Lin, C. Y., et al. “Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis.” Journal of Fourier Analysis and Applications, vol. 24, no. 2, Apr. 2018, pp. 451–505. Scopus, doi:10.1007/s00041-017-9523-0.
Lin CY, Su L, Wu HT. Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis. Journal of Fourier Analysis and Applications. 2018 Apr 1;24(2):451–505.
Journal cover image

Published In

Journal of Fourier Analysis and Applications

DOI

ISSN

1069-5869

Publication Date

April 1, 2018

Volume

24

Issue

2

Start / End Page

451 / 505

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics