Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Allan variance (AVAR), also known as two-sample variance is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan. It is expressed mathematically as The Allan deviation (ADEV), is the square root of Allan variance. It is also known as sigma-tau, and is expressed mathematically as The M-sample variance, is a measure of frequency stability using M samples, time T between measures and observation time . M-sample is expressed as The Allan variance is intended to estimate stability due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Allan deviation describe frequency stability, i.e. the stability in frequency. See also the section entitled "Interpretation of value" below. There are also different adaptations or alterations of Allan variance. Notably the modified Allan variance, the total variance, and the Hadamard variance. There also exist time stability variants such as time deviation or time variance.

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