A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. A theorem which obtains the structure function (covariance of the nth differences) of such a process in terms of the differences of a single function of one time variable is proven. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.