The above Rectangular Impulse Function is given. It's height is $A$ and it's width is $T$.
The question is the following:
If the Fourier Transform of the above function is in the form of $$F(ω)=X*si(ωT)$$ what is $X$?
I tried it and I can't seem to be able to find a constant $X$ to describe the Fourier Transform in the wanted form. If you look up any table, the answer would be the following: $$F(ω)=A*T*si(ω*T/2)$$
I do not think it is possible to define a constant $X$ that would be able to turn $$si(ω*T/2)$$ into $$si(ωT)$$ since it's outside of the si input arguments. Am I right? Is it possible to define $X$?