  Recently the study of modeling a non-stationary signal as a superposition of
amplitude and frequency-modulated Fourier-like oscillatory modes has been a
very active research area. The synchrosqueezing transform (SST) is a powerful
method for instantaneous frequency estimation and component separation of
non-stationary multicomponent signals. The short-time Fourier transform-based
SST (FSST for short) reassigns the frequency variable to sharpen the
time-frequency representation and to separate the components of a
multicomponent non-stationary signal. Very recently the FSST with a
time-varying parameter, called the adaptive FSST, was introduced. The
simulation experiments show that the adaptive FSST is very promising in
instantaneous frequency estimation of the component of a multicomponent signal,
and in accurate component recovery. However the theoretical analysis of the
adaptive FSST has not been carried out. In this paper, we study the theoretical
analysis of the adaptive FSST and obtain the error bounds for the instantaneous
frequency estimation and component recovery with the adaptive FSST and the
2nd-order adaptive FSST.
