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Coloured noise has a non-uniform spectral distribution; however, over
a finite bandwidth corresponding perhaps to a single communications channel, the power
spectral density might appear flat, hence the term bandlimited white
Gaussian noise.
Not only is it necessary for the spectrum to be flat, but the statistics of the noise must
be such that the envelope distribution of the bandlimited noise must be Gaussian in nature to fully satisfy the Shannon condition. Fortunately this holds approximately true
for the majority of practical narrowband communications systems.
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