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I'd like to ask the following question:

Why are physical noise processes (e.g. Johnson noise from a resistor) frequently assumed to be Gaussian processes? It seems that the central limit theorem, which says that the sum of many random variables is Gaussian distributed, is not enough, because a Gaussian process not only has $x(t)$ Gaussian distributed for each $t$, but also has $x(t_1)$ and $x(t_2)$ jointly Gaussian for any $t_1$ and $t_2$.

Is this question appropriate for this site? I posted a version of it on Physics Stack Exchange but I'd like to know if the users here would welcome this type of question in the future.

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    $\begingroup$ In my opinion, questions like that would be welcome. $\endgroup$ – MBaz Jun 28 '15 at 0:49
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    $\begingroup$ i think it's appropriate. $\endgroup$ – robert bristow-johnson Sep 19 '16 at 23:23
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Question about physical applicability of noise models are quite appropriate here.

Indeed, no actual signal or noise realization can be perfectly modeled by a particular distribution, for several reasons: discretized data, limited numbers of samples, the non-perfect behavior of the acquisition chain (nonlinearity, saturation, jitter) are common limits. For instance, the idea that an average of $n$ uncorrelated Gaussian noises reduce in amplitude as $1\sqrt{n}$ is greatly limited by quantization or rounded data.

A second aspect is how tractable algorithms are with a certain noise models. Sometimes, one prefers an optimal tractable model, that may work even for other noises, because the approximation is good enough. The question Filtering performance on Poisson noise with quadratic data-fidelity was for instance related to the applicability of a Gaussian noise assumption for Poisson noises.

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