Editing Allan variance (section)

===''α''–''μ'' mapping===
The detailed mapping of a phase modulation of the form

:<math>S_x(f) = \frac{1}{4\pi^2} h_\alpha f^{\alpha - 2} = \frac{1}{4\pi^2} h_\alpha f^\beta,</math>

where

:<math>\beta \equiv \alpha - 2,</math>

or frequency modulation of the form

:<math>S_y(f) = h_\alpha f^\alpha</math>

into the Allan variance of the form

:<math>\sigma_y^2(\tau) = K_\alpha h_\alpha \tau^\mu</math>

can be significantly simplified by providing a mapping between ''α'' and ''μ''. A mapping between ''α'' and ''K''<sub>''α''</sub> is also presented for convenience:<ref name=IEEE1139/>

:{| class="wikitable"
|+ Allan variance ''α''–''μ'' mapping
|-
!''α''
!''β''
!''μ''
!''K''<sub>''α''</sub>
|-
| −2
| −4
| 1
|<math>\frac{2\pi^2}{3}</math>
|-
| −1
| −3
| 0
|<math>2\ln 2</math>
|-
| 0
| −2
| −1
|<math>\frac{1}{2}</math>
|-
| 1
| −1
| −2
|<math>\frac{3[\gamma+\ln(2\pi f_H\tau)]-\ln 2}{4\pi^2}</math>
|-
| 2
| 0
| −2
|<math>\frac{3f_H}{4\pi^2}</math>
|}