  We analyze the stability properties of the Synchrosqueezing transform, a
time-frequency signal analysis method that can identify and extract oscillatory
components with time-varying frequency and amplitude. We show that
Synchrosqueezing is robust to bounded perturbations of the signal and to
Gaussian white noise. These results justify its applicability to noisy or
nonuniformly sampled data that is ubiquitous in engineering and the natural
sciences. We also describe a practical implementation of Synchrosqueezing and
provide guidance on tuning its main parameters. As a case study in the
geosciences, we examine characteristics of a key paleoclimate change in the
last 2.5 million years, where Synchrosqueezing provides significantly improved
insights.
