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Shannon's capacity formula

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persistence911

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I was in taught howw to proves the shannons capacity formular using by takng into conideration a n-hyperspace of uncertanity where the noise resides. It more like the geomteric proof of Shannon formular

I have two problems
1) he modelled signals like a round circle and noise around it like a round circle. and he said the sphere of uncertanity must not overlap. Is it more like a wireless networks with noise around the environment? I did like an insight into this proof

2) I don't seem to understand the Nyquist sampling theorem of n=2BT it is like the concepts of frequency has been Muddled Up with the perioid. I know the realtionship between frequency f = 1/t but when sampled time concepts come into play I am confused could anyone shed more light on this.

Thanks I am sorry my question is kind of long .
 

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