Colors of noise

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 f^I for some exponent I 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.