The Synchrosqueezing algorithm for time-varying spectral analysis: robustness properties and new paleoclimate applications

TL;DR

The paper investigates the stability of the Synchrosqueezing transform for time-frequency analysis, demonstrating its robustness to noise and perturbations, and applies it to paleoclimate data for improved insights.

Contribution

It provides a stability analysis of Synchrosqueezing and introduces a practical implementation with parameter guidance, applying it to paleoclimate data.

Findings

Synchrosqueezing is robust to noise and perturbations.

The method improves analysis of noisy, nonuniform data.

Application reveals new insights into paleoclimate changes.

Abstract

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.