间歇混沌合成1/f噪声的相关特性分析

本文利用非线性随机微分方程来合成间歇混沌信号,针对该信号表现出的1/f噪声特征,在不同消失矩的小波基下进行相关特性分析.仿真结果发现,在功率谱的中间频段内,该信号的功率谱密度表现出典型的1/f噪声特性,其小波变换系数方差与相应的小波尺度呈对数线性关系;且在该频段内,部分尺度下该间歇性信号的小波变换系数的相关性随小波基的消失矩的增大而减小,在另一部分尺度下该相关性则随着消失矩的增大而增大.实验结果表明,随小波消失矩的增大,并非在所有尺度下小波变换对该间歇性信号均具有去相关作用.论文讨论了小波变换系数的方差和尺度的关系,详细分析了小波变换系数的相关性随小波消失矩的变化趋势.

AnaIysis of CorreIation Characteristics of 1/f Noise Generated by Intermittency

In this paper the nonlinear stochastic differential equation is used to generalize an intermittency signal,and the correlation of its 1/f noise characteristics under the wavelet bases with different vanishing moments are analyzed.The simulation results show that in the middle band of the frequency spectrum,its power spectrum density (PSD)shows typical 1/fnoise characteristics,and the relationship of the signal’s wavelet transformation coefficient variance and the correspond-ing wavelet scale is linear under logarithm coordinate.In this frequency band,under some scales the signal’s wavelet trans-formation coefficient correlations decrease with the vanishing moments growing,while in other scales,the correlations in-crease with the vanishing moment increasement.These results indicate that wavelet transformation does not always bring decorrelation to the intermittency signal.The relationship of the wavelet transformation coefficients’variances and the scale, and the tendency of coefficients’correlations with wavelet vanishing moments changing are analyzed.