1. ## Fourier Transform Problem

I'm having a bit of an issue working out the following problem

$\displaystyle p(t) =$

$\displaystyle 1, for |t|<= 0.5$
$\displaystyle 0, for |t| > 0.5$

Can someone give me some help with this please?

2. Originally Posted by jezzyjez
I'm having a bit of an issue working out the following problem

$\displaystyle p(t) =$

$\displaystyle 1, for |t|<= 0.5$
$\displaystyle 0, for |t| > 0.5$

Can someone give me some help with this please?
$\displaystyle \hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt$

$\displaystyle = \int_{-0.5}^{0.5} e^{-2\pi i \xi t} dt$.

can ya finish..?

$\displaystyle \hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt$
$\displaystyle = \int_{-0.5}^{0.5} e^{-2\pi i \xi t} dt$.
Does it work through to $\displaystyle \frac {\sin \pi \omega}{2 \pi \omega}$?
Does it work through to $\displaystyle \frac {\sin \pi \omega}{2 \pi \omega}$?
I got $\displaystyle \frac{\sin(\pi \xi)}{\pi \xi}$ (by the way latex for $\displaystyle \xi$ is \xi.)