Fourier transform limit of finite signal

In summary, the conversation discusses the problem of showing that the Fourier Transform of a finite energy signal approaches zero as the frequency tends to infinity. The participants mention using Parseval's theorem or the Fourier Transform in its cosine and sine form to solve the problem, but are still struggling to find a solution. The question is from a past exam and is causing difficulty for someone studying for an Electronics Math exam.
  • #1
omaciu
2
0
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)|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.
 
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  • #2
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.
 

1. What is the Fourier transform limit of a finite signal?

The Fourier transform limit of a finite signal refers to the maximum frequency resolution that can be achieved when using the Fourier transform to analyze a finite signal. This limit is determined by the length of the signal and the sampling rate.

2. How is the Fourier transform limit calculated?

The Fourier transform limit can be calculated by dividing the sampling rate by the length of the signal. This will give the maximum frequency resolution in hertz (Hz).

3. How does the Fourier transform limit affect signal analysis?

The Fourier transform limit determines the level of detail that can be captured in the frequency domain when analyzing a signal. A higher limit means a finer resolution and more detail, while a lower limit means a coarser resolution and less detail.

4. Can the Fourier transform limit be exceeded?

No, the Fourier transform limit is a fundamental limit that cannot be exceeded. Any attempt to exceed this limit will result in aliasing, where higher frequencies are erroneously represented as lower frequencies.

5. How can the Fourier transform limit be improved?

The Fourier transform limit can be improved by increasing the length of the signal or by using a higher sampling rate. This will result in a higher frequency resolution and allow for more detailed analysis of the signal.

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