I have been given the fourier transform for $f\left(x\right) = 1/x$ as
$\hat f = -iπ \,{\rm sgn}\left(x\right)$
I need to find the Fourier Transform of $\frac{\sin x}{x^2}$ using convolution somehow
My attempt was to use $f\left(x\right) = 1/x$ and find some $g\left(x\right)$ such that $f*g\left(x\right)$ would be $\frac{\sin x}{x^2}$ but I cannot find such a $g\left(x\right)$