# Probability of periodic signal in gaussian white noise time series

Suppose I have time series data that is accurately modeled as gaussian white noise with mean and variance $$\mu, \sigma^2$$. I would like to write down a probability density characterizing the probability of observing a periodic signal in the gaussian noise. The 6th slide here: https://astrostatistics.psu.edu/su12/lectures/TSA_EDF_SumSch.pdf

provides a density, but I'm struggling to understand where it comes from.