Editing Brownian noise (section)

==Production==
[[File:2D Brown noise.png|thumb|right|A two-dimensional Brownian noise image, generated with a [https://www.mathworks.com/matlabcentral/fileexchange/121108-coloured-noise computer program]]]
[[File:3D Brown noise.gif|thumb|right|A 3D Brownian noise signal, generated with a [https://www.mathworks.com/matlabcentral/fileexchange/121108-coloured-noise computer program], shown here as an animation, where each frame is a 2D slice of the 3D array]]
Brown noise can be produced by [[integral|integrating]] [[white noise]].<ref>{{cite web|url=http://www.dsprelated.com/showmessage/46697/1.php|title=Integral of White noise|year=2005|access-date=2010-04-30|archive-date=2012-02-26|archive-url=https://web.archive.org/web/20120226024012/http://www.dsprelated.com/showmessage/46697/1.php|url-status=dead}}</ref><ref>{{cite web|url=http://paulbourke.net/fractals/noise/|title=Generating noise with different power spectra laws
|first= Paul |last=Bourke|date=October 1998
}}
</ref> That is, whereas ([[Digital data|digital]]) white noise can be produced by randomly choosing each [[sample (signal)|sample]] independently, Brown noise can be produced by adding a random offset to each sample to obtain the next one. As Brownian noise contains infinite spectral power at low frequencies, the signal tends to drift away infinitely from the origin. A [[leaky integrator]] might be used in audio or electromagnetic applications to ensure the signal does not “wander off”, that is, exceed the limits of the system's [[dynamic range]]. This turns the Brownian noise into [[Ornstein–Uhlenbeck process|Ornstein–Uhlenbeck]] noise, which has a flat spectrum at lower frequencies, and only becomes “red” above the chosen cutoff frequency.

Brownian noise can also be computer-generated by first generating a white noise signal, Fourier-transforming it, then dividing the amplitudes of the different frequency components by the frequency (in one dimension), or by the frequency squared (in two dimensions) etc.<ref name="Das-thesis">{{cite thesis |last=Das |first=Abhranil |date=2022 |title=Camouflage detection & signal discrimination: theory, methods & experiments (corrected) |type=PhD |publisher=The University of Texas at Austin |url=http://dx.doi.org/10.13140/RG.2.2.32016.07683 | doi=10.13140/RG.2.2.32016.07683}}</ref> Matlab programs are available to generate Brownian and other power-law coloured noise in one<ref>{{Cite web |last=Zhivomirov |first=Hristo |date=1 August 2013 |title=Pink, Red, Blue and Violet Noise Generation with Matlab |url=https://www.mathworks.com/matlabcentral/fileexchange/42919-pink-red-blue-and-violet-noise-generation-with-matlab |access-date=9 November 2024 |website=MathWorks}}</ref> or  any number<ref>{{Cite web |last=Das |first=Abhranil |date=23 November 2022 |title=Colored Noise |url=https://www.mathworks.com/matlabcentral/fileexchange/121108-colored-noise |access-date=9 November 2024 |website=MathWorks}}</ref> of dimensions.