基于小波变换的混沌信号特征研究

Study on Characteristics of Chaotic Signal with Wavelet Analysis

应用小波方法将混沌信号的频谱特征和吸引子的几何结构相结合进行研究,结果表明,在不同尺度上对混沌信号进行连续小波变换时,其小波系数具有很强的相似性,但不能够完全重构原来的吸引子.对信号进行多尺度分解后发现其低频系数部分基本能够重现原吸引子的结构特征,而高频系数部分不能实现这一目标.为了定量刻画混沌信号在小波变换条件下的分形特征,计算了其在不同尺度时的关联维数,并分析了关联维数计算的影响因素.

This paper studies the characteristics of chaotic signal by combining its frequency spectrum and geometry structure. In the process of analyzing chaotic time series, the phase space reconstruction technology is applied to recover its dynamic features. After choosing reasonable embedding dimension and delay time, the strange chaotic attractor shows self similarity structure. By applying wavelet transformation to deal with chaotic signal, results show that the wavelet transformation coefficients of different scales are similar to each other. However, they are unsuitable to reconstruct the attractor for its distortion. With multi scale decomposition, the low frequency part of the coefficients can recover the original attractor clearly. In order to characterize the fractal under wavelet transformation, the correlation dimension is calculated, and different factors are analyzed as well.