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Coloured Noise
By: Steve Adams. G0KVZ

This was originally presented to the Vange Amateur Radio Society on the 13th July 2006.

Anyone who has an interest in Electronics or audio, will be familiar with the term 'White Noise' but most are unaware that there are many other colours of noise. Noise is referred to in this way, as an analogy with the way that light may be altered by the use of filters.

This analogy then naturally extends to other 'colors'. Just as you can use a piece of colored glass to transform white light into, say, a deep red hue, you can use filters on other kinds of signals to alter the balance of frequency components so that the noise is no longer 'white' but has some other quality.

White Noise. (Click HERE For an audio sample.)

Best described as a type of noise that is produced by combining sounds of all different frequencies that can be heard by the human ear.
common definition - power density is constant over a finite frequency range.

AKA Johnson noise.
White noise (or minimum-information noise), is so called by analogy with white light which is a uniform mixture of all the different possible colors. In the frequency (Fourier) analys is often used in signal processing, white noise is a uniform mixture of random energy at every frequency.
Often, CDs offer `white noise' as background sound to relax, like waves lapping on a beach or wind sounds.
Is this actually white noise, or is it something else?
Is white noise even a relaxing sound?

Wind, waves, or similar natural sounds are not exactly white noise - often they are closer to pink noise, but they also have additional modulation. Pure white noise is not particularly soothing, perhaps because it is not something we encounter in nature, and our perceptual systems are acutely matched to the natural world.
The advantage of a noise signal is that it can mask out more specific sounds - like the neighbors talking, or cars going by - and submerge them in a steady, continuous sound with no abrupt changes to distract or disturb us. Thus, it makes sense that the closest natural matches to white noise, like the slow undulation of waves at the seaside, can form soothing and effective background noise maskers - a natural sound, but containing no suprises or structure to pull our minds away.

white noise: 0 dB/oct reference noise with equal power density (equal power per hertz; Johnson noise)

You hear white noise when no signal is being broadcast over a television channel or radio station.
It's not just an annoying, unpleasant sound – some people use it to sleep better, e.g. by running a fan during the night.
This works because steady sound at all frequencies can mask all kinds of other noises that might disturb a light sleeper.
There are even commercial products that emit white noise to block out the snoring noises of one's partner, to help an infant sleep more soundly, or to drown out a conversation you want to keep private! White noise can also be used to determine the frequency response of mechanical equipment.

Pink Noise. (Click HERE for an audio sample.)

Pink noise (common definition) power density decreases 3dB per octave with increasing frequency (density proportional to 1/f) over a finite frequency range which does not include DC. Each octave contains the same amount of power. Many point out that this is not a trivial filtering problem.

AKA flicker noise.

Graphic equalizers also divide signals into bands logarithmically and report power by octaves; audio engineers put pink noise through a system to test whether it has a flat frequency response in the useful spectrum.

Pink noise is also commonly used to model phase noise in electronic communications systems.

Pink noise sounds more like a hiss mixed with a rumble, like the noise inside a flying passenger jet.

Brown noise. (Click HERE for an audio sample.)

A less commonly referred to 'color' of noise is 'brown noise'. This is supposed simulate Brownian motion, a kind of random motion that shifts in steady increments. 'Brown noise' decreases in power by 6 dB per octave.

Brown noise (Jon M. Risch, rbmccammon) power density decreases 6dB per octave with increasing frequency (density proportional to 1/f^2) over a frequency range which does not include DC. Is not named for a power spectrum that suggests the color brown, rather, the name is a coruption of Brownian motion. If we were going to pick a color, red might be good since pink noise lies between this noise and white noise. Unfortuantly, red is already taken. AKA "random walk" or "drunkard's walk" noise.

Brown noise sounds like rumbling.

Red noise. (Click HERE for an audio sample.)

(common definition within the oceanographic field) oceanic ambient noise (ie, noise distant from the sources) is often described as "red" due to the selective absorption of higher frequencies." Orange noise (anonymous contribution) (Anyone foolish enough to want the spectrum?)

red noise also called brown noise: -6 dB/oct decreasing density (most amount of low frequency energy or power; used in oceanography; power proportional to 1/frequency-squared); popcorn noise.

Blue noise. (Click HERE for an audio sample.)

Power density increases 3dB per octave with increasing frequency (density proportional to f) over a finite frequency range.

This can be good noise for dithering.

blue (or azure) noise: +3 dB/oct increasing noise density (power proportional to frequency).

The converse of pink noise, where energy increases for higher frequencies, is called blue noise, again by analogy with light. Blue noise isn't very interesting as a sound (it also sounds like a hiss) but has some important applications in image and video signals.

Purple noise

AKA violet noise.

The reverse of 'brown noise'

power density increases 6dB per octave with increasing frequency (density proportional to f^2) over a finite frequency range. Differentiated white noise.

(power proportional to frequency-squared; most amount of high frequency energy or power).

Green Noise

"Green Noise" which was used to simulate voice bandwidth for testing communication channels.
It is said to be flat from 500 Hz to about 2 kHz and then rolled off at 9 db/octave. Below 500 Hz it rolled off at 6 db ?? per octave.

Black noise

Definitions vary wildly, ranging from:

1. whatever comes out of an active noise control system and cancels an existing noise, leaving the world world noise free.
2. Silence (zero power density with a few random spikes allowed).
3. Black noise (seen in the sales literature for an ultrasonic vermin repeller) power density is constant for a finite frequency range above 20kHz.

Grey noise

noise subjected to a psychoacoustic equal loudness curve (such as an inverted a-weight curve) over a given range of frequencies, so that it sounds like it is equally loud at all frequencies.
This would be a better definiton of "white noise" than the "equal power at all frequencies" definition, since real "white light" has the power spectrum of a 5400K black body, not an equal power spectrum.

GrayNoise can be defined as a time domain waveform where each next sample is chosen by shuffling bits in a digital word of 'N'-bits length. It has also been called 'bit-flip' noise is some obscure literature, and creates a low rumbly, grainy noise.

Its spectrum is very flat from about 7 hz - 500 hz, and then falls off at about 3db / octave up to the nyquist frequency.
Of all the digital noises, it has the highest ratio (or rather, the closest) of peak to RMS signal energy.