Time deviation

Time deviation (TDEV),^[1] also known as ${\displaystyle \sigma _{x}(\tau )}${\displaystyle \sigma _{x}(\tau )}, measures the time stability of a clock source's phase over an observation interval, expressed as a standard deviation of the time variations. This indicates the time instability of the signal source. This is a scaled variant of frequency stability of Allan deviation. It is commonly defined from the modified Allan deviation, but other estimators may be used.

Time variance (TVAR), symbolised as ${\displaystyle \sigma _{x}^{2}(\tau )}${\displaystyle \sigma _{x}^{2}(\tau )}, is the time stability of phase versus observation interval tau. It is a scaled variant of modified Allan variance.

TDEV is a metric often used to determine an aspect of the quality of timing signals in telecommunication applications and is a statistical analysis of the phase stability of a signal over a given period. Measurements of a reference timing signal will refer to its TDEV and maximum time interval error (MTIE) values, comparing them to specified masks or goals.

The most common estimator uses the modified Allan variance

${\displaystyle \sigma _{x}^{2}(\tau )={\frac {\tau ^{2}}{3}}\operatorname {mod} \sigma _{y}^{2}(n\tau _{0})}${\displaystyle \sigma _{x}^{2}(\tau )={\frac {\tau ^{2}}{3}}\operatorname {mod} \sigma _{y}^{2}(n\tau _{0})}

where ${\displaystyle \tau =n\tau _{o}}${\displaystyle \tau =n\tau _{o}}.^{[Add definitions of n and τ₀ ]} The 3 in the denominator normalizes TVAR to be equal to the classical variance if the deviations in x are random and uncorrelated (white noise).

Alternatively, TDEV, which is the square-root of TVAR, may be derived from MDEV modified Allan deviation

${\displaystyle \sigma _{x}(\tau )={\frac {\tau }{\sqrt {3}}}\operatorname {mod} \sigma _{y}(n\tau _{0})}${\displaystyle \sigma _{x}(\tau )={\frac {\tau }{\sqrt {3}}}\operatorname {mod} \sigma _{y}(n\tau _{0})}

• Signal processing metrics
• Measurement
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