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 meander Brownian meander In the mathematical theory of probability, Brownian meander formula_1 is a continuous non-homogeneous Markov process defined as follows: Let formula_2 be a standard one-dimensional Brownian motion, and formula_3, i.e. the last time before "t" = 1 when formula_4 visits formula_5. Then the Brownian meander is defined by the following: In words, let formula_7 be the last time before 1 that a standard Brownian motion visits formula_5. (formula_9 almost surely.) We snip off and discard the trajectory of Brownian motion before formula_7, and scale the remaining part so that it spans a time interval of length 1. The scaling