Brownian noise: Information from Answers.com

For similar phrases, see Brown note (disambiguation).

Colors of noise
White
Pink
Brown/Red
Grey

Brown noise spectrum

In science, Brownian noise ( Sample (help·info)), also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion hence its alternative name of random walk noise. The term "Brown noise" comes not from the color, but after Robert Brown, the discoverer of Brownian motion.

1 Explanation
2 Power spectrum
3 Production
- 3.1 Sample
4 See also
5 External links
6 References

Explanation

The graphic representation of the sound signal mimics a Brownian pattern. Its spectral density is inversely proportional to f², meaning it has more energy at lower frequencies, even more so than pink noise. It decreases in power by 6 dB per octave and, when heard, has a "damped" or "soft" quality compared to white and pink noise. The sound is a low roar resembling a waterfall or heavy rainfall. See also purple noise, which is a 6 dB increase per octave.

Power spectrum

A Brownian signal is expressed mathematically as the integral of a white noise signal, $d W (t)$ , namely a Wiener process

$W(t) = \int _{-\infty}^{+\infty} dW(t)$

White noise has a constant spectrum $S (ω) = S 0$ . The Fourier transform has the general property ^[1]

$\mathcal{F}[f^\prime(t)](\omega) = \imath \omega \mathcal{F}[f(t)](\omega)$

Since white noise is the derivative of Brownian motion (more correctly Brownian motion is the integral of white noise, as the derivative of a random function is not defined cf. ^[2]) we conclude that the spectrum for Brownian noise is $\frac{S_0}{\imath\omega}$ , therefore the power spectrum is given by

$S(\omega)= \frac{S_0^2}{\omega^2}$

Production

Brown noise can be produced by integrating white noise. That is, whereas (digital) white noise can be produced by randomly choosing each sample independently, Brown noise can be produced by adding a random offset to each sample to obtain the next one.

Sample

Brown noise

10 seconds of Brown noise

Problems listening to this file? See media help.

External links

Brown noise in wave(.wav) format, 1 minute long
Simply Noise, a free online white, pink and brown/red noise generator, uses Flash

References

^ A statistical model of flicker noise, Barnes, J.A. and Allan, D.W. Proceedings of the IEEE, Volume: 54 Issue: 2 Feb. 1966, Page(s): 176- 178 and references therein
^ Handbook of stochastic methods, C.W. Gardiner, Springer Verlag, Berlin

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Brownian noise

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