摘要
通过研究有限离散二进小波变换与非线性动力学相空间重构的关系，从相空间重构的角度解释小波变换处理混沌时序的合理性，指出混沌时序的离散小波变换实质上相当于在混沌时序重构的相空间中，混沌吸引子向离散滤波器向量投影的结果。在一定程度内混沌的特性不变。在滤波器向量所张开的平面上可以观察到混沌吸引子的投影：讨论了嵌入维数、时间延迟等与离散二进小波变换尺度间的联系。
The rationalization of the use of wavelet transform on chaots time series is explained on the view of phasespace reconstruction, according to the study of the relation between the finite discrete binary wavelet transform and nonlinear dynamical phasespace reconstruction. Its put forward that the discrete wavelet transform of chaos time series means that in the phasespace reconstructed attractor, it takes the projection on the filter axis, and to a certain extent the characteristic of chaos is not changed. In the plane of the filter vector, the strange attractor can be observed. The relation between the embedding dimension, time delay and the scale of the discrete binary wavelet is also discussed.
出处
《振动工程学报》
EI
CSCD
1999年第1期27-32,共6页
Journal of Vibration Engineering
基金
国家自然科学基金
陕西省自然科学基金
关键词
非线性力学
混沌
小波变换
相空间重构
non linear mechanics
chaos
wavelet transform
phasespace reconstruction
