fourier transform of a finite-energy random process
Hi all,
I've got the following problem: I have a random process in time-domain, call it )
; assuming that it's a finite-energy process (e.g. it's mean value \})
is non-zero only for 
), I can consider the Fourier transform:
=\int_{-\infty}^{\infty} h(t)e^{-jwt}\, dt)
Now, if has a joint PDF of N-th order )
, what's the joint PDF of N-th order of the process )
?
I tried to tackle the problem in this way: considering a fixed value for frequency 
, I can extract a r.v. )
from the random process :
=\int_{-\infty}^{\infty} h(t)e^{-j\bar{w}t}\, dt)
If I approximate the integral as:
\simeq\sum_{i=0}^{t_0/{\Delta}\tau} h(i{\Delta}\tau)e^{-j\bar{w}i{\Delta}\tau}{\Delta}\tau)
I can consider as a function of the finite set of random variables )
. This means that the PDF of is a sort of convolution of the PDFs of the r.v. (scaled by the exponentials)... does this make sense? :)
Is there a better solution to my original problem?
Thanks indeed!
