The probability density of a maximum likelihood mean frequency estimator

We have obtained the probability density function of a mean frequency estimator that equates the mean to the location of the peak of the discrete power spectrum. The density is valid for a model signal that straddles at most two spectral coefficients and is contaminated by white noise. Extension to other models is straightforward, albeit algebracially laborious. Theoretical results are verified on simulations. Because the estimator may be candidate for mean velocity retrieval throughout the troposphere with a Doppler radar, it is compared to the commonly used (on Doppler weather radars) autocovariance estimator.