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 finite 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 SNRs. Theoretical performance curves are thereby calculated (mean square error versus SNR) that establish the existence of a threshold effect. Until now, the existence of a threshold effect 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.