利用小波多尺度分解算法实现混沌系统的噪声减缩

REDUCTION OF NOISE IN CHAOTIC SYSTEMS BY WAVELET MULTISCALING DECOMPOSITION ALGORITHM

应用小波多尺度分解算法进行噪声减缩，从混沌背景中分离周期信号、噪声及其他混沌信号．小波多尺度分解算法能够区分不同尺度的信号是利用小波变换在时、频两域具有突出信号局部特征的能力以及小波变换是一线性变换的特点．提出的方法仅利用信号的尺度特性，克服了先前的噪声减缩要知道产生混沌信号的数学模型，并且要求叠加在混沌背景中的其他信号的幅度相对混沌背景信号的幅度很小的假定．给出了从 Ｌｏｒｅｎｚ 混沌背景中提取正弦信号、白噪声和 Ｃｈｕａ’ｓ 电路产生的混沌信号的计算机模拟结果．

We apply the wavelet multiscaling decomposition algorithm,which has been developed for noise reduction,to the extraction of periodic signal,noise and other chaotic signal from chaotic background.This algorithm utilizes the characteristic that wavelet transform has an outstanding local feature in time\|frequency domains and it is a linear transform.Therefore it can distinguishes signals with different scales.In contrast to the previous methods our method uses the feature of signal scales and dose not demand restrictive assumptions that we must know the mathematical model of the chaotic background and that the amplitude of signal is smaller than that of the chaotic background.The results of computer simulation are given for extracting the sine signal,white noises (distributed uniformly or in Gaussion shape) and Chua's chaotic signal from Lorenz chaotic background. PACC: 0545; 0540