Find the Fourier transform in $F$ of $$ f(t)=\frac{\sin(\pi t/T)}{\pi t/T} $$
It is known that: $$ F\{u(t+\tau)-u(t-\tau)\}=\frac{\sin(2\pi F \tau)}{\pi F} $$ Using the duality theorem: $$ F\{F(t)\}=2\pi f(-2\pi F) $$
I get
$$ F\{f(t)\}=2\pi T [u(-2\pi F+1/2T)-u(-2\pi F-1/2T)] $$
How do I proceed from here so that the final answer would be $$ T\left[u\left(-F+\frac{1}{2T}\right) - u\left(-F-\frac{1}{2T}\right) \right] $$