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Hilbert transform of white gaussian noise

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EngIntoHW

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Hi,

Given a white gaussian noise: n ~ N(0, No/2)
Let n^ be the hilbert transform of n.

Is it correct to say that: n^ ~ N(0, No/2).

I know how to prove that n^ is also a white gaussian noise, and that E[n^] = 0.
But I don't know if it's correct that Var[n^] equals No/2.

Thank you :)
 
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