I'm preparing for an exam in the signals and systems class I'm taking. One of the practice exams has a problem that requires you to take the Fourier transform of $\text{sinc}(4t)$.
From a table of Fourier transform pairs I found: $\dfrac{\omega_b}{\pi}\text{sinc}\left(\dfrac{\omega_b t}{\pi} \right)\Rightarrow \text{rect}(\omega/2\omega_b)$.
Using this I tried to match the given $\text{sinc}(4t)$ by rewriting it as $\dfrac14\dfrac{4\pi}{\pi}\text{sinc}\left(\dfrac{4\pi t}{\pi} \right)$. From this I get that $\omega_b = 4\pi$ and thus the Fourier transform should yield $\dfrac{1}{4}\text{rect}\left(\omega/8\pi \right)$.
But, in the exam solutions they show the Fourier transform to yield $\dfrac{\pi}{4}\text{rect}(\omega/8)$.
Any ideas where I'm going wrong?