I know, that the white noise is called "white noise", because it comes from physics and has something to do with the spectral decomposition (is that right?) of the white light? I am not familiar with signal theory, so could anyone explain me why it is called white noise, especially the relation to the terms light, spectra and so?


closed as off topic by ttnphns, whuber Apr 21 '13 at 1:15

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    $\begingroup$ The power spectral density of a white noise process (random process) has constant value for all frequencies. Someone thought that this was a property of white light (equal energy at all frequencies (in a certain range of frequencies)) and named the random process white noise by analogy. People liked the name and it stuck. In fact, white light has equal energy at all wavelengths, not frequencies, but it is too inconvenient to correct the name now. $\endgroup$ – Dilip Sarwate Apr 20 '13 at 21:01
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    $\begingroup$ I'm suprised this got closed, given how often white noise/whitening/etc come up. $\endgroup$ – Matt Krause Jun 23 '17 at 15:06
  • $\begingroup$ This is statistical physics. Physical statistics would mean something else, e.g., height, weight of subject. I would encourage interest in physical applications of statistics because it imposes proper rules on units, and equations the likes of which are completely incorrect when ignored. To put it another way, if your equations are not physically correct, they are not correct at all. $\endgroup$ – Carl Jun 24 '17 at 1:02

White noise is a signal (e.g., a sound or image) that has approximately equal power in every frequency band. In other words, its power spectral density (PSD) or power spectrum, is flat. (If you're unfamilar, the PSD/Power Spectrum/Spectrum is a plot showing the spectral content of a signal; that is, it shows the amount of power in/at each frequency or frequency band). People sometimes also use the term for sequence of uncorrelated random variables.

The White Noise page at wikipedia has several examples, if you want to see what it looks like, but the "ssssh" sound of turbulantly flowing air or the static on a detuned analog TV set are pretty reasonable approximations.

The name arises from an analogy with white light, which was thought to contain equal energy at all frequencies. This is actually not quite correct--it should be all wavelengths--but the name appears to have stuck and it's not clear to me how literal it was meant to begin with. The Oxford English dictionary reports that it was used as early as 1922, but it looks like the term didn't really catch on until the 1940s:

1922 Nature 1 Apr. 414/2: Just as the spectrum of a hot body normally consists of a continuous spectrum of white light, together with certain spectrum lines the wave~lengths of which are characteristic of the radiating material, so an element emitting X-rays not only gives out ‘white’ radiation, but superposes its characteristic lines on the general spectrum.

1943 Jrnl. Aeronaut. Sci. 10 129/1 Inside the plane it is different; there all frequencies added together at once are heard, producing a noise which is to sound what white light is to light... That white noise is annoying needs little argument.

In many, or probably even most contexts, white noise has little to do with light itself. There are other "coloured" noises which have different statistical properties. Red noise, for example, has a power spectrum dominated by low frequencies. As with white noise, the name may have been inspired by the fact that red light is at the low frequency end of the visible spectrum. However, a realization of (e.g.) red noise may not necessarily appear red, and a red-hued patch of noise may not be "red noise".

  • $\begingroup$ The spectrogram in your link just happens to use a colormap that makes pinkish noise appear pink; it could have just as easily been drawn using blues or greens. That said, it does seem likely that red and blue noise are also "inspired" the fact that red/blue light is dominated by low/high frequencies (respectively). Thanks for pointing that out! However, the point I really want to stress is that a patch of noise with a pinkish hue is not necessarily "pink noise" and a realization of pink noise may not appear pink. $\endgroup$ – Matt Krause Sep 2 '17 at 2:33
  • $\begingroup$ Yes, you are right and the image I linked is not a realization of white and pink noise. I delete my comment because I can't just delete the misleading link. However, it would be interesting to see a realization of those noises using light. $\endgroup$ – Pere Sep 2 '17 at 9:02

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