Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise

TL;DR

This paper introduces a bootstrap framework for quantifying uncertainty in time-frequency representations generated by SST under complex nonstationary noise, supported by theoretical analysis and practical EEG data applications.

Contribution

It develops a Gaussian approximation and bootstrap method for uncertainty quantification in SST-based TFRs under nonstationary noise, with theoretical validation and real-world EEG analysis.

Findings

The Gaussian approximation accurately models TFRs under nonstationary noise.

The bootstrap method effectively quantifies uncertainty in practical scenarios.

Application to EEG data demonstrates the method's utility in real-world signal analysis.

Abstract

We propose a bootstrapping framework to quantify uncertainty in time-frequency representations (TFRs) generated by the short-time Fourier transform (STFT) and the STFT-based synchrosqueezing transform (SST) for oscillatory signals with time-varying amplitude and frequency contaminated by complex nonstationary noise. To this end, we leverage a recent high-dimensional Gaussian approximation technique to establish a sequential Gaussian approximation for nonstationary processes under mild assumptions. This result is of independent interest and provides a theoretical basis for characterizing the approximate Gaussianity of STFT-induced TFRs as random fields. Building on this foundation, we establish the robustness of SST-based signal decomposition in the presence of nonstationary noise. Furthermore, assuming locally stationary noise, we develop a Gaussian autoregressive bootstrap for uncertainty quantification of SST-based TFRs and provide theoretical justification. We validate the proposed methods with simulations and illustrate their practical utility by analyzing spindle activity in electroencephalogram recordings. Our work bridges time-frequency analysis in signal processing and nonlinear spectral analysis of time series in statistics.