when computing the Fourier transform of $\mbox{rect}(\frac{x}{2})$ where it's equal to $1$ from $-1<x<1$ and zero for $|x|>1$.
When computing I ended up with $\frac{\sin(2\pi s)}{\pi s}$. I know $\mbox{sinc}(s)$ is defined as $\frac{\sin(\pi s)}{\pi s}$ however I'm not sure how much answer relates to $\mbox{sinc}$ as using the properties of the shifted rect it should be $2\mbox{sinc}(2x)$. e.g. is $\frac{\sin(2\pi s)}{\pi s}= 2\mbox{sinc}(2s)$? thanks!