Flickermoth: 1/f Pink Noise
Measurement, Noise & the Lab arc, page 134 of 193. Back to The Pixelated Physics Universe
Who they are
Flickermoth has one line, and says it often: “Averaging longer. regretting longer.”
Flickermoth is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Flicker (1/f) noise: spectral density S(f) ∝ 1/fα with α ≈ 1. When the fluctuating quantity is fractional frequency y (flicker FM, Sy(f) ∝ 1/f), the Allan deviation stops falling and flattens into a floor, σy(τ) = const, so averaging longer stops helping; for white FM it falls as τ−1/2.
$$ \begin{gathered} S(f) \propto \frac{1}{f^{\alpha}}, \qquad \alpha \approx 1 \\ S_y(f) \propto \frac{1}{f} \;\Rightarrow\; \sigma_y(\tau) = \text{const} \\ \text{white FM: } \sigma_y(\tau) \propto \tau^{-1/2} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $S(f)$ | noise power spectral density | — |
| $f$ | Fourier frequency | Hz |
| $\alpha$ | spectral exponent | — |
| $y$ | fractional frequency | — |
| $\sigma_y(\tau)$ | Allan deviation | — |
| $\tau$ | averaging time | s |
Sources
- J. B. Johnson, Phys. Rev. 26, 71 (1925) (low-frequency 'flicker effect')
- D. W. Allan, Proc. IEEE 54, 221 (1966)
Crossovers
Flickermoth meets Chuanna (Chua's Double Scroll). Chuanna's double scroll never repeats, and its spectrum is broadband. Flickermoth's 1/f noise is a different kind of broadband signal; it shows up in many systems, and there isn't one cause for all of them.
Flickermoth meets Seisma (Gutenberg–Richter Law). Seisma's earthquakes follow a power law in size, and Flickermoth's noise follows a power law in frequency. Both have been linked to self-organised criticality, though that link is debated for each.
Flickermoth meets Phaselocke (Lock-In Amplifier). Flickermoth's 1/f noise grows at low frequencies. Phaselocke dodges it by moving the signal up to a reference frequency where the noise is lower.
Wear the lore
Concept keywords: 1/f Pink Noise, Flickermoth, Measurement, Noise & the Lab, physics lore, Pixelated Physics