Editing Allan variance (section)

===Measurement bandwidth limits===
A measurement system is expected to have a bandwidth at or below that of the [[Nyquist rate]], as described within the [[Shannon–Hartley theorem]]. As can be seen in the power-law noise formulas, the white and flicker noise modulations both depends on the upper corner frequency <math>f_H</math> (these systems is assumed to be low-pass filtered only). Considering the frequency filter property, it can be clearly seen that low-frequency noise has greater impact on the result. For relatively flat phase-modulation noise types (e.g. WPM and FPM), the filtering has relevance, whereas for noise types with greater slope the upper frequency limit becomes of less importance, assuming that the measurement system bandwidth is wide relative the <math>\tau</math> as given by

:<math>\tau \gg \frac{1}{2\pi f_H}.</math>

When this assumption is not met, the effective bandwidth <math>f_H</math> needs to be notated alongside the measurement. The interested should consult NBS TN394.<ref name=NBSTN394/>

If, however, one adjust the bandwidth of the estimator by using integer multiples of the sample time <math>n\tau_0</math>, then the system bandwidth impact can be reduced to insignificant levels. For telecommunication needs, such methods have been required in order to ensure comparability of measurements and allow some freedom for vendors to do different implementations. The ITU-T Rec. G.813<ref name=ITUTG813>ITU-T Rec. G.813: [http://www.itu.int/rec/T-REC-G.813/recommendation.asp?lang=en&parent=T-REC-G.813-200303-I ''Timing characteristics of SDH equipment slave clock (SEC)''], ITU-T Rec. G.813 (03/2003).</ref> for the TDEV measurement.

It can be recommended that the first <math>\tau_0</math> multiples be ignored, such that the majority of the detected noise is well within the passband of the measurement systems bandwidth.

Further developments on the Allan variance was performed to let the hardware bandwidth be reduced by software means. This development of a software bandwidth allowed addressing the remaining noise, and the method is now referred to [[modified Allan variance]]. This bandwidth reduction technique should not be confused with the enhanced variant of [[modified Allan variance]], which also changes a smoothing filter bandwidth.