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
.
Read more about this topic: Brownian Noise
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