I am looking to evaluate the following definite integral involving Dirichlet kernel and sinc function with phase. \begin{equation}I(d) = \int_{-\infty}^{\infty} \frac{\sin[N(k^{"}-k^{'})]}{\sin(k^{"}-k^{'})} \frac{\sin(c(k^{"}-k^{'}))}{c(k^{"}-k^{'})} \frac{\sin(Nk^{'})}{\sin(k^{'})} \frac{\sin(ck^{'})}{ck^{'}} \exp(ik^{'}d+i\phi(k^{'})) rect \Big(\frac{k^{'}}{k_0}\Big) dk^{'} \end{equation}
Seems to be difficult due to Dirichlet kernel. Thank you in advance.