The limit of frequency estimation

In phase and frequency measurements, the measured phase and frequency are not the true phase and frequency but the ones which are disturbed by noises, due to the effects of the noise processes. The effects of three noise processes, i.e., White PM, White FM, and Random Walk FM, on the estimations of phase and frequency is discussed. It is indicated that the properties of these two estimations are very different. In phase estimation, the error can be reduced by properly selecting suitable smoothing length NT and smaple interval T. But in frequency estimation, the error cannot be reduced arbitrarily by means of improving estimator or measurement equipment. The precision of frequency is limited by the intrinsic noises in the clock.