论文标题
用随时间变化的参数分析自适应同步转换
Analysis of Adaptive Synchrosqueezing Transform with a Time-varying Parameter
论文作者
论文摘要
最近开发了同步Queezing变换（SST），以分离非平稳性多组分信号的组件。基于连续的小波变换的SST（WSST）重新分配了信号连续小波变换到频率变量的比例变量，并逐渐频率表示。最近在论文“自适应同步qysqueezing变换的情况下，具有时间变化的WSST的WSST，称为自适应WSST，具有非平稳信号分离的时变参数”。该论文中提出了具有自适应WSST的非平稳多组分信号的良好分离条件和选择时间变化参数的方法。此外，该论文中的仿真实验表明，自适应WSST在估计多组分信号的瞬时频率和准确的组件恢复方面非常有前途。但是，尚未研究自适应WSST的理论分析。在本文中，我们进行了这样的分析，并获得了与自适应WSST和二阶自适应WSST一起恢复组件的误差界限。这些结果提供了与自适应WSST非平稳多组分信号分离的数学保证。
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.
