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

Chen-Yun Lin University of Toronto Li Su Academia Sinica Hau-Tieng Wu University of Toronto

Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:1704.42001

Journal of Fourier Analysis and Applications , 2017.2
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 (deshape 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.
Adaptive non-harmonicmodel · Cepstrum, Short-time cepstral transform, Instantaneous frequency, Synchrosqueezing transform, De-shape STFT, De-shape SST
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@inproceedings{chen-yun2017wave-shape,
  title={Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis},
  author={Chen-Yun Lin, Li Su, and Hau-Tieng Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170424233953531501744},
  booktitle={Journal of Fourier Analysis and Applications },
  year={2017},
}
Chen-Yun Lin, Li Su, and Hau-Tieng Wu. Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis. 2017. In Journal of Fourier Analysis and Applications . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170424233953531501744.
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