A generalized synchrosqueezing transform for enhancing signal time–frequency representation

High-quality time–frequency representation (TFR) is important for reliable signal analysis. The diffusions of the TFR energy along time and/or frequency axes lead to ambiguous TFR and hence misleading signal analysis results. Synchrosqueezing is an adaptive and invertible transform developed to improve the quality or readability of the wavelet-based TFR by condensing it along the frequency axis. However, the original synchrosqueezing method could be handicapped by time-dimension diffusions of the wavelet coefficients. As such, we propose a generalized synchrosqueezing transform (GST) approach to deal with the diffusions in both time and frequency dimensions. For the signal with a constant frequency, we have shown that the wavelet diffusion only occurs at frequency dimension. Based on this observation, the original signal with time-varying instantaneous frequency is mapped to another analytical signal with constant frequency to facilitate the synchrosqueezing. A time-scale domain restoration operation is then presented to obtain a TFR with concentrated wavelet ridge. The performance of the proposed GST for signal TFR enhancement has been demonstrated by our simulation study.

► We report a generalized synchrosqueezing transform. ► It can perform multiple time–frequency (TF) transforms within one framework. ► It produces clearer TF representations with less computations and distortion. ► It mitigates the TF resolution dilemma reflected by the Heisenberg principle.