Homework Help: Fourier transform limit of finite signal

1. Dec 21, 2011

omaciu

So this is a very simple question that I am having some trouble figuring out:

Let s(t) be a finite energy signal with Fourier Transform S(w).
Show that $$\lim_{w \to \infty } S(w) = 0$$

We know by defintion that the FT of this signal is $\int$s(t)e$^{-jwt}$dt and also that ∫|s(t)|2dt < ∞.

I'm a little lost on how I can start proving this. I thought about something using Parseval's theorem but I have no idea. Or maybe I can use the FT in it's ∫s(t)cos(wt)dt - j∫s(t)sin(wt)dt form? I have no idea. I'm sure the solution is much simpler than I think it is.

Last edited: Dec 21, 2011
2. Dec 22, 2011

omaciu

Nobody has any clue? I'm still stuck. I'm studying for an Electronics Math exam and this question (from a past exam) is really stumbling me.