ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM-TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS

• 成果类型: Article
• 署名作者: Sourisseau, Matt; Wu, Hau-Tieng; Zhou, Zhou
• 署名单位: University of Toronto; Duke University; Duke University; University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2203
• 发表日期: 2022
• 页码: 2694-2712
• 关键词: instantaneous frequency; spectral-analysis; reassignment

摘要

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and nonnull 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.