Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application

Analysis of signals with oscillatory modes crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this lifting the 2-dimensional time-frequency representation 3-dimensional representation, called time-frequency-chirp rate (TFC) by adding one extra chirp parameter so that are disentangled higher dimension. The chirplet transform an algorithm for idea, which leads TFC representation. However, practice, we found it has strong “blurring” effect axis, limits its application real-world data. Moreover, our knowledge, have limited mathematical understanding literature. Motivated need data analysis, paper, propose synchrosqueezed (SCT) enhances given transform. resulting concentrated high contrast can better distinguish different frequencies. basic idea use phase information determine reassignment rule sharpens determined We also analyze and provide theoretical guarantees SCT.