信号分形维数估计的研究与实现*

基于序列分形自仿射特性，提出一种实现一维信号分形维数估计的方法。按不同尺度将信号序列分段为映射区间和象区间，采用搜索算法确定与各象区间最优匹配的映射区间，并根据迭代函数系统理论估计信号的分形维数。以分形维数已知的MackeyGlass和Lorenz信号为例，仿真表明提出的方法能准确估计信号的分形维数，对实际应用具有一定的参考价值。

Research and implementation of fractal dimension estimation

This paper proposed a method to implement fractal dimension estimation based on the self-affine property of signals.It decomposed the signal series to mapping and mapped segments,and adopted a searching algorithm to find the mapping sections that match best for each mapped sect.It estimated fractal dimension by the iterative function system.Simulations on Mackey-Glass time series and Lorenz system indicate that the proposed method can estimate the fractal dimension accurately.