File:5 regimes of Allan variance as a function of averaging time.png

English: Diagram of Allan variance as a function of averaging time, showing the 5 typical regimes. See Chapter 3 and 5 for details on the 5 regimes.

1. white/flicker phase-modulation noise (PM): At the highest frequency, phase noise dominates. This corresponds to ${\displaystyle \sigma (\tau )\propto \tau ^{-1}}$. However, White PM has ${\displaystyle S[f]=f^{3}}$ but Flicker PM has ${\displaystyle S[f]=f^{2}}$. The Allan variance plot does not distinguish them. It requires Modified Allan variance plot to distinguish them. 2. White frequency-modulation noise (FM): at a lower frequency, white noise in frequency dominates. This corresponds to ${\displaystyle \sigma (\tau )\propto \tau ^{-1/2},S[f]=f^{0}}$ 3. Flicker FM: ${\displaystyle \sigma (\tau )\propto \tau ^{0},S[f]\propto f^{-1}}$. This is also called "pink noise". 4. Random Walk FM: ${\displaystyle \sigma (\tau )\propto \tau ^{+1/2},S[f]\propto f^{-2}}$. This is also called "brown noise" or "brownian noise". In this regime, the frequency of the system executes a random walk. In other words, ${\displaystyle df/dt}$ becomes a white noise. 5. Frequency drift: ${\displaystyle \sigma (\tau )\propto \tau ^{+1},S[f]\propto f^{-3}}$. In this regime, the frequency of the system executes a pink noise walk. In other words, ${\displaystyle df/dt}$ becomes a pink noise.

Source: NIST Special Publication 1065 Handbook of Frequency Stability Analysis

Figure 3. (a) Sigma tau diagram