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 Ephraim and Roberts (2005) on the covariance of the log-periodogram by additionally taking averaging over local frequencies into account. Moreover, we provide a simple expression for the non-integer moments of a non-central chi-squared distribution.

翻译：我们提出了零均值平稳高斯过程的对数平均周期图协方差的近似表达式。我们的研究成果扩展了Ephraim和Roberts（2005）关于对数周期图协方差的工作，额外考虑了局部频率上的平均化。此外，我们还给出了非中心卡方分布非整数矩的简单表达式。