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Math Help - Difference between Gaussian noise and white Gaussian noise?

  1. #1
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    Difference between Gaussian noise and white Gaussian noise?

    Hi,

    I read on Wikipedia:
    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.
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  2. #2
    Moo
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    Hello,

    Look at the definition of correlation 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...
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  3. #3
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    Quote Originally Posted by algorithm View Post
    Hi,

    I read on Wikipedia:


    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
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