Allan deviation

The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers, named after David W. Allan and expressed mathematically as ${\displaystyle \sigma _{y}^{2}(\tau )}$. The Allan deviation (ADEV), also known as sigma-tau, is the square root of Allan variance, ${\displaystyle \sigma _{y}(\tau )}$.

The M-sample variance is a measure of frequency stability using M samples, time T between measures and observation time ${\displaystyle \tau }$. M-sample variance is expressed as

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