What is White Gaussian Noise (WGN)?

Explains White Gaussian Noise (WGN) from a Signals and Systems perspective.

** Note that I unfortunately made a minor typo when I wrote the equation for the p.d.f.: The square root symbol in the denominator of the prefactor should extend further to include the sigma squared term, or alternatively if the square root is kept as it is, then it should be just sigma, not sigma squared.
** Another point to make is that I should have mentioned that the noise power, sigma^2, that I wrote at the bottom of the page, is taken over a unit of bandwidth. In other words, it is assuming that the WGN has been sampled at the output of an ideal low pass filter, with bandwidth 1 Hz (ie. between -0.5 Hz and 0.5 Hz). This is something that is often done in textbooks without mentioning it explicitly. Of course, without considering a limited bandwidth, the noise power would be infinite, since the area under the power spectral density "flat line" is infinite. Or in other words, the height of the "delta" in the autocorrelation function is infinity (since the N_0/2 label on the delta function relates to the area of the delta, which is infinitely thin and infinitely high. For more details on the delta function, see the links below).

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