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Fourier transform of a Gaussian random variable

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Faudy

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fourier transform gaussian

Hello,

My received signal is r(t) = x(t) + b(t)
where x(t) is a deterministic signal
and b(t) an AWGN ~ N(0,s^2)
This signal has a Gaussian distribution ~ N(x(t),s^2).

I think that the fourier transform of this signal denoted R(f)
follows a Gaussian distribution as well.

I'm I right?
Which parameters should I take?

Thanks!
 

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