# Nyquist's information

1. Jul 25, 2011

### xts

What is a Nyquist's information in discrete measurements?

We perform a measurement of some physical object, giving a result value in interval [0,1] in some units. The value has a gaussian statistical error of some known $\sigma$ (by order of magnitude comparable to 1).
We do lots ($\rightarrow \infty$) of such measurements of various real objects, our only a priori knowledge is that true values have some unknown distribution bounded within [0,1].

What is a maximal average information (in Shannon-Nyquist meaning) carried by such measurement? Intuition tells me that Nyquist's law should apply here (with some proportionality factor maybe).

Had anyone read (or even better: written...) any article on such topics? I would be really grateful for a reference!

Last edited: Jul 25, 2011
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