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 variance 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 MAVAR or MVAR, the total variance, and the Hadamard variance. There also exist time stability variants such as time deviation TDEV or time variance TVAR. Allan variance and its variants have proven useful outside the scope of timekeeping and are a set of improved statistical tools to use whenever the noise processes are not unconditionally stable, thus a derivative exists.

The general *M*-sample variance remains important since it allows dead time in measurements and bias functions allows conversion into Allan variance values. Nevertheless, for most applications the special case of 2-sample, or "Allan variance" with is of greatest interest.

Read more about Allan Variance: Background, Interpretation of Value, Estimators, Confidence Intervals and Equivalent Degrees of Freedom, Power-law Noise, Linear Response, Time and Frequency Filter Properties, Bias Functions, Measurement Issues, Practical Measurements, Research History, Educational and Practical Resources, Uses

### Other articles related to "allan variance":

**Allan Variance**- Uses

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**Allan variance**is used as a measure of frequency stability in a variety of precision oscillators, such as crystal oscillators, atomic clocks and frequency-stabilized ... The

**Allan variance**is also used to characterize the bias stability of gyroscopes, including fiber optic gyroscopes and MEMS gyroscopes ...

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