Minimum variance of frequency estimations for a sinusoidal signal with low noise

Consideration is given to frequency estimates for continuous data trains of a fixed length amounting to at least five oscillations of a sinusoidal signal of constant frequency accompanied by low-level noise. The minimum variance of the frequency estimation is derived in terms of the noise spectral density at frequencies close to that of the signal. The extent to which several practical methods of frequency measurement can reach this limit is analysed. The case in which the frequency of the signal source may vary slightly within each data train is also included.