The exponential accuracy of Fourier and Chebyshev differencing methods
SIAM Journal on Numerical Analysis
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Improving the readability of time-frequency and time-scalerepresentations by the reassignment method
IEEE Transactions on Signal Processing
Characterization of signals by the ridges of their wavelettransforms
IEEE Transactions on Signal Processing
Time-scale energy distributions: a general class extending wavelettransforms
IEEE Transactions on Signal Processing
One or Two Frequencies? The Empirical Mode Decomposition Answers
IEEE Transactions on Signal Processing
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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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.