  The synchrosqueezing transform (SST) has been developed as a powerful
EMD-like tool for instantaneous frequency (IF) estimation and component
separation of non-stationary multicomponent signals. Recently, a direct method
of the time-frequency approach, called signal separation operation (SSO), was
introduced to solving the problem of multicomponent signal separation. While
both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the
second step of the two-step SST method in component recovery (mode retrieval).
In addition, SSO is simple: the IF of a component is estimated by a
time-frequency ridge of the SSO plane; and this component is recovered by
simply plugging the time-frequency ridge to the SSO operation. In recent paper
"Direct signal separation via extraction of local frequencies with adaptive
time-varying parameters", after showing that the SSO operation is related to
the adaptive short-time Fourier transform (STFT), the authors obtained a more
accurate component recovery formula derived from the linear chirp (also called
linear frequency modulation signal) approximation at any local time and they
also proposed a recovery scheme to extract the signal components one by one
with the time-varying window updated for each component. However the
theoretical analysis of the recovery formula derived from linear chirp local
approximation has not been studied there. In this paper, we carry out such
analysis and obtain error bounds for IF estimation and component recovery.
These results provide a mathematical guarantee to the proposed adaptive
STFT-based non-stationary multicomponent signal separation method.
