2D Second-Order Time–Frequency Synchrosqueezing Transform: For Non-stationary Signals Well-Localized Components Extraction and Separation

The time–frequency analysis (TFA) method is an effective tool to separate and extract main components for non-stationary signals such as vibration signals and seismic signals, which are time-varying and affected by high noise. However, suffering from the Heisenberg uncertainty principle and cross terms of time–frequency result, conventional TFA methods usually produce vague time–frequency representations (TFRs). As a branch of the TFA method, current redistributive compressive transforms enable to generate clear TFR. However, these techniques are limited to a singular type of signal, which is not applicable to deal with complicated signals in production. In order to enhance the applicability and the time–frequency (TF) aggregation capability, this paper proposes a promoted TFA method 2D-FTSST2 based on the synchrosqueezing transform combining two-dimensional information of time and frequency domains. For an accurate IF estimate, we also define a time redistribution operator, which can describe strong time and frequency-varying signals. This algorithm not only provides a high-resolution decomposition of multicomponent signals but also enables to extract main features in noisy environments. Experiments on simulated signals and real data confirm the validity and effectiveness of the proposed algorithm.