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Ok well the way i did it was i broke it down trigonometrically first then went on to do the integration on the two resulting terms. I did not double check the results though. After checking i see i must have done something wrong.
Having checked the results, i am getting 1/T now too.
It sounds as though you were able to solve this by using integration by parts ?
As said before, I did some research on the internet and it appeared it could only be solved by using contour integrals or complex integrals whatever that means.
I am not too bothered about the fact you get 1/abs(T) as I am dealing with time and frequencies.
Thanks for your time, checking this out - much appreciated.
I am not having much success with the second integration of sinc^2 (π(f-fc)T).
I am thinking it must also be 1/T as from any integration point of view the only difference between it and the first integration is that this one is displaced in frequency by fc. The areas under the curves should be exactly the same ?
Contour integration would probably mean considering f to be a complex variable with real and imaginary parts:
You'd have to look into how to do that for this problem.
If you try different values for T in the first problem you had, you quickly see that 1/abs(T) is probably right and of course for values that are only positive 1/T is probably right. So if you do the same for your new problem you should see the same. This works on a try by try basis because it's easier to integrate when T or Fc is a constant numerical value like 1,2,3,... etc. So it should work for every positive value tried for T or Fc after you replace it and then do the integration by your usual method. Granted this isnt a definite proof, but may still be useful for a given range of the variable.