# Fourier transform f(x)=sinax/x, a>0

## Homework Statement

I am trying to show given f(x)=(sinax)/x, a>0

that the transform is 0, |k|>a
(pi/2)^1/2, |k|<a

## The Attempt at a Solution

so far i have f transform =1/(2pi)^1/2.[integral from -inf to +inf]exp[-ikx](sinax)/x.dk, i am concerned about the singularity at x =0, does this compel me to use contour integration?

You could do contour integration, but since you know the answer, it's easier to show it's right. Write sin(ax)/x as (exp(iax)-exp(-iax))/2ix. Now compare this expression with $$\int^a_{-a} e^{i k x} dk$$. Do you see the relation between your function and the fourier transform of a step function?