离散白噪声序列循环自相关函数估计的误差分析

Research on Performance of Suppressing Noise by Cyclic Auto Correlation Function

在理想情况下，平稳白噪声在某一循环频率α上的循环自相关函数为零，因此对于具有循环平稳特性的信号利用循环自相关函数取代传统的自相关函数可以有效地抑制噪声。但在实际场合中由于数据长度有限，噪声循环自相关函数的估计量并不为零，因此将影响循环平稳方法的性能。本文推导了有限长数据下噪声循环自相关函数与数据长度之间的量化关系，给出了相应的物理解释，并通过Ｍｏｎｔｅ－Ｃａｒｌｏ实验验证了有关结论。

Under ideal condition, the cyclic auto correlation function of stationary white noise is zero over certain cyclic frequency α . So it is possible to suppress the effect of noise when processing the cyclostationary signals, where the conventional auto correlation function is replaced by the cyclic auto correlation function. Unfortunately, the estimation of the cyclic auto correlation function of the white noise is not zero due to the limited data length in some real environment. Accordingly, the performance of cyclostationary method may be negatively affected. In this paper, the quantitative relation between the cyclic auto correlation function of the white noise and its available data length is deduced, and the corresponding physical explanation is also given. Finally, the conclusion is proved by Monte Carlo experiments.