Pink noise

Pink noise (), also known as 1/f noise or flicker 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 as being intermediate between white noise and red noise.

Description

There is equal energy in all octaves. In terms of power at a constant bandwidth, 1/f noise falls off at 3 dB per octave.

The human auditory system, which uses a roughly logarithmic concept of frequency approximated by the Bark scale, does not perceive all audible frequencies with equal sensitivity; signals at about 1 kHz appear to be loudest, and the 'loudness' of other frequencies appears to drop as the frequency changes from the 1 kHz 'peak'. However, humans may 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 useful spectrum.

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 $f_1$ to $f_2$ is proportional to $\log(f_2/f_1)$ and if $f_2$ is infinity, so is the energy. Similarly, the energy of a pink noise signal would be infinite for $f_1=0$ . This is not a surprise, though, because a signal containing frequencies down to zero extends infinitely in time.

Practically, noise can only be pink over a certain frequency interval. For $f_2$ , there is an upper limit to the frequencies that can be measured. In electronics, white noise will be stronger than pink noise anyway above some corner frequency. Interestingly, there is no known lower bound to pink noise in electronics. Measurements made down to $10^{-6}$ 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 $f_1=1/T$ where $T$ is the time the device is switched on.

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

Occurrence

1/f noise occurs in many physical, biological and economic systems. In physical systems it is present in some meteorological data series, the electromagnetic radiation output of some astronomical bodies, and in most electronic devices. In biological systems it is present in heart beat rhythms and the statistics of DNA sequences. Pink noise is also found in many electrical readings of the human brain. 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).

Some researchers describe it is as being ubiquitous. It should be noted that at high enough frequencies 1/f noise is never dominant.

Electronic devices

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

Origin

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

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. ^*
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. online in [http://www.lanl.gov/DLDSTP/Flicker_Noise_1978.pdf PDF format
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.

External links

Noise

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