子波变换平滑的混沌信号检测

Detection of Chaos Based on Wavelet Transforms

将近几年兴起的子波变换、分形理论应用于带观测噪声混沌信号的检测。基于快速子波变换导出了平滑算子，将其对时序信号进行处理，并根据它在一定的尺度范围内具有标度不变的性质，利用改进的Ｇ－Ｐ算法计算其分数维数，对带有观测噪声的Ｌｏｒｅｎｚ吸引子波的混沌运动进行了检测。实验结果表明，该方法具有较好检测混沌现象的能力。

The method in which the wavelet transforms and fractal theories are applied to detect the chaotic signals with the additive observal noises is presented in the paper. Smoothingoperator is derived from wavelet transforms and used to process the chaotic time series. According to its character of no--scale interval in certain scales,a detective example of the noisy chaotic behavior produced by Lorenz attractor is provided by using the improved G--P algorithm tocalculate its fractal dimension. The result shows that the method introduced here expressesgood ability to chaos detection.