Those integrals do not converge. Period.
I'm being reluctant when finding integrals involving complex exponentials, of the form:
This is because I do not know what to do with infinities multiplied by a complex number, but I know as
Is there a way to solve this without getting into Fourier transform? I know that generalized functions are involved in those integrals, but can we got an answer without going through that?
Alright, before closing the thread, I would like to say, In a course on basic signal proecssing, they establish the following:
Now, by inverse transform, and exchanging variables, we get the that the Fourier transform of f(t)=1 is . Is this mathematically accepted?
NB The delta here is the Dirac delta