White noise spectrum. Flat power spectrum. (logarithmic frequency axis)
White noise is a signal (or process), named by analogy to white light, with a flat frequency spectrum<1>. In other words, the signal has equal power in any band of a given bandwidth (power spectral density). For example, with a white noise audio signal, the range of frequencies between 40 Hz and 60 Hz contains the same amount of sound power as the range between 4000 Hz and 4020 Hz has.
Pink noise
Pink noise spectrum. Power density falls off at 10 dB/decade (-3 dB/octave).
The frequency spectrum of pink noise is linear in logarithmic space; it has equal power in bands that are proportionally wide.<1><2> This means that pink noise would have equal power in the frequency range from 40 to 60 Hz as in the band from 4000 to 6000 Hz. Since humans hear in such a proportional space, where a doubling of frequency (an octave) is perceived the same regardless of actual frequency (40–60 Hz is heard as the same interval and distance as 4000–6000 Hz), every octave contains the same amount of energy and thus pink noise is often used as a reference signal in audio engineering. The power density, compared with white noise, decreases by 3 dB per octave (density proportional to 1/f ). For this reason, pink noise is often called "1/f noise".
Since there are an infinite number of logarithmic bands at both the low frequency (DC) and high frequency ends of the spectrum, any finite energy spectrum must have less energy than pink noise at both ends. Pink noise is the only power-law spectral density that has this property: all steeper power-law spectra are finite if integrated to the high-frequency end, and all flatter power-law spectra are finite if integrated to the DC, low-frequency limit.
Brown(ian) noise
Brown spectrum (-6 dB/octave)
In fields that adopt precise definitions, the terminology "red noise", also called Brown noise or Brownian noise, will usually refer to a power density which decreases 6 dB per octave with increasing frequency (density proportional to 1/f2)<1> over a frequency range which does not include DC (in a general sense, does not include a constant component, or value at zero frequency). In areas where terminology is used loosely, "red noise" may refer to any system where power density decreases with increasing frequency.<3>
The first definition can be generated by an algorithm which simulates Brownian motion or by integrating white noise. "Brown" noise is not named for a power spectrum that suggests the color brown; rather, the name is a corruption of Brownian motion. "Red noise" describes the shape of the power spectrum, with pink being between red and white. Also known as "random walk" or "drunkard's walk" noise.
