On second-order statistics of the log-average periodogram

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.