I was wondering what happens when calculating the fourier transform of a fonction, the limit does not exist.
Let me explain this with an example :
I have the function difined by :
f(t) = e^t when -infinity < t < 0
We then calcul the fourier transform :
F(jw) = integral (-infinity -> 0) f(t) e^-jwt dt F(jw) = integral (-infinity -> 0) e^(1-jw)t dt F(jw) = [e^(1-jw)t / (1-jw)] between 0 and -infinity.
Here we can't calcul the limit in -infinity. Can we say that :
F(jw) = 1 / (1-jw) ?
If it is wrong, why ? And what can we do ?
(If it can help, the original question is to calcul the fourier transform of the function f(t) defined by e^t between -infinity and 0 AND e^-t between 0 and infinity).
Thank you guys,
PS : I don't know if there is a proper formating of mathematic formulas, sorry about that if it does :(.