How to obtain the CTFT of a rect in terms of f in hertz (from the formula in terms of $ \omega $)
Recall:
$ x(t)=\left\{\begin{array}{ll}1, & \text{ if }|t|<T,\\ 0, & \text{else.}\end{array} \right. $
$ \mathcal{X}(\omega)=\frac{2 \sin \left( T \omega \right)}{\omega} $
To obtain X(f), use the substitution
$ \omega= 2 \pi f $.
More specifically
$ X(f)=\mathcal{X}(2\pi f)=\frac{\sin \left(2\pi Tf \right)}{\pi f} \ $
