Wave-shape function analysis -- when cepstrum meets time-frequency analysis
This work addresses signal processing challenges in fields like physiology, music, and biology, but appears incremental as it builds on existing cepstrum and time-frequency methods.
The authors tackled the problem of analyzing oscillatory signals with time-varying frequency, amplitude, and non-sinusoidal patterns by combining cepstrum and nonlinear time-frequency analysis, resulting in the de-shape synchrosqueezing transform algorithm that was validated on simulated and real-world signals.
We propose to combine cepstrum and nonlinear time-frequency (TF) analysis to study mutiple 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.