I wanted to do the following Fourier Transform but I can't:
$$G(t-t')=\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{\exp{i\frac{\omega}{c}\big[v.t.Q\big(1+\frac{r\sin \phi}{Q^2}\big)\big]}}{v.t.Q\big(1+\frac{r\sin \phi}{Q^2}\big)}\times \exp{i\omega\big(t-t'\big)}\, d\omega.$$
Where, $Q^2= 1+\frac{s^2}{(v.t)^2}$; $s= $ constant and $v=$constant, $c=$constant;
$r$ is a dimensionless parameter and $r<<s$, so, we can neglect the term $r^2/s^2$ and so on.
Would you kindly suggest me how I can compute this integral.
I think the answer will be the following:
Suppose, $S=v.t.Q \big(1+\frac{r\sin \phi}{Q^2} \big)$ and this $S$ is not the function of $\omega$; therefore, introducing the Dirac Delta function, it becomes, $G(t-t')= \frac{\delta \big(t-t'-\frac{S}{c}\big)}{S}$.