Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have a pretty simple question which I thought I do not need to make a topic about, but Google is actually not helping, which is surprising. So here it goes:

How can white noise have infinite power if its variance is finite?

As far as I am aware, the following is always valid for a stationary zero-mean random process X which is classified as white noise (i.e. flat power spectrum)

[itex]R_{x}(t)|_{t=0}= power = E[X^2(t)] = \sigma^2 \cdot \delta(t)|_{t=0} = infinite = Var[X(t)] = \sigma^2 = finite[/itex]

assuming that the statisics of the random process are anything with the finite variance, for example, Gaussian distribution. So, yeah, I'm looking at the AWGN.

So, what gives?

And I am aware of the physique of the realistic white processes, however I'm purely interested in the theoretical point of view here, so let's assume that this white process does have an infinite power. How is that possible when we also assumed that its variance is finite?

Many thanks in advance.

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# Variance of a white noise

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