Colors of noise

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Colors of noise
White noise
Pink noise
Brown/Red noise
Grey noise

Although noise is a random signal, it can have characteristic statistical properties. Spectral density (power distribution in the frequency spectrum) is such a property, which can be used to distinguish different types of noise. This classification by spectral density is given "color" terminology, with different types named after different colors, and is common in different disciplines where noise is an important factor (like acoustics, electrical engineering and physics).

Many of these definitions assume a signal with components at all frequencies, with a spectral density per unit of bandwidth proportional to 1/f^β. For instance, white noise is flat, with β = 0, while brown has β = 2.

Contents 1 Technical definitions 2 Others 3 References 4 See also 5 External links

[edit] Technical definitions

The color names for these different types of sounds are derived from a loose analogy between the spectrum of frequencies of sound wave present in the sound (as shown in the blue diagrams) and the equivalent spectrum of light wave frequencies. That is, if the sound wave pattern of "blue noise" were translated into light waves, the resulting light would be blue, and so on.

White noise

White noise is a signal (or process) with equal energy per cycle (hertz), producing a flat frequency spectrum in linear space, named by analogy to white light.

White spectrum

In other words, the signal has equal power in any linear band, at any center frequency, having a given bandwidth. For example, the 20 Hz frequency range between 40 and 60 Hz contains the same amount of power as the range between 4000 and 4020 Hz.

An infinite-bandwidth white noise signal is purely a theoretical construct. By having power at all frequencies, the total power of such a signal would be infinite. In practice, a signal is "white" if it has a flat spectrum over a defined frequency band.

Pink noise

The frequency spectrum of pink noise is flat in logarithmic space; it has equal power in bands that are proportionally wide. 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 is seen as the same size 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. That is, the human auditory system perceives approximately equal magnitude on all frequencies. The power density, compared with white noise, decreases by 3 dB per octave (density proportional to 1/f).

Brown (or red) noise

Brown noise is similar to pink noise, but with a power density decrease of 6 dB per octave with increasing frequency (density proportional to 1/f²) over a frequency range which does not include DC (in a general sense, does not include a constant component, or value at zero frequency). It 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. Also known as "random walk" or "drunkard's walk" noise.

Blue (or azure) noise

Blue noise's (FS-1037C) power density increases 3 dB per octave with increasing frequency (density proportional to f) over a finite frequency range. In computer graphics, the term "blue noise" is sometimes used more loosely as any noise with minimal low frequency components and no concentrated spikes in energy. This can be good noise for dithering (Mitchell, 1987); retinal cells are arranged in a blue-noise-like pattern for this reason (Yellot, 1983).

Purple (or violet) noise

Purple noise's power density increases 6 dB per octave with increasing frequency (density proportional to f²) over a finite frequency range. It is also known as differentiated white noise or violet noise.

Grey noise

Grey noise is noise subjected to a psychoacoustic equal loudness curve (such as an inverted A-weighting curve) over a given range of frequencies, so that it sounds like it is equally loud at all frequencies. Some people say that this would be a better definition of "white noise" than the "equal power at all frequencies" definition, since white light never has an equal power spectrum, but rather can have a range of spectra, for example that of a 5400K black body.

Various noise models are employed in analysis, many of which fall under the above categories. AR noise or "autoregressive noise" is such a model, and generates simple examples of the above noise types, and more.

The Federal Standard 1037C Telecommunications Glossary defines white, pink, blue, and black.

[edit] Others

There are also many "less official" colors.

Red noise

Red noise has more than one definition:

1. A synonym for brown noise, as above [1]
2. A synonym for pink noise, as above [2]
3. Oceanic ambient noise (that is, noise from distant sources) is often described as "red" due to the selective absorption of higher frequencies by the ocean. (Common definition within the oceanographic field, contributed to a newsgroup by P.J. Rovero in 1996.) [3]

Orange noise

Orange noise is quasi-stationary noise with a finite power spectrum with a finite number of small bands of zero energy dispersed throughout a continuous spectrum. These bands of zero energy are centered about the frequencies of musical notes in whatever scale is of interest. Since all in-tune musical notes are eliminated, the remaining spectrum could be said to consist of sour, citrus, or "orange" notes.

Green noise

1. Green noise is supposedly the background noise of the world. A really long term power spectrum averaged over several outdoor sites. Rather like pink noise with a hump added around 500 Hz. [4]
2. The mid-frequency component of white noise, used in halftone dithering [5]
3. Bounded brown noise [6]

Black noise

Black noise, or silent noise, has several different definitions:

1. Silence
2. Noise with a 1/f^β spectrum, where β > 2 (Manfred Schroeder, "Fractals, chaos, power laws"). Used in modeling various environmental processes. Is said to be a characteristic of "natural and unnatural catastrophes like floods, droughts, bear markets, and various outrageous outages, such as those of electrical power." Further, "because of their black spectra, such disasters often come in clusters."
3. Noise that has a frequency spectrum of predominantly zero power level over all frequencies except for a few narrow bands or spikes. Note: An example of black noise in a facsimile transmission system is the spectrum that might be obtained when scanning a black area in which there are a few random white spots. Thus, in the time domain, a few random pulses occur while scanning. [7]
4. Whatever comes out of an active noise control system and cancels an existing noise, leaving the world noise free. The comic book character Iron Man used to have a "black light beam" that could darken a room like this, and popular sci-fi has a tendency to portray active noise control in this light.
5. As seen in the sales literature for an ultrasonic vermin repeller, black noise with a power density that is constant for a finite frequency range above 20 kHz. More accurately, ultrasonic white noise. This black noise is like the so-called black light with frequencies too high to be sensed, but still capable of affecting the environment.

Noisy white

In telecommunication, the term noisy white has the following meanings:

1. In facsimile or display systems, such as television, a nonuniformity in the white area of the image, i.e., document or picture, caused by the presence of noise in the received signal.
2. A signal or signal level that is supposed to represent a white area on the object, but has a noise content sufficient to cause the creation of noticeable black spots on the display surface or record medium.

Noisy black

In telecommunication, the term noisy black has the following meanings:

1. In facsimile or display systems, such as television, a nonuniformity in the black area of the image, i.e., document or picture, caused by the presence of noise in the received signal.
2. A signal or signal level that is supposed to represent a black area on the object, but has a noise content sufficient to cause the creation of noticeable white spots on the display surface or record medium.

[edit] References

• Mitchell, Don P., "Generating Antialiased Images at Low Sampling Densities." Computer Graphics, volume 21, number 4, July 1987.
• Yellott, John I. Jr., "Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina." Science, volume 221, pp. 382-385, 1983.

[edit] See also

• Mains hum - also known as the AC power hum
• Synesthesia - the psychological association of different senses, including sounds with colors

[edit] External links

• The colors of noise newsgroup posting
• Some colored noise examples
• Rane' Pro Audio Reference definition of "noise color"
• Black Noise and Population Persistence
• A "c" program for generating noise with the same spectrum as a given source audio file