1/f Noise: The Mystery That May Be Its Own Fourier Transform
An Interesting Fourier Transform – 1/F Noise
Power laws have a remarkable property: their Fourier transforms are also power laws. This leads to a fascinating symmetry—when the time-domain decay rate is t^-0.5, the frequency-domain magnitude is ω^-0.5. This is exactly the amplitude spectrum of 1/f noise, a ubiquitous yet unexplained phenomenon. The author suggests that 1/f noise might be its own Fourier transform, a clue that could finally crack an 80-year-old physics mystery.
It’s clear that something is still missing.
- tgv
Wikipedia has an article with some other information on pink noise (a more common name), including a random generator: https://en.wikipedia.org/wiki/Pink_noise. Some music generation algorithms use pink noise, as it (supposedly) strikes a better balance between randomness and predictability.
- mturmon
The piece ends with the observation that maybe the fact that 1/f noise is its own Fourier transform is a clue.
Turns out this property is not unusual. There are many such pairs - there’s a reasonably well-known journal paper with a construction technique.
- lars
The comment section at the bottom of the article is pretty interesting. 20 years of people thinking about this.