Colors of noise

visible spectrum

The term white noise is fairly common. People unfamiliar with its technical meaning will describe some sort of background noise, like a fan, as white noise. Less common are terms like pink noise, red noise, etc.

The colors of noise are defined various ways, but they’re all based on an analogy between the power spectrum of the noisy signal and the spectrum of visible light. This post gives the motivations and intuitive definitions. I may give rigorous definitions in some future post.

White noise has a flat power spectrum, analogous to white light containing all other colors (frequencies) of light.

Pink noise has a power spectrum inversely proportional to its frequency f (or in some definitions, inversely proportional to fα for some exponent α near 1). Visible light with such a spectrum appears pink because there is more power toward the low (red) end of the spectrum, but a substantial amount of power at higher frequencies since the power drops off slowly.

The spectrum of red noise is more heavily weighted toward low frequencies, dropping off like  1/f2, analogous to light with more red and less white. Confusingly, red noise is also called Brown noise, not after the color brown but after the person Robert Brown, discoverer of Brownian motion.

Blue noise is the opposite of red, with power increasing in proportion to frequency, analogous to light with more power toward the high (blue) frequencies.

Grey noise is a sort of psychologically white noise. Instead of all frequencies having equal power, all frequencies have equal perceived power, with lower actual power in the middle and higher actual power on the high and low end.

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9 thoughts on “Colors of noise

  1. s/frequencies/power/ in two places in the final sentence, but an interesting note nevertheless. Thanks!

  2. “Green noise” is a term you occasionally hear in computer graphics. It comes up because it’s the frequency spectrum of halftone screens, which are still important (e.g. in laser printing).

  3. It is always worth noting in the discussion of noise colours, that although (because?) of the 1/f power spectrum of pink noise, it has equal energy per octave (or third octave, decade, or other logarithmic frequency spacing).

  4. In stochastic caluclus, the usual white noise process is the “derivative” of Wiener process ( d W_t ). What would be the analog of those other types of noise?

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