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

Chen Yun Lin, Li Su, Hau Tieng Wu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)451-505
Number of pages55
JournalJournal of Fourier Analysis and Applications
Issue number2
StatePublished - Apr 1 2018


  • Adaptive non-harmonic model
  • Cepstrum
  • De-shape SST
  • De-shape STFT
  • Instantaneous frequency
  • Short-time cepstral transform
  • Synchrosqueezing transform

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Applied Mathematics


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