THRESHOLD EFFECTS IN MULTIHARMONIC MAXIMUM-LIKELIHOOD FREQUENCY ESTIMATION

This paper derives a general expression for the mean square error in e stimating the fundamental frequency of a multiharmonic signal from a f inite sequence of noisy measurements. The distinguishing feature of th is expression is that it is applicable at values of signal-to-noise ra tio (SNR) within the threshold region, in contrast to earlier expressi ons (the Cramer-Rao bounds) that are valid only at high SNRs. Theoreti cal performance curves are thereby calculated (mean square error versu s SNR) that establish the existence of a threshold effect. Until now, the existence of a threshold effect was demonstrable only by simulatio n. Examples are given comparing various multiharmonic estimation scena rios to the single tone case under comparable conditions. The theoreti cal performance curves in these examples are corroborated by Monte Car lo simulation.