Editing Colors of noise (section)

==Technical definitions==

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<ref>{{cite web|title=ATIS Telecom Glossary|url=https://www.atis.org/glossary/normative.aspx|website=atis.org|publisher=Alliance for Telecommunications Industry Solutions|access-date=16 January 2018}}</ref><ref>{{cite web|title=Federal Standard 1037C|url=https://its.ntia.gov/research-topics/federal-standard-1037c/|website=Institute for Telecommunication Sciences|publisher=Institute for Telecommunication Sciences, National Telecommunications and Information Administration (ITS-NTIA)|access-date=30 November 2022}}</ref> defines white, pink, blue, and black noise.

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.{{Citation needed|date=January 2018}}
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===White noise===
{{Main|White noise}}

[[Image:White noise spectrum.svg|thumb|right|White noise has a flat power spectrum.]]

[[White noise]] is a [[Signal (electrical engineering)|signal]] (or process), named by analogy to [[Electromagnetic spectrum#Visible radiation (light)|white light]], with a flat [[frequency spectrum]] when plotted as a linear function of frequency (e.g., in Hz). In other words, the signal has equal [[power (physics)|power]] in any band of a given [[Bandwidth (signal processing)|bandwidth]] ([[power spectral density]]) when the bandwidth is measured in [[hertz|Hz]].  For example, with a white noise audio signal, the range of frequencies between 40 [[hertz|Hz]] and 60&nbsp;Hz contains the same amount of sound power as the range between 400&nbsp;Hz and 420&nbsp;Hz, since both intervals are 20&nbsp;Hz wide. Note that spectra are often plotted with a logarithmic frequency axis rather than a linear one, in which case equal physical widths on the printed or displayed plot do not all have the same bandwidth, with the same physical width covering more Hz at higher frequencies than at lower frequencies. In this case a white noise spectrum that is equally sampled in the logarithm of frequency (i.e., equally sampled on the X axis) will slope upwards at higher frequencies rather than being flat. However it is not unusual in practice for spectra to be calculated using linearly-spaced frequency samples but plotted on a logarithmic frequency axis, potentially leading to misunderstandings and confusion if the distinction between equally spaced linear frequency samples and equally spaced logarithmic frequency samples is not kept in mind.<ref name="Peters-2012">{{cite web|url=https://physics.mercer.edu/hpage/psd-tutorial/psd.html|author=Randall D. Peters|date=2 January 2012|title=Tutorial on Power Spectral Density Calculations for Mechanical Oscillators}}</ref>

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===Pink noise===
{{Main|Pink noise}}

<!-- Image is wrong. Pink noise should fall at 10dB/dec. [[Image:Pink-noise-db-logf.png|thumb|right|Pink spectrum <br>(log frequency axis)]] -->
[[File:Pink noise spectrum.svg|thumb|right|Pink noise spectrum. Power density falls off at 10&nbsp;dB/decade (−3.01&nbsp;dB/octave).]]

The frequency spectrum of [[pink noise]] is linear in [[logarithmic scale]]; it has equal power in bands that are proportionally wide.<ref>{{cite web|url=https://www.its.bldrdoc.gov/fs-1037/dir-027/_4019.htm|url-status=dead|archive-url=https://web.archive.org/web/20210608074332/https://www.its.bldrdoc.gov/fs-1037/dir-027/_4019.htm|archive-date=8 June 2021|title=Definition: pink noise|website=its.bldrdoc.gov}}</ref> This means that pink noise would have equal power in the frequency range from 40 to 60&nbsp;Hz as in the band from 4000 to 6000&nbsp;Hz. Since humans hear in such a proportional space, where a doubling of frequency (an octave) is perceived the same regardless of actual frequency (40–60&nbsp;Hz is heard as the same interval and distance as 4000–6000&nbsp;Hz), every octave contains the same amount of energy and thus pink noise is often used as a reference signal in [[audio engineering]]. The [[spectral power density]], compared with white noise, decreases by 3.01&nbsp;[[decibel|dB]] per [[octave]] (10&nbsp;dB per [[Decade_(log_scale)|decade]]); density proportional to 1/''f''.  For this reason, pink noise is often called "1/''f'' noise".

Since there are an infinite number of logarithmic bands at both the low frequency (DC) and high frequency ends of the spectrum, any finite energy spectrum must have less energy than pink noise at both ends.  Pink noise is the only power-law spectral density that has this property: all steeper power-law spectra are finite if integrated to the high-frequency end, and all flatter power-law spectra are finite if integrated to the DC, low-frequency limit.{{citation needed|date=May 2014}}

{{Listen|filename=Pink noise.ogg|title=10 seconds of pink noise|description=}}
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===Brownian noise===
{{Main|Brownian noise}}

[[Image:Brown noise spectrum.svg|thumb|right|Brown spectrum (−6.02&nbsp;dB per octave)]]

[[Brownian noise]], also called Brown noise, is noise with a power density which decreases 6.02&nbsp;dB per octave (20&nbsp;dB per decade) with increasing frequency (frequency density proportional to 1/''f''{{i sup|2}}) over a frequency range excluding zero ([[direct current|DC]]). It is also called "red noise", with pink being between red and white.

Brownian noise can be generated with temporal [[Integral|integration]] of [[white noise]]. "Brown" noise is not named for a power spectrum that suggests the color brown; rather, the name derives from [[Brownian motion]], also known as "random walk" or "drunkard's walk". 
{{Listen|filename=Brown noise.ogg|title=10 seconds of Brown noise|description=}}
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===Blue noise===
[[Image:Blue noise spectrum.svg|thumb|right|Blue spectrum (+3.01&nbsp;dB per octave)]]

Blue noise is also called azure noise. Blue noise's power density increases <math>10\log_{10}2 = </math> 3.01&nbsp;dB per octave with increasing frequency (density proportional to ''f''&nbsp;) over a finite frequency range.<ref>{{cite web|url=https://www.its.bldrdoc.gov/fs-1037/dir-005/_0685.htm|url-status=dead|archive-url=https://web.archive.org/web/20210608074403/https://www.its.bldrdoc.gov/fs-1037/dir-005/_0685.htm|archive-date=8 June 2021|title=Definition: blue noise|website=its.bldrdoc.gov}}</ref> 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 [[dither]]ing.<ref>{{cite book | last1=Mitchell | first1=Don P. | title=Proceedings of the 14th annual conference on Computer graphics and interactive techniques | chapter=Generating antialiased images at low sampling densities | year=1987 | volume=21 | issue=4 | pages=65–72 | doi=10.1145/37401.37410| isbn=0897912276 | s2cid=207582968 }}</ref> [[Retina]]l cells are arranged in a blue-noise-like pattern which yields good visual resolution.<ref>{{cite journal | last1 = Yellott | first1 = John I. Jr | year = 1983 | title = Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina | journal = Science | volume = 221 | issue = 4608| pages = 382–85 | doi = 10.1126/science.6867716 | pmid = 6867716 | bibcode = 1983Sci...221..382Y | url = https://escholarship.org/uc/item/0qq9b8zx }}</ref>

[[Cherenkov radiation]] is a naturally occurring example of almost perfect blue noise, with the power density growing linearly with frequency over spectrum regions where the permeability of index of refraction of the medium are approximately constant. The exact density spectrum is given by the [[Frank–Tamm formula]]. In this case, the finiteness of the frequency range comes from the finiteness of the range over which a material can have a [[refractive index]] greater than unity. Cherenkov radiation also appears as a bright blue color, for these reasons.



{{Listen|filename=Blue noise.ogg|title=10 seconds of blue noise|description=}}
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===Violet noise===
[[Image:Violet noise spectrum.svg|thumb|right|Violet spectrum (+6.02&nbsp;dB/octave)]]

Violet noise is also called '''purple noise'''. Violet noise's power density increases 6.02&nbsp;dB per octave with increasing frequency<ref>Transactions of the American Society of Heating, Refrigerating and Air-Conditioning Engineers 1968 [https://books.google.com/books?doi=aTJSAAAAMAAJ&q=%22purple+noise%22] Quote: 'A "purple noise," accordingly, is a noise the spectrum level of which ''rises'' with frequency.'</ref><ref>{{cite conference | doi=10.1109/PLANS.1996.509090 | first1=Q. J. | last1=Zhang | first2=K.-P. | last2=Schwarz | title=Estimating double difference GPS multipath under kinematic conditions| book-title=Proceedings of the Position Location and Navigation Symposium – PLANS '96 | publisher=[[IEEE]] | location= Atlanta, GA, USA | conference = Position Location and Navigation Symposium – PLANS '96 |pages=285–91 | date = April 1996}}</ref> "The spectral analysis shows that GPS acceleration errors seem to be violet noise processes. They are dominated by high-frequency noise." (density proportional to ''f''&nbsp;<sup>2</sup>) over a finite frequency range. It is also known as [[Derivative|differentiated]] white noise, due to its being the result of the differentiation of a white noise signal.

Due to the diminished sensitivity of the human ear to high-frequency hiss and the ease with which white noise can be electronically differentiated (high-pass filtered at first order), many early adaptations of dither to digital audio used violet noise as the dither signal.{{Citation needed|date=March 2020}}

Acoustic thermal noise of water has a violet spectrum, causing it to dominate [[hydrophone]] measurements at high frequencies.<ref name="Hildebrand2009">{{cite journal | doi=10.3354/meps08353 | title=Anthropogenic and natural sources of ambient noise in the ocean | date=2009 | first1=John A. | last1=Hildebrand | pages = 478–480 | journal=Marine Ecology Progress Series| volume=395 | bibcode=2009MEPS..395....5H | doi-access=free }}</ref> "Predictions of the thermal noise spectrum, derived from classical statistical mechanics, suggest increasing noise with frequency with a positive slope of 6.02&nbsp;dB octave<sup>−1</sup>." "Note that thermal noise increases at the rate of 20&nbsp;dB decade<sup>−1</sup>"<ref>{{cite journal | last1 = Mellen | first1 = R. H. | date=1952 | title= The Thermal-Noise Limit in the Detection of Underwater Acoustic Signals | journal = The Journal of the Acoustical Society of America | volume = 24 | issue=5 | pages = 478–80 | doi=10.1121/1.1906924| bibcode = 1952ASAJ...24..478M }}</ref>

{{Listen|filename=Purple noise.ogg|title=10 seconds of violet noise|description=}}
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===Grey noise===
{{Main|Grey noise}}

[[Image:Gray noise spectrum.svg|thumb|right|Grey spectrum]]
[[Grey noise]] is random white noise subjected to a [[Psychoacoustics|psychoacoustic]] equal loudness curve (such as an inverted [[A-weighting curve]]) over a given range of frequencies, giving the listener the perception that it is equally loud at all frequencies.{{Citation needed|date=March 2010}} This is in contrast to standard white noise which has equal strength over a linear scale of frequencies but is not perceived as being equally loud due to biases in the human [[equal-loudness contour]].

{{Listen|filename=Gray noise.ogg|title=10 seconds of grey noise|description=}}
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===Velvet noise===
[[Image:Velvet_Noise_Spectrum.jpg|thumb|right|Velvet noise spectrum]]
Velvet noise is a sparse sequence of random positive and negative impulses. Velvet noise is typically characterised by its density in taps/second. At high densities it sounds similar to white noise; however, it is perceptually "smoother".<ref name="Välimäki2013">{{cite journal | doi=10.1109/TASL.2013.2255281 | title=A Perceptual Study on Velvet Noise and Its Variants at Different Pulse Densities | date=2013 | first1=Vesa | last1=Välimäki | first2=Heidi-Maria | last2=Lehtonen |first3=Marko | last3=Takanen | pages = 1481–1488 | journal= IEEE Transactions on Audio, Speech, and Language Processing| volume=21 | issue=7 | s2cid=17173495 }}</ref> The sparse nature of velvet noise allows for efficient time-domain [[convolution]], making velvet noise particularly useful for applications where computational resources are limited, like real-time [[reverberation]] algorithms.<ref>{{cite conference | first1=Hanna | last1=Järveläinen | first2=Matti | last2=Karjalainen | title=Reverberation Modeling Using Velvet Noise | publisher=[[Audio Engineering Society|AES]] | location= Helsinki, Finland | conference = 30th International Conference: Intelligent Audio Environments | date = March 2007}}</ref><ref>{{cite web |url=https://ccrma.stanford.edu/~keunsup/screverb.html | title = The Switched Convolution Reverberator, Lee et. al.}}</ref> Velvet noise is also frequently used in decorrelation filters.<ref>{{cite conference | first1=Benoit | last1=Alary | first2=Archontis | last2=Politis | first3=Vesa | last3=Välimäki | title= Velvet-Noise Decorrelator | location= Edinburgh, UK | conference = 20th International Conference on Digital Audio Effects (DAFx-17) | date = September 2017}}</ref>

{{Listen|filename=Velvet noise.ogg|title=2 seconds of velvet noise.}}

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