同步压缩变换（SST）是近年来发展起来的一种用于分离非平稳多分量信号的方法。基于连续小波变换的SST（WSST）将信号的连续小波变换的尺度变量重新分配为频率变量，并且锐化时间-频率表示。本文提出了一种时变参数的WSST算法，称为自适应WSST算法，它是在“Adaptive synchroscushinging transform with a time-varying parameter for non-stationary signal separation”一文中提出的。本文给出了自适应WSST对非平稳多分量信号良好分离的条件和时变参数的选取方法。仿真实验表明，自适应WSST在估计多分量信号的瞬时频率和准确恢复多分量信号方面具有很好的应用前景。然而，自适应WSST的理论分析还没有研究。在本文中，我们进行了这样的分析，并获得误差界与自适应WSST和二阶自适应WSST的组件恢复。这些结果为自适应WSST分离非平稳多分量信号提供了数学保证。
英文摘要：
The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet transform of a signal to the frequency variable and sharpens the time-frequency representation. The WSST with a time-varying parameter, called the adaptive WSST, was introduced very recently in the paper "Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation". The well-separated conditions of non-stationary multicomponent signals with the adaptive WSST and a method to select the time-varying parameter were proposed in that paper. In addition, simulation experiments in that paper show that the adaptive WSST is very promising in estimating the instantaneous frequency of a multicomponent signal, and in accurate component recovery. However the theoretical analysis of the adaptive WSST has not been studied. In this paper, we carry out such analysis and obtain error bounds for component recovery with the adaptive WSST and the 2nd-order adaptive WSST. These results provide a mathematical guarantee to non-stationary multicomponent signal separation with the adaptive WSST.
Airflow recovery from thoracic and abdominal movements using Synchrosqueezing Transform and Locally Stationary Gaussian Process Regression
Clemson University（克莱姆森大学）；University of North Carolina at Greensboro（北卡罗来纳大学格林斯伯勒分校）；Perelman School of Medicine at the University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；Duke University（杜克大学）；National Center for Theoretical Sciences（国家理论科学研究中心）
Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies
