Hi all,
I've got the following problem: I have a random process in time-domain, call it h(t); assuming that it's a finite-energy process (e.g. it's mean value E\{h(t)\} is non-zero only for 0<t<t_0), I can consider the Fourier transform:
H(w)=\int_{-\infty}^{\infty} h(t)e^{-jwt}\, dt
Now, if h(t) has a joint PDF of N-th order f_h(h_1,h_2,...,h_N), what's the joint PDF of N-th order of the process H(w)?

I tried to tackle the problem in this way: considering a fixed value for frequency \bar{w}, I can extract a r.v. H(\bar{w}) from the random process H(w):
H(\bar{w})=\int_{-\infty}^{\infty} h(t)e^{-j\bar{w}t}\, dt
If I approximate the integral as:
H(\bar{w})\simeq\sum_{i=0}^{t_0/{\Delta}\tau} h(i{\Delta}\tau)e^{-j\bar{w}i{\Delta}\tau}{\Delta}\tau
I can consider H(\bar{w}) as a function of the finite set of random variables h(i{\Delta}\tau). This means that the PDF of H(\bar{w}) is a sort of convolution of the PDFs of the r.v. h(i{\Delta}\tau) (scaled by the exponentials)... does this make sense?
Is there a better solution to my original problem?

Thanks indeed!