Brownian noise a white noise signal: meaning that Brownian motion is the integral of the white noise formula_2, whose power spectral density is flat: Note that here formula_4 denotes the Fourier transform, and formula_5 is a constant. An important property of this transform is that the derivative of any distribution transforms as from which we can conclude that the power spectrum of Brownian noise is 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
Brownian noise it has more energy at lower frequencies, even more so than pink noise. It decreases in power by 6 dB per octave (20 dB per decade) 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 violet noise, which is a 6 dB "increase" per octave. Strictly, Brownian motion has a Gaussian probability distribution, but "red noise" could apply to any signal with the 1/"f" frequency spectrum. A Brownian motion, also called a Wiener process, is obtained as the integral of