Fourier Transform of Step Function: Solve & Learn

[sleventh]

i must find the Fourier transform of a step function f(x)=$$\left\{$$ B$$\Leftrightarrow$$ |x|$$\leq$$ a ; 0$$\Leftrightarrow$$ |x|> a$$\right\}$$


no all equations I've been reading and methods of solving are for functions relative to time. I'm not sure how to handle this situation since it position dependent.

thank you very much for any help or references

 

[LCKurtz]

Use:

$$\hat f(\omega) = \int_{-\infty}^\infty f(x) e^{-2\pi i \omega x}\, dx$$

Some authors may put $1 / \sqrt{(2\pi)}$ in front of the integral.