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The '''modified Allan variance (MVAR)''',<ref name=NISTSP1065>NIST SP 1065: [http://tf.nist.gov/timefreq/general/pdf/2220.pdf] ''Handbook of Frequency Stability Analysis''</ref> also known as mod&nbsp;&sigma;<sub>''y''</sub><sup>2</sup>(&tau;), is a variable bandwidth modified variant of [[Allan variance]], a measurement of frequency stability in [[clock]]s, [[oscillator]]s and [[amplifier]]s. Its main advantage relative to Allan variance is its ability to separate [[white noise|white phase noise]] from [[flicker noise|flicker phase noise]].
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The '''modified Allan deviation (MDEV)''',<ref name=NISTSP1065/> also known as mod&nbsp;&sigma;<sub>''y''</sub>(&tau;), is the deviation variant of the modified Allan variance.
 
==Background==
The [[Allan variance]] has a drawback in that it is unable to separate the white phase modulation (WPM) from the flicker phase modulation (FPM). Looking that their response to [[Allan variance#Power-law noise|Power-law noise]] it is clearly seen that WPM and FPM has almost the same response to tau, but WPM is linearly sensitive to the system bandwidth ''f''<sub>''H''</sub> 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 <ref name=FCS35.470-1981>David W. Allan and James A. Barnes: ''A modified "Allan variance" with increased oscillator characterization ability'', 35th Annual Frequency Control Symposium, 1981</ref> using time error samples as
 
:<math>\operatorname{mod}\sigma_y^2(n\tau_0) = \frac{1}{2\tau^2}\left\langle \left[ \frac{1}{n}\sum_{i=0}^{n-1}x_{i+2n}-2x_{i+n}+x_i\right]^2 \right\rangle</math>
 
or with [[Allan variance#Average fractional frequency|average fractional frequency]] time series
 
:<math>\operatorname{mod}\sigma_y^2(n\tau_0) = \frac{1}{2}\left\langle \left[ \frac{1}{n}\sum_{i=0}^{n-1}\bar{y}_{i+n}-\bar{y}_i\right]^2 \right\rangle</math>
 
where ''n'' is the integer number of samples averaged over.
 
==Estimators==
The modified Allan variance estimator for time error time series is
 
:<math>\operatorname{mod}\sigma_y^2(n\tau_0) = \frac{1}{2n^4\tau_0^2(N-3n+1)}\sum_{j=0}^{N-3n} \left\{ \sum_{i=j}^{j+n-1} x_{i+2n}-2x_{i+n}+x_i\right\}^2</math>
 
or with [[Allan variance#Average fractional frequency|average fractional frequency]] time series
 
:<math>\operatorname{mod}\sigma_y^2(n\tau_0) = \frac{1}{2n^4(M-3n+2)}\sum_{j=0}^{M-3n+1} \left\{ \sum_{i=j}^{j+n-1} \left( \sum_{k=i}^{i+n-1}\bar{y}_{k+n}-\bar{y}_k\right) \right\}^2</math>
 
==References==
<references/>
 
[[Category:Clocks]]
[[Category:Signal processing metrics]]

Latest revision as of 08:13, 30 December 2014



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A Commonplace Stockman sample supplies three completely different blade sizes and shapes. The principle blade and one of the two smaller blades are hinged from the identical handle end. The third blade is hinged from the other handle finish, which is nested in the same deal with blade slot of the opposite smaller blade. This pattern gerber pocket knife is known as a Stockman as a result of the usage of knives just like this was intently related to reducing tasks carried out by folks engaged on ranches and in livestock yards. The spey blade was saved sharp and used for neutering livestock. The coping blade was used for element carving and inletting tasks.

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