Given a rational expression (already in simplest form) with unique coefficients $a,b,c,d,e,f$
$$g(\omega)=\frac{a\cos(\omega)^2-b\cos(\omega)+c}{d\cos(\omega)^2-e\cos(\omega)+f}$$
How would I go about finding the inverse Fourier transform of $g$?
I'm not even sure where to start.