2
$\begingroup$

I've heard of $\frac{1}{f^0}$ noise (white noise), $\frac{1}{f}$ (pink, or sometimes tan noise), and $\frac{1}{f^2}$ (brown noise). But why no $\frac{1}{f^{0.5}}$ or $\frac{1}{f^{\pi-2}}$ noise. Do these exist or are they just rounded of to pink noise. Also I read that the exponent must lie between 0 and 2 but whats wrong with $\frac{1}{f^3}$ noise?

EDIT: by exist I mean do they have waveforms that oscillate, whether or not we can hear them I find irrelevant.

$\endgroup$
4
  • $\begingroup$ And what you mean by "exist" in this case? You can generate $1/f^3$ noise, but everything with exponent larger than 2 is named "black noise" and defined almost as a silence (with zero power density with a few random spikes allowed). $\endgroup$
    – m0nhawk
    Oct 19 '15 at 10:47
  • $\begingroup$ @m0nhawk by exist I mean do the have waveforms the are oscillate, whether or not we can hear them I find irrelevant. $\endgroup$
    – tox123
    Oct 26 '15 at 1:27
  • 2
    $\begingroup$ Would Signal Processing or Cross Validated be a better home for this question? $\endgroup$
    – Qmechanic
    Oct 26 '15 at 8:52
  • $\begingroup$ Sure, you can in principle have any frequency distribution you want. Whether or not any physical processes in the real world create noise with that spectrum is another question, but you can easily generate it on a computer. $\endgroup$
    – tparker
    Aug 5 '17 at 0:57
2
$\begingroup$

These terms simply refer to the spectral distribution of energy as a function of frequency. So with Pink Noise the energy falls off as an inverse of frequency. Brown Noise as a function of the square of the frequency. Hence it is quite possible to program (say) a digital filter to remove energy as an arbitrary power function of frequency - or even increase it! It's just that nobody really bothers to do it except (presumably) for very specialist tasks. Pink Noise, for example, is often used in testing the frequency response of speaker systems because by limiting high frequencies in a predictable way can help protect tweeters from overload.

$\endgroup$
4
  • $\begingroup$ Actually, creating a digital filter with a given response is a major challenge, and it's not always possible to do it exactly. In particular, I think a $1/f$ (aka "3 dB/octave") filter is not possible. Of course you can approximate it with an FFT or by a clever combination of other filters, but there will always be deviations from the ideal response. $\endgroup$
    – Nathaniel
    Oct 26 '15 at 8:46
  • 1
    $\begingroup$ @Nathaniel Everything is an approximation - even the analog circuits they are based upon $\endgroup$
    – user56903
    Oct 26 '15 at 9:32
  • 1
    $\begingroup$ Not in the sense I intended. A 6 dB/Octave filter ($1/f^2$), for example, can be implemented exactly using a simple IIR method. $\endgroup$
    – Nathaniel
    Oct 26 '15 at 9:41
  • $\begingroup$ So there can be any g (f) noise assuming the domain and range g are a subset of the positive reals $\endgroup$
    – tox123
    Nov 2 '15 at 14:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.