Allan Variance

The Allan variance, named after David W. Allen, also known as two-sample variance, is a measurement of accuracy in clocks. It is defined as one half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. For most real-world systems, the Allan variance depends on the time period used between samples: therefore it is a function of the sample period, as well as the distribution being measured. A low Allan variance is a characteristic of a clock with good stability over the measured period. The Allan variance is given by
\sigma_y^2(\tau) = \frac{1}{2} \langle(y_{n+1} - y_n)^2\rangle
where y_n is the normalized frequency departure, averaged over sample period n, and \tau is the time per sample period. The samples are taken with no dead-time between them. Source: from Federal Standard 1037C

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