An Interesting Fourier Transform – 1/F Noise

An Interesting Fourier Transform – 1/F Noise(dsprelated.com)

33 points by q7m 3 days ago | 7 comments

tgv 50 minutes ago |

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.

rcxdude 21 minutes ago | |

Pink noise is also perceptually flat noise, because it contains the same energy in each octave (or decade). 'truly' white noise (equal energy for equal bandwidth) tends to sound quite tinny/hissy in comparison.

mturmon 2 hours ago |

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.

fch42 2 hours ago | |

The paper linked at the "see also" section ? (thx)

lars 1 hour ago |

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

TeMPOraL 1 hour ago |

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.

rcxdude 1 hour ago | |

It's not completely unexplained. Roughly speaking you can get that power spectrum in the limit when you are adding up many different events where the magnitude of the event is inversely proportional to its likelihood (and in practice, there is a limit to the magnitude of the events that will cause it to level off at some point, but for some processes this is not measurable even over decades). The main mystery in most cases is what exactly is the physical process that is causing it. For some electronics it looks like it is due to trapped charges sometimes tunneling around, but it doesn't explain every case of it in electronics let alone everything else. Convective thermal effects can also be a good candidate in a lot of systems, since turbulence also has 1/f noise properties.

(Also, the low frequency range on a DFT can look weird for reasons other than noise: it'll also tend to rise up if there's any longer-term structure to the signal as well, so you need to be careful interpreting them blindly if you're trying to measure noise)