闪烁噪声的自相关函数及其表征

闪烁噪声是一种非平稳随机过程,其功率谱密度函数在频率低端（ｆ＝０）发散,无法直接利用Ｗｉｅｎｅｒ－Ｋｈｉｎｔｃｈｉｎｅ关系得到它的自相关函数,本文采用“降阶－积分”方法,得到了频率源中闪烁调频噪声的自相关函数的解析表达式。根据这一结果,分析了频率稳定度的表征原理,指出了频率稳定度表征的实质是将非平稳过程转化为平稳过程并求取时间平均。最后,通过时域分析得到了闪烁噪声的Ａｌｌａｎ方差表达式。

Flicker Noise Autocorrelation Function and its Characterization

The flicker noise is a non-stationary random process. Because the flicker noise spectrum density function is divergent at low frequency (f=0), its autocorrelation function can not be directly deduced from the Wiener-Khintchine relation. With the method of "order-reducing and integration", the autocorrelation function of flicker noise is derived. According to this result, the principle of characterization of frequency stability is analyzed. It is pointed out that the principle of characterization of frequency stability is to transfer a non-stationary process into a stationary one and then to average it in time. Finally, the Allan variance of flicker noise is derived based on the time domain analysis.