An innovative and adaptive acquisition of correct features from massive datasets with solid mathematical support is the core of modern data analysis. One particular interest in medicine is extracting the hidden dynamics from the observed time series, which is composed of multiple oscillatory signals with non-sinusoidal oscillations, time varying amplitude, and time varying frequency, while contaminated with heteroscedastic noise. In this talk, I will discuss few progresses in solving this kind of problem based on the cepstrum idea, particular the wave shape function analysis via de-shape short time Fourier transform, and their theoretical properties. We then apply the developed method to two medical problems – (1) extract fetal ECG signal from the single lead maternal abdominal ECG signal; (2) extract instantaneous heart rate and instantaneous respiratory rate from the PPG signal during exercise. If time permits, some open problems will be discussed.