In this paper, we propose a new time–frequency analysis (TFA) method termed longitudinal synchrosqueezing transform (LSST). As a post-processing time–frequency analysis method, the theory of this method is based on the Reassignment method (RM) and Fourier-based synchrosqueezing transform (FSST). LSST combines the advantages of RM and FSST in signal processing and avoids their drawbacks. Compared with RM and FSST, this method can achieve compact time–frequency representation (TFR) while retaining the ability of modes extraction and reconstruction. However, when addressing strong frequency modulation (FM) signals, there will still be energy smear in the TFR generated by LSST. Therefore, longitudinal synchroextracting transform (LSET) is further proposed to cope with signals with strong FM components and generate TFR with high energy concentration. On the basis of LSST, we only keep the energy most relevant to the instantaneous frequency (IF) of the signal through the Dirichlet function to obtain LSET. LSET estimates the signal's instantaneous frequency using a second-order approximation, which enables an accurate characterization of fast time-varying features of the signal at large window size range and it is more robust against noise. In addition, the proposed method is applied to the early fault diagnosis of rotor rub-impact and the fault feature extraction of rolling bearings under variable speed. Compared with other advanced TFA technologies, the simulated and measured signals can verify the effectiveness and competitiveness of the proposed method.
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