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Parseval's Relation Fourier Transform Question

This is an example from Oppenheim's Signals and Systems book, the example continues but i couldn't understand how we found 5/8 for E as book suggests. I tried to apply the formula but i obtained a different result so i'd appreciate it if you can tell me how we get the value. Also as the title already suggests we're supposed to use Parseval's Relation.

At last, if you have any advice or source recommendations on how to really understand all the properties and get better at Fourier Series and Transforms for signals class, I'd truly be grateful for that.

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You need to evaluate a integral over the square of some function that is given to you in diagram 4.18. You can do that by looking closely:

that's just squaring the diagram 4.18 (a). I'll just draw the positive-\$\omega\$ half:


|X(jω)|²
   ^
   |
   |
π  |                —————————————————
   |                |               |
   |                |               |
   |                |               |
   |                |               |
   |                |               |
π/4|————————————————                |
   |                                |
———+——————————————————————————————————> ω
   0               0.5              1

So, the integral over the whole thing is 2(because there is not only the positive, but also the negative half) × (0.5×π/4) × (0.5×π)

That's 5/4π.

Multiply with the 1/(2π) in front of the integral, you get 5/8. Basic math!

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