# Another Fourier Inversion Problem

1. Jun 4, 2006

### cloud18

Find the inverse transform of

$$\frac{\sin{a\omega}}{\omega}$$

I know the step function has a transform of this form, so I as able to find the inverse transform by assuming it was some step function and then looked for the right constants.

However, I would like to also know how to do it by the definition:

$$f(x) = \frac{1}{2\pi} \lim{\int{\overline{f}(\omega)e^{-i\omega x} d\omega}}$$

Where the limit is L--> infinity and the integration limits are -L to +L.

I think this must be done by contour integration? Can someone show me how to setup the contour integral?