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.

翻译：本文提出了一种自助法框架，用于量化短时傅里叶变换及其衍生的同步压缩变换对受复杂非平稳噪声污染的时变振幅与频率振荡信号所产生的时频表示的不确定性。为此，我们利用近期的高维高斯近似技术，在温和假设下为非平稳过程建立了序列高斯近似。这一结果具有独立的理论价值，为将STFT导出的时频表示作为随机场进行近似高斯性刻画提供了理论基础。在此基础上，我们证明了在非平稳噪声存在下基于SST的信号分解具有鲁棒性。进一步，在局部平稳噪声假设下，我们开发了一种高斯自回归自助法用于量化基于SST的时频表示的不确定性，并提供了理论依据。我们通过仿真验证了所提方法的有效性，并通过分析脑电图记录中的纺锤波活动展示了其实用价值。本研究连接了信号处理中的时频分析与统计学中时间序列的非线性谱分析。