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Synchrosqueezing transform (SST) is a currently proposed novel postprocessing time-frequency (TF) analysis tool. It has been widely shown that SST is able to improve TF representation. However, so far, how to improve the TF resolution while ensuring the accuracy of signal reconstruction is still an open question, particularly for the vibration signal with time-varying instantaneous frequency (IF) characteristics, due to the fact that the vibration signals of mechanical equipment usually contain many types of noise generated by harsh operating conditions, and the SST will mix these noise into the real signal. Our first contribution is using the Gaussian modulated linear chirp (GMLC) signal model to represent the general nonstationary signals. The GMLC signal model can more accurately represent the time-varying nonstationary signal, compared with the SST signal model composed of linear phase function and constant amplitude. Our second contribution in this work is proposing a method to improve the TF resolution and reconstruction accuracy for nonstationary signals with time-varying IF, which we coined the second-order synchroextracting transform (SET2). In SET2, we apply the GMLC to deduce the nonstationary signal model and then only use the energy at the IF to characterize the TF distribution, which improves the TF while reducing the impact of noise on the real signal.
Bao et al. (Wed,) studied this question.