Brownian Noise - Power Spectrum

Power Spectrum

A Brownian motion also called a Wiener process is obtained as the integral of a white noise signal, ,

meaning that Brownian motion is the integral of the white noise whose power spectral density is flat

Note that here denotes the Fourier transform and 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

.