A Few Notes on Variance of Frequency Estimated Applying Analytical Leakage Compensation

One of the most accurate and commonly accepted methods for spectral analysis, i.e., estimation of frequency from samples of a signal, is analytical leakage compensation, briefly called analytical solution (AS). The AS estimate is negligibly biased, but it is the whole class of solutions whose variance depends on a free parameter named K. Thus, an important step in AS algorithm is calculation of optimal K
_opt
, which selects the minimum variance solution from theoretically infinite set. The original paper provides complete set of needed formulae, and here a few other relations are discussed, which can be used to further reduce the variance, if properly applied according to the specified criterion.