Pink noise 46202 225914505 2008-07-16T00:09:44Z Dbutler1986 191680 {{technical}} {{Colors of noise}} [[Image:Pink noise spectrum.png|thumb|Pink noise spectrum graphed logarithmically]] '''Pink noise''' or '''1/f noise''' is a [[signal (information theory)|signal]] or process with a [[frequency spectrum]] such that the [[spectral density|power spectral density]] is proportional to the reciprocal of the frequency. Pink Noise has an equal amount of energy per octave. The name arises from being intermediate between [[white noise]] (1/f<sup>0</sup>) and red noise (1/f<sup>2</sup>, more commonly known as [[Brownian noise]]). Within the scientific literature the term '''1/f noise''' is used a little more loosely to refer to any noise with a [[spectral density|power spectral density]] of the form, :<math>S(f) \propto 1/f^\alpha</math> where <math>f</math> is frequency and 0 < ''α'' < 2, with ''α'' usually close to 1. These "1/f-like" noises occur widely in nature and are a source of considerable interest in many fields. The term ''[[flicker noise]]'' is sometimes used to refer to <math>1/f</math> noise, although this is more properly applied only to its occurrence in electronic devices due to a [[direct current]]. [[Benoît Mandelbrot|Mandelbrot]] and Van Ness proposed the name ''fractional noise'' (sometimes since called ''fractal noise'') to emphasise that the exponent of the spectrum could take non-integer values and be closely related to [[fractional Brownian motion]], but the term is very rarely used. {{listen|filename=Pink noise.ogg|title=Pink noise as sound|description=10 seconds of pink noise, [[normalized]] to -1 [[dBFS]] [[peak amplitude|peak]]|format=[[Ogg]]}} == Description == There is equal energy in all [[octave]]s (or similar log bundles). In terms of power at a constant bandwidth, 1/f noise falls off at 3 [[decibel|dB]] per octave. At high enough frequencies 1/f noise is never dominant. (White noise is equal energy per hertz.) [[Image:Noise.jpg|thumb|Pink noise (left) and [[white noise]] (right) on an [[FFT]] [[spectrogram]] with linear frequency vertical axis (on a typical audio or similar spectrum analyzer the pink noise would be flat, not downward-sloping, and the white noise rising)]] 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 equalizer]]s 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. Systems that do not have a flat response can be equalized by creating a "mirror image" using a graphic equalizer. Because pink noise has a tendency to occur in natural physical systems it is often useful in audio production. Pink noise can be processed, filtered, and/or effects can be added to produce desired sounds. Pink noise generators are commercially available. 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 specific range of frequencies. For <math>f_2</math>, there is an upper limit to the frequencies that can be measured. One parameter of noise, the peak versus average energy contents, or [[crest factor]], is important for testing purposes, such as for [[audio amplifier|amplifier]] and [[loudspeaker]] capabilities. Various crest factors of pink noise can be used in simulations of various levels of [[dynamic range compression]] in music signals. A defined creast factor is also important for durability or heat tests on [[loudspeaker]]s or power [[amplifiers]], because the signal power is direct function of the crest factor. On some digital pink noise generators the crest factor can be specified because the algorithm can be adjusted to never exceed certain levels. == 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 [http://redwood.psych.cornell.edu/people/david.html 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.<ref name="Kuittinen">[http://mlab.uiah.fi/~eye/mediaculture/noise.html Noise in Man-generated Images and Sound<!-- Bot generated title -->]</ref> There are no simple mathematical models to create pink noise. It is usually generated by filtering white noise.<ref name="Kuittinen"/><ref>[http://www.firstpr.com.au/dsp/pink-noise/ DSP Generation of Pink Noise<!-- Bot generated title -->]</ref> 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. === Electronic devices === {{main|Flicker noise}} A pioneering researcher in this field was [[Aldert van der Ziel]]. 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 10<sup>−6</sup> Hz (taking several weeks) have not shown a ceasing of pink-noise behaviour.{{Fact|date=March 2008}} 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. A pink noise source is sometimes included on [[analog synthesizer]]s (although a white noise source is more common), both as a useful audio sound source for further processing, and also a source of random control voltages for controlling other parts of the synthesizer. == See also == * [[White noise]] * [[Noise (physics)]] * [[Brownian noise]] * [[Statistics]] * [[Audio signal processing]] * [[Self-organised criticality]] * [[Fractal]] * [[Colors of noise]] * [[Crest factor]] * [[Architectural acoustics]] * [[Sound masking]] == References == ===Footnotes=== <references/> ===Notations=== * {{cite journal | author = Dutta, P. and Horn, P. M. |date= 1981 | title = Low-frequency fluctuations in solids: <math>1/f</math> noise | journal = [[Reviews of Modern Physics]] | volume = 53 | pages = 497–516 | doi = 10.1103/RevModPhys.53.497 }} * {{cite journal | author = Field, D. J. |date= 1987 | title = Relations Between the Statistics of Natural Images and the Response Profiles of Cortical Cells | journal = Journal of the Optical Society of America A | volume = 4 | pages = 2379–2394 | url = http://redwood.psych.cornell.edu/papers/field_87.pdf }} * {{cite journal | author = Gisiger, T. |date= 2001 | title = Scale invariance in biology: coincidence or footprint of a universal mechanism? | journal = [[Biological Reviews]] | volume = 76 | pages = 161–209 | doi = 10.1017/S1464793101005607 }} * {{cite journal | author = Johnson, J. B. |date= 1925 | title = The Schottky effect in low frequency circuits | journal = [[Physical Review]] | volume = 26 | pages = 71–85 | doi = 10.1103/PhysRev.26.71 }} * {{cite journal | author = Press, W. H. |date= 1978 | title = Flicker noises in astronomy and elsewhere | journal = Comments on Astrophysics | volume = 7 | pages = 103–119 | url = http://www.lanl.gov/DLDSTP/Flicker_Noise_1978.pdf }} * {{cite journal | author = [[Walter Schottky|Schottky, W.]] |date= 1918 | title = Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern | journal = [[Annalen der Physik]] | volume = 362 | pages = 541–567 | doi = 10.1002/andp.19183622304 }} * {{cite journal | author = [[Walter Schottky|Schottky, W.]] |date= 1922 | title = Zur Berechnung und Beurteilung des Schroteffektes | journal = [[Annalen der Physik]] | volume = 373 | pages = 157–176 | doi = 10.1002/andp.19223731007 }} * {{cite journal | author = Keshner, M. S. | date = 1982 | title = <math>1/f</math> noise | journal = Proceedings of the IEEE | volume = 70 | issue = 3 | pages = 212–218 | doi = 10.1109/PROC.1982.12282 }} * {{cite website | author = Li, W. | date = 1996–present | title = A bibliography on <math>1/f</math> noise | url = http://www.nslij-genetics.org/wli/1fnoise/ }} * {{cite journal | author = [[Benoît Mandelbrot|Mandelbrot, B. B.]] and Van Ness, J. W. | date = 1968 | title = Fractional Brownian motions, fractional noises and applications | journal = [[SIAM Review]] | volume = 10 | issue = 4 | pages = 422–437 | doi = 10.1137/1010093 }} == External links == * [http://www.eng.ox.ac.uk/samp/powernoise_soft.html Matlab software for generating 1/f noise, or more generally, 1/f^alpha noise] * [http://www.nslij-genetics.org/wli/1fnoise/ A Bibliography on 1/f Noise] * [http://www.esseraudio.com/ttg.htm Test Tone Generator — Windows Software that can create pink noise with selectable crest factor] * [http://www.audiocheck.net/testtones_index.php A collection of various test tones playable online (White/Pink/Brown Noises)] * [http://whitenoisemp3s.com/?p=22 Pink noise in wave(.wav) format (1 minute)] * [http://www.firstpr.com.au/dsp/pink-noise/ DSP Generation of Pink (1/f) Noise — Discussion of various algorithms, with code samples] * [http://www.blackholemedia.com/noise/ Noise — an open-source program that creates pink noise on the Macintosh] * The [http://www.alsa-project.org/ ALSA] utility [http://www.die.net/doc/linux/man/man1/speaker-test.1.html ''speaker-test'' under Linux defaults to producing pink noise] * [http://www.TropicalCoder.com/AudioTestFileGen.htm Pink Noise and Sine Wave Generator utility that outputs Window's PCM audio files (*.wav) that play in your audio player] [[Category:Noise]] [[cs:Růžový šum]] [[de:1/f-Rauschen]] [[es:Ruido rosa]] [[eo:Rozkolora bruo]] [[fr:Bruit rose]] [[it:Rumore rosa]] [[ja:ピンクノイズ]] [[pl:Szum różowy]] [[ru:Фликкер-шум]] [[fi:Vaaleanpunainen kohina]] [[sv:Skärt brus]] [[uk:Рожевий шум]]