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

• Published in: Signal processing Vol. 93; no. 5; pp. 1079 - 1094
• Main Authors: Thakur, Gaurav, Brevdo, Eugene, Fučkar, Neven S., Wu, Hau-Tieng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2013; Elsevier
• Subjects: Algorithms; Applied sciences; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Gaussian; Information, signal and communications theory; Instantaneous frequency; Nonstationary signal analysis; Perturbation methods; Robustness; Sampled data; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Spectra; Synchrosqueezing; Telecommunications and information theory; Time-frequency reassignment; Time-varying spectrum; Transforms; Tuning; Time-varying spectrum; Time-frequency reassignment; Instantaneous frequency; Synchrosqueezing; Nonstationary signal analysis; Time-frequency analysis; Spectral properties; Non stationary condition; Perturbation; Algorithm; Time variation; Implementation; Case study; Guidance; Gaussian noise; Spectrum analysis; White noise; Signal processing; Robustness; Signal analysis; Time analysis
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2012.11.029

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. ► We study the stability of the Synchrosqueezing transform for spectral analysis. ► Synchrosqueezing is shown to be robust to bounded errors and Gaussian white noise. ► We describe a numerical implementation and compare it with other techniques. ► We apply Synchrosqueezing to proxies describing the evolution of the global climate.