Parsevall’s theorem?

Question

Use Parsevall’s theorem to find E=∫[(sin 2πt/t)cos1000πt]² dt from – infinity to + infinity

Answer 1

Parsevall's theorem says that the total integral (from -∞ to ∞) of any function's square is the same the integral of the square of its Fourier Transform.

You must use the unitary form of the Fourier Transform. See:
http://en.wikipedia.org/wiki/Fourier_transform#Definitions

So you have:
1/√(2π) ∫ sin (2πt)cos1000πt) e^(-iωt) / t dt

The result is X(ω), and then we just compute:

∫ X(ω) ² dω

Both of those integrals are, of course, taken over the whole real line. So now we just have to evaluate them. I'm going to leave that up to you because I don't have the time or patience to work that out, and because I want you to do some of your homework on your own. But since no one else is answering except with "??" I wanted to try to at least guide you towards the answer.

Answer 2

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