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Hello,

when we want to get the magnitude of the Fourier frequency spectrum of a functionfwe typically calculate [tex]F(\omega)=\int_{\mathbb{R}}f(x)e^{-i\omega x}dx[/tex]

and then consider [itex]|F(\omega)|[/itex].

We can do this as long the signal (=function) is deterministic, that is, only one single known valuef(x)is associated to everyx.

What happens when f(x) isnotdeterministic anymore? In other words, we don't know what is the exact value off(x), but we can say only thatf(x)follows a certain probability density function. For example I could say that [tex]f(x) \sim \mathcal{U}(-1 , 1)[/tex] which means that for a givenx,f(x)is now a random variable having uniform probability distribution between -1 and 1.

If we plotted such a "function" againstxwe would see a noisy plot with amplitudes between -1 and 1.

I would like to calculate the magnitude of the Fourier spectrum of such a function, but I don't know from where to start. what can we say about [itex]|F(\omega)|[/itex]? Any hint?

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# Fourier transform of noise

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