The title kinda says it all. I know it is possible to have a RV with its Ch function being the periodic triangular wave. This RV can be achieved via the Fourier transform and then converting the cosine of $+$ and $-$ to complex exponentials. But since my new function isn't even periodic, this method cannot be applied. Is there any other similar process to get the RV relating to the above mentioned Ch function?
Actually, I just want to find any RV whose ch function will be zero outside $[-1,1]$
$f(x)=\frac 1{\pi} \frac {1-\cos\, x} {x^{2}}$ is a density function on $\mathbb R$ and its characteristic function is $1-|t|$ for $|t| \leq 1$, $0$ for $|t|>1$.