Characterizing frequency stability: a continuous power-law model with discrete sampling

This paper examines several aspects of the Allan variance and the modified Allan variance. New expressions for these variances are derived for noise processes that produce power spectral densities with both integer and noninteger powers (α) in their functional dependence on f. A single expression, continuous over α, is presented for each of these variances. Also investigated are the effects of discrete sampling and finite data length. Discrete equations are developed and compared with more familiar continuous expressions. In addition, the uncertainty of the estimates for the Allan variance and the modified Allan variance for fully overlapping data usage is presented. The uncertainties can be calculated for arbitrary α. The results presented are compared with computer simulations and found to be in excellent agreement