When investigating the stability of crystal oscillators and atomic clocks, it was found that they did not have a phase noise consisting only of white noise, but also of flicker frequency noise. These noise forms become a challenge … See more

Allan variance is defined as one half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. The Allan variance depends on the time period used between samples, therefore, … See more

Oscillator model
The oscillator being analysed is assumed to follow the basic model of
The oscillator is assumed to have a nominal frequency of , given in cycles per second (SI unit: hertz). The nominal angular frequency See more

The Allan variance will treat various power-law noise types differently, conveniently allowing them to be identified and their strength estimated. As a convention, the measurement system width (high corner frequency) is denoted fH.
As found in and in … See more

M-sample variance
The -sample variance is defined (here in a modernized notation form) as
where is the clock reading (in seconds) measured at time , or with average fractional frequency time series
where is … See more

This definition is based on the statistical expected value, integrating over infinite time. The real-world situation does not allow for such time … See more

Statistical estimators will calculate an estimated value on the sample series used. The estimates may deviate from the true value and the range of values which for some probability … See more