We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then, a central limit theorem result for SST is established. {As an example}, we provide a block bootstrap scheme based on the established SST theory to test if a given time series contains oscillatory components.

翻译：本文对非线性型时频分析中的工具——同步压缩变换( SST )在零假设与非零假设情形下进行了统计分析。通过仔细分析相关的多元复高斯随机变量，量化了SST中不同量之间复杂的非线性相互作用。具体而言，我们给出了相依且非正则复高斯随机变量的商分布，进而建立了SST的中心极限定理。作为应用实例，我们基于所建立的SST理论提出了一种块自助法方案，用于检验给定时间序列是否包含振荡成分。