We present an approximate expression for the covariance of the log-average periodogram for a zero mean stationary Gaussian process. Our findings extend the work of [1] on the covariance of the log-periodogram by additionally taking averaging over adjacent frequencies into account. Moreover, we provide a simple expression for the non-integer moments of a non-central chi-squared distribution.

翻译：本文针对零均值平稳高斯过程，提出了对数平均周期图协方差的近似表达式。我们的研究成果拓展了文献[1]中关于对数周期图协方差的工作，额外考虑了相邻频率上的平均效应。此外，我们还给出了非中心卡方分布非整数阶矩的简明表达式。