Pink noise

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(Redirected from 1/f noise)

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

Image:Pink noise spectrum.png

Pink noise (sample (help·info)), also known as 1/f noise, is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency. It occurs in many fields of study and takes its name from being intermediate between white noise and red noise (more commonly Brown or Brownian noise).

1 Description
2 Occurrence
- 2.1 Electronic devices
- 2.2 Sample
3 See also
4 References
5 External links

[edit] Description

There is equal energy in all octaves (or similar log bundles). In terms of power at a constant bandwidth, 1/f noise falls off at 3 dB per octave. At high enough frequencies 1/f noise is never dominant. (White noise is equal energy per hertz.)

Image:Noise.jpg

The human auditory system, which processes frequencies in a roughly logarithmic fashion approximated by the Bark scale, does not perceive them with equal sensitivity; signals in the 2-4-kHz octave sound loudest, and the loudness of other frequencies drops increasingly, depending both on the distance from the peak-sensitivity area and on the level. However, humans still differentiate between white noise and pink noise with ease.

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 spectrum of interest.

From a practical point of view, producing true pink noise is impossible, since the energy of such a signal would be infinite. That is, the energy of pink noise in any frequency interval from <math>f_1</math> to <math>f_2</math> is proportional to <math>\log(f_2/f_1)</math>, and if <math>f_2</math> is infinity, so is the energy. Similarly, the energy of a pink noise signal would be infinite for <math>f_1=0</math>. This is not a surprise, though, because a signal containing frequencies down to zero extends infinitely in time.

Practically, noise can be pink only over a certain range of frequencies. For <math>f_2</math>, there is an upper limit to the frequencies that can be measured.

One important parameter of noise, the peak versus average energy contents, or crest factor, cannot be specified for pink noise, because it depends on <math>f_1</math> and therefore on the time a device is running.

[edit] Occurrence

1/f noise occurs in many physical, biological and economic systems. Some researchers describe it as being ubiquitous. In physical systems it is present in some meteorological data series, the electromagnetic radiation output of some astronomical bodies, and in almost all electronic devices (referred to as flicker noise). In biological systems, it is present in heart beat rhythms and the statistics of DNA sequences. In financial systems it is often referred to as a long memory effect. Also, it is the statistical structure of all natural images (images from the natural environment), as discovered by David Field (1987).

Richard F. Voss and J. Clarke claim that almost all musical melodies, when each successive note is plotted on a scale of pitches, will tend towards a pink noise spectrum.[1]

There are no simple mathematical models to create pink noise. It is usually generated by filtering white noise.[2]

There are many theories of the origin of 1/f noise. Some theories attempt to be universal, while others are applicable to only a certain type of material, such as semiconductors. Universal theories of 1/f noise are still a matter of current research.

[edit] Electronic devices

Main article: Flicker noise

A pioneering researcher in this field was Aldert van der Ziel. More can be found on the external bibliography link given below.

In electronics, white noise will be stronger than pink noise (flicker noise) above some corner frequency. Interestingly, there is no known lower bound to pink noise in electronics. Measurements made down to <math>10^{-6}</math> Hz (such a measurement takes several weeks!) have not shown a ceasing of pink-noise behaviour. Therefore one could state that in electronics, noise can be pink down to <math>f_1=1/T</math> where <math>T</math> is the time the device is switched on.

[edit] Sample

Pink noise (file info) — play in browser (beta)
- 10 seconds of pink noise. Generated by Adobe Audition. Normalized to -1 dB. No dithering.
- Problems listening to the file? See media help.

[edit] See also

[edit] References

Dutta, P. and Horn, P. M. (1981), Low-frequency fluctuations in solids: 1/f noise. Rev. Mod. Phys. 53, 497–516.
Field, D.J. (1987). "Relations Between the Statistics of Natural Images and the Response Profiles of Cortical Cells". Journal of the Optical Society of America A 4 2379–2394. PDF
Gisiger, T. (2001), Scale invariance in biology: coincidence or footprint of a universal mechanism? Biol. Rev. 76, 161–209.
Johnson, J. B. (1925), The Schottky effect in low frequency circuits. Phys. Rev. 26, 71–85.
Press, W. H. (1978), Flicker noises in astronomy and elsewhere. Comments Astrophys. 7, 103–119.
Schottky, W. (1918), Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern. Ann. Phys. (Berlin) 362, 541–567.
Schottky, W. (1922), Zur Berechnung und Beurteilung des Schroteffektes. Ann. Phys. (Berlin) 373, 157–176.