# Fourier Transform Problem

• Apr 29th 2010, 09:57 AM
jezzyjez
Fourier Transform Problem
I'm having a bit of an issue working out the following problem

$p(t) =$

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

Can someone give me some help with this please?
• Apr 29th 2010, 10:19 AM
Quote:

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

$p(t) =$

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

Can someone give me some help with this please?

$\hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt$

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

can ya finish..?
• Apr 29th 2010, 11:35 AM
jezzyjez
Quote:

$\hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt$

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

can ya finish..?

Does it work through to $\frac {\sin \pi \omega}{2 \pi \omega}$?
• Apr 29th 2010, 11:46 AM
Does it work through to $\frac {\sin \pi \omega}{2 \pi \omega}$?
I got $\frac{\sin(\pi \xi)}{\pi \xi}$ (by the way latex for $\xi$ is \xi.)