Threshold effects in multiharmonic maximum likelihood frequency estimation

This paper derives a general expression for the mean square error in estimating the fundamental frequency of a multiharmonic signal from a nite sequence of noisy measurements The distinguishing feature of this expression is that it is applicable at values of signal to noise ratio SNR within the threshold region in contrast to earlier expressions the Cramer Rao bounds that are valid only at high SNR s Theoretical performance curves are thereby calculated mean square error versus SNR that establish the existence of a threshold e ect Until now the existence of a threshold e ect was demonstrable only by simulation Examples are given comparing various multiharmonic estimation scenarios to the single tone case under comparable conditions The theoretical performance curves in these examples are corroborated by Monte Carlo simulation