Diagram of modified Allan variance as a function of averaging time, showing the 6 typical regimes.[1]
0. White phase-modulation noise (PM): At the highest frequency, white phase noise dominates. This corresponds to .
1. Flicker phase-modulation noise (PM): at a lower frequency, flicker phase noise dominates. This corresponds to .
2. White frequency-modulation noise (FM): at a lower frequency, white noise in frequency dominates. This corresponds to
3. Flicker FM: . This is also called "pink noise".
4. Random Walk FM: . This is also called "brown noise" or "brownian noise". In this regime, the frequency of the system executes a random walk. In other words, becomes a white noise.
5. Frequency drift: . In this regime, the frequency of the system executes a pink noise walk. In other words, becomes a pink noise.
The modified Allan deviation (MDEV),[2] also known as modσy(τ), is the deviation variant of the modified Allan variance.