An Interesting Fourier Transform – 1/F Noise

1/f noise basically kills averaging. You collect more signal but at the same time equally more noise.

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.

The comment section at the bottom of the article is pretty interesting. 20 years of people thinking about this.

Just as interesting and surprising to me is that this 0-100Hz line is unexplained. Given that signal processing is the foundation of pretty much all digital technology, as well as the analog technologies that came before, I've kind of assumed every segment of a frequency plot be well studied and understood, with half a dozen of names to choose for (doublesine quefrency this, Kowalski-Shannon that...) and a heap of decades old textbooks about it.

I confirm, the low frequency range looks weird on every DFT plot I ever saw, particularly the audio ones. I just assumed it has something to do with ADC and is probably explained on Wikipedia. It's literally one of the last place on Earth when I'd expect to find unsolved mysteries.

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.