On Second-Order Statistics of the Log-Average Periodogram for Gaussian Processes

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.