I am trying to take the inverse Fourier transform of the following function: $$\left(1+\frac{b^2+a^2}{f^2}+\frac{b^2a^2}{f^4}\right)$$ where $a$ and $b$ are real numbers and $f$ is the frequency. So basically I want to get to the time data that gives this frequency spectrum. However Mathematica can't provide an answer and after working through I am left with $~\sin(\infty)~$ and $~\cos(\infty)~$terms which don't appear to cancel. Hoping someone knows some alternative method.
Thanks