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. Furthermore, we provide a block bootstrap scheme based on the established SST theory to test if a given time series contains oscillatory components.

翻译：我们提供非线性类型时间频率分析工具的统计分析,即无核和无核情况下同步挤压变异(SST)工具的统计分析。SST中不同数量的复杂非线性交互作用通过仔细分析相关的多变量复杂高斯随机变量加以量化。具体地说,我们提供了依赖性和不适当的复合高斯随机变量的商数分布。然后,确定了SST的中心限值结果。此外,我们提供了基于既定的SST理论的块式靴套件计划,以测试某一时间序列是否包含串列组件。