The modified Allan variance (MVAR),
also known as mod ''σ
y''
2(''τ''), is a variable bandwidth modified variant of
Allan variance
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clock
A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meetin ...
, a measurement of frequency stability in
clock
A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the ...
s,
oscillator
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s and
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
s. Its main advantage relative to Allan variance is its ability to separate
white phase noise from
flicker phase noise.
The modified Allan deviation (MDEV),
[ also known as mod ''σy''(''τ''), is the deviation variant of the modified Allan variance.
]
Background
The Allan variance
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clock
A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meetin ...
has a drawback in that it is unable to separate the white phase modulation (WPM) from the flicker phase modulation (FPM). Looking at their response to Power-law noise it is clearly seen that WPM and FPM have almost the same response to tau, but WPM is linearly sensitive to the system bandwidth ''fH'' whereas FPM is only weakly dependent on it. Thus, by varying the system bandwidth the WPM and FPM noise forms may be separated. However, it is impractical to alter the hardware of the measurement system. By post-processing the sample-series and implementing a software bandwidth a modified Allan variance measure can be given capable of resolving the noise forms.
Definition
The modified Allan variance is defined for using time error samples as
:
or with average fractional frequency
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
time series and
:
where ''n'' is the integer number of samples averaged over.
Estimators
The modified Allan variance estimator for time error time series is
:
or with average fractional frequency
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
time series
:
References
Clocks
Signal processing metrics