Hello, I considered a statistically independent continuous random process f(x) such that Cov(f(x),f(y))=0 for x[itex]\neq[/itex]y and Cov(f(x),f(x))=σ2. Then I would like to compute the correlation function of the Fourier transform of f, that is [itex]Cov\left( F(u),F(v)\right)[/itex]. The result I got from my calculations is that [itex]Cov\left( F(u),F(v)\right)=0[/itex] when u[itex]\neq[/itex]v, and [itex]Cov\left( F(u),F(u)\right)=\sigma^2[/itex]. So again, also the Fourier transform of f is supposed to be statistically independent. At first I thought that this makes sense, but then I started to wonder why F(u) and F(-u) are supposed to be uncorrelated? We know that F(u)=F(-u)*, so the negative frequencies theoretically depend fully on the positive frequencies (they are actually redundant as one is the complex conjugate of the other). How should I interpret this result? Is it wrong?