  Synchrosqueezing transform (SST) is a useful tool for vibration signal
analysis due to its high time-frequency (TF) concentration and reconstruction
properties. However, existing SST requires much processing time for large-scale
data. In this paper, some fast implementation methods of SST based on
downsampled short-time Fourier transform (STFT) are proposed. By controlling
the downsampling factor both in time and frequency, combined with the proposed
selective reassignment and frequency subdivision scheme, one can keep a balance
between efficiency and accuracy according to practical needs. Moreover, the
reconstruction property is available, accomplished by an approximate but direct
inverse formula under downsampling. The effects of parameters on the
concentration, computing efficiency, and reconstruction accuracy are also
investigated quantitatively, followed by a mathematic model of reassignment
behavior with decimate factors. Experimental results on an aero-engine and a
spindle show that the fast implementation of SST can effectively characterize
the non-stationary characteristics of the large-scale vibration signal to
reveal the mechanism of mechanical systems.
