On the probability density of a maximum likelihood mean frequency estimator

A simplified derivation of the probability density function of a mean frequency estimator that equates the mean to the location of the peak of the discrete power spectrum is presented. Although the model in which the signal straddles at most two spectral coefficients is emphasized, the general case of arbitrary signal leakage is also worked out in detail. Previous work on this topic implies that n! (n - 1)-tuple integrals must be evaluated for an n-sample DFT estimator. Our approach demonstrates that the derivation can proceed in a much more straightforward manner.