How do we calculate Fourier Transform of $x(t) = \frac{\sin at}{\pi t}$?

35 Views Asked by At

I have tried using the integration by parts method, with 3 terms: $\int l' m n = lmn - \int l m' n - \int lm n'$.

I put $l′= e^{-jwt}$, $m = sin (at)$ and $n = \frac{1}{t}$.

Meaning $l = \frac{-e^{-jwt}}{jw}$, $m′ = acos (at)$ and $n' = \frac{-1}{t^2}$.

I don't seem to be getting the correct answer though. What am I doing wrong?

P.S. My first time on this site, sorry if I posted something in the wrong way.