Discrete Time Fourier Tranform of $\frac{sin(n-2)\frac{\pi}{3}}{(n-2)\pi}$

Question

I don't know how to go about solving this. I can see that this can easily be manipulated into the sinc function, but I don't know where that gets me.

Answer 1

So you have to compute $$ f(x)=\sum_{n=-\infty}^\infty c_n e^{-2\pi i⋅ nx} $$ with $$ c_n=\frac{\sin((n−2)⋅\tfracπ3)}{(n−2)π} =\int_{-1/6}^{1/6}e^{2\pi i⋅ (n-2)s}\,ds. $$ The idea of the Dirichlet kernel could be helpful.