The continuous wavelet transform (CWT)-based synchrosqueezing transform (SST) is a special type of the reassignment method which not only enhances the energy concentration of CWT in the time-frequency plane, but also separates the components of multicomponent signals. The “bump wavelet” and Morlet's wavelet are commonly used continuous wavelets for SST. There is a parameter in these wavelets which controls the widths of the time-frequency localization window. In most literature on SST, this parameter is a fixed positive constant. In this paper, we consider the CWT with a time-varying parameter (called the adaptive CWT) and the corresponding SST (called the adaptive SST). We also introduce the 2nd-order adaptive SST. We analyze the separation conditions for non-stationary multicomponent signals with the local approximation of linear frequency modulation mode. We derive well-separated conditions of a multicomponent signal based on the adaptive CWT. We propose methods to select the time-varying parameter so that the corresponding adaptive SSTs of the components of a multicomponent signal have sharp representations and are well-separated. We provide comparison experimental results to demonstrate the efficiency and robustness of the proposed adaptive SST in separating components of multicomponent signals with fast varying frequencies.

基于连续小波变换（CWT）的同步压缩变换（SST）是一种特殊的重新分配方法，它不仅提高了CWT在时频平面上的能量集中度，而且分离了多分量信号的分量。“凹凸小波”和Morlet小波是用于SST的常用连续小波。这些小波中有一个参数可以控制时频本地化窗口的宽度。在大多数有关SST的文献中，此参数是固定的正常数。在本文中，我们考虑具有时变参数的CWT（称为自适应CWT）和相应的SST（称为自适应SST）。我们还介绍了二阶自适应SST。我们用线性频率调制模式的局部逼近分析非平稳多分量信号的分离条件。我们基于自适应CWT得出多分量信号的良好分离条件。我们提出了选择随时间变化的参数的方法，以使多分量信号的分量的相应自适应SST具有清晰的表示并且可以很好地分离。我们提供比较实验结果，以证明所提出的自适应SST在分离具有快速变化频率的多分量信号的分量方面的效率和鲁棒性。我们提出了选择随时间变化的参数的方法，以使多分量信号的分量的相应自适应SST具有清晰的表示形式并且被很好地分离。我们提供比较实验结果，以证明所提出的自适应SST在分离具有快速变化频率的多分量信号的分量方面的效率和鲁棒性。我们提出了选择随时间变化的参数的方法，以使多分量信号的分量的相应自适应SST具有清晰的表示并且被很好地分离。我们提供比较实验结果，以证明所提出的自适应SST在分离具有快速变化频率的多分量信号的分量方面的效率和鲁棒性。