Power-law Noise
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.
| Power-law noise type | Phase noise slope | Frequency noise slope | Power coefficient | Phase noise | Allan variance | Allan deviation |
| white phase modulation (WPM) | ||||||
| flicker phase modulation (FPM) | ||||||
| white frequency modulation (WFM) | ||||||
| flicker frequency modulation (FFM) | ||||||
| random walk frequency modulation (RWFM) |
As found in and in modern forms.
The Allan variance is unable to distinguish between WPM and FPM, but is able to resolve the other power-law noise types. In order to distinguish WPM and FPM, the modified Allan variance need to be employed.
The above formulas assume that
and thus that the bandwidth of the observation time is much lower than the instruments bandwidth. When this condition is not met, all noise forms depend on the instruments bandwidth.
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