基于小波变换的混沌信号相空间重构研究

应用小波变换和非线性动力学方法研究了混沌信号在相空间中的行为，指出混沌时间序 列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投 影，与Packard等人提出的相空间重构方法本质上是一致的.实验结果表明，混沌信号经过 小波变换后，吸引子轨迹与原有轨迹具有相似的结构，同时，系统的关联维数、Kolmogorov 熵等非线性不变量仍然得到保留.这些结果表明，利用小波变换研究混沌信号是有效的. 关键词： 小波变换 相空间重构 混沌信号 脑电信号

Study on phase-space reconstruction of chaotic signal based on wavelet transform

Using the methods of the wavelet transform and the nonlinear dynamics, the behavior of chaotic signals in phase space is studied. It is indicated that, in phase space reconstruction, the wavelet transform of chaotic time series is essentially a projection of strange attractor on the axis of the space that filter vectors opened, which in correspondance with the method of phase space reconstruction proposed by Packard et al. The experimental results show that, after doing wavelet transform, the architecture of attractor trajectory is similar to the original one, and the nonlinear invariants such as correlation dimension and Kolmogorov entropy are reserved. These results show that wavelet transform is effective for studying chaotic signal.