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The signal to noise ratio is simple, and is usually defined in the context of simple Gaussian local-level models. In the cause of non-gaussian signal or noise models, do people do things more complicated then the ratio of the variances of the two distributions?

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2 Answers 2

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I think signal to noise ratio is very common in signal processing regardless of the form of the noise distribution. It is like the reciprocal of the coefficient of variation not the ratio of two variances.

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  • $\begingroup$ Can someone tell me why i would get a downvote for my response? $\endgroup$ May 3, 2012 at 17:07
  • $\begingroup$ Different people on the site have different values regarding what 'deserves' a downvote. Assuming that everyone has a general interest in improving the board, downvotes are usually accompanied by a suggestion for improvement. However, that's not always the case, so sometimes it is a mystery. $\endgroup$
    – Macro
    May 3, 2012 at 19:00
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Speaking from an engineering viewpoint, there are many different definitions of signal to noise ratio (see for example, this question on dsp.SE) depending on the application and the author, and the key property that they all share is that the performance parameters of interest (e.g. bit error rate) generally are monotone functions of the signal to noise ratio. In the presence of Gaussian noise, it is often possible to calculate explicitly the parameter of interest as a function of the signal to noise ratio. In other kinds of noise, one might have to be content with bounds. But in all instances, all engineers are in agreement that large signal to noise ratio is better than small signal to noise ratio even if they cannot agree on what is meant by signal to noise ratio, and are unable to determine exactly how the signal to noise ratio determines the parameters of interest to them.

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