# Fourier Transform

1. Feb 1, 2009

### razorwind

Determine the Fourier transform of the following signals: $$x(t) = \frac{1}{(1+t^2)}$$

I start off by doing $$X(f) = \int{x(t)*e^{-j2\pi{}ft} dt}$$

So i plug in x(t) into that equation, but i'm lost as to how to integrate it. Am i going in the right direction?

Also: x(t)=abs(t) for $$-2\leq{}t\leq{}2$$

I am splitting it to -t for $$-2\leq{}t\leq{}0$$ and t for $$0\leq{}t\leq{}2$$ then doing the transform with the equation above. Is it allowed to split it into 2 integrals? So it ends up being $$X(f) = \int{-t*e^{-j2\pi{}ft} dt}$$ + $$\int{t*e^{-j2\pi{}ft} dt}$$ and I simplify from there.

Last edited: Feb 1, 2009