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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 [tex]\lim_{w \to \infty } S(w) = 0[/tex]

We know by defintion that the FT of this signal is [itex]\int[/itex]s(t)e[itex]^{-jwt}[/itex]dt and also that ∫|s(t)|

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.

Let s(t) be a finite energy signal with Fourier Transform S(w).

Show that [tex]\lim_{w \to \infty } S(w) = 0[/tex]

We know by defintion that the FT of this signal is [itex]\int[/itex]s(t)e[itex]^{-jwt}[/itex]dt and also that ∫|s(t)|

^{2}dt < ∞.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.

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