Multiple enhanced synchrosqueezing in the time–frequency–chirprate space

Abstract

It is challenging to analyze multi-component signals with crossover instantaneous frequencies (IFs), both in producing high-resolution time–frequency representations and disentangling intrinsic modes. One of the most promising attempts is lifting the two-dimensional TFRs to three-dimensional time–frequency–chirprate (TFC) representations. However, the strong “blurring” effect in the chirp rate (CR) axis makes it rather challenging to estimate accurate IF and CR trajectories. Driven by this need, a method to provide highly energy-concentrated TFC representation, called multiple enhanced synchrosqueezing chirplet transform (MESCT), is proposed in this paper. MESCT is an enhanced iterative framework that combines multi-synchrosqueezing and multi-taper techniques. MESCT estimates IF and CR using phase information from different chirplet transform results with different windows, which provides more accurate estimates for reassignment. Then, three-dimensional multi-synchrosqueezing operations subsequently concentrate the ambiguous energy. As a result, MESCT accurately sharpens the TFC representations, even around the crossing points. Thus, accurate IF and CR trajectories can be jointly estimated by the three-dimensional ridge detection algorithm. Finally, crossover modes can be retrieved with high precision based on accurate trajectory estimation. A series of numerical experiments, both simulations and real-world cases, are considered to demonstrate the effectiveness and advantages of the proposed method.