# Difference between Gaussian noise and white Gaussian noise?

• Feb 9th 2011, 02:56 AM
algorithm
Difference between Gaussian noise and white Gaussian noise?
Hi,

Quote:

Originally Posted by Wikipedia
Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution. This says nothing of the correlation of the noise in time or of the spectral density of the noise. Labeling Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term "white Gaussian noise" to be precise. Gaussian noise is sometimes misunderstood to be white Gaussian noise, but this is not the case.

If a signals amplitude values are normally distributed, doesn't that imply that different samples of the source are uncorrelated (because their values are random)?

This is why I don't understand why labelling a noise source as "Gaussian" says nothing about it's correlation.

Thanks.
• Feb 11th 2011, 11:34 PM
Moo
Hello,

Look at the definition of correlation (Surprised) It's not because values are random that they're uncorrelated !! Imagine you choose the number X=2 randomly. It's multiplied by 2 in order to get a final result, Y. Thus the final result is chosen randomly at last ! Are X and Y uncorrelated ?

There is no relationship between uncorrelation and the distribution. Except if you have a certain case of random vector, but that's another story...
• Feb 12th 2011, 12:25 AM
CaptainBlack
Quote:

Originally Posted by algorithm
Hi,

If a signals amplitude values are normally distributed, doesn't that imply that different samples of the source are uncorrelated (because their values are random)?

This is why I don't understand why labelling a noise source as "Gaussian" says nothing about it's correlation.

Thanks.

Let $X_i,\ i=1,2,...$ be iid Gaussian RVs.

Now consider:

$Y_i=\alpha X_i +(1-\alpha)X_{i+1}\ i=1,2,... ;\ \ \alpha \in [0,1]$

Now the $Y$'s are Gaussian with the same mean as the $X$'s and calculable variance, but if $\alpha \ne 1$ they are correlated.

CB