3.8 Determine the DTFT (Discrete time Fourier Transform) for discrete time function

Find DTFT \(X(\Omega )\) of \(x[n]= \sin (\frac {\pi n}{8})\). By definition

\begin{align*} X(\Omega ) &= \sum _{n=-\infty }^{\infty } x[n] e^{-i\Omega n} \end{align*}

Mathematica

Clear["Global`*"]; 
x[n_] := Sin[(Pi*n)/8]; 
X = FourierSequenceTransform[x[n], n, w, FourierParameters -> {1, 1}] // Simplify
 

Which gives

(-(1/2))*I*(DiracComb[(Pi - 8*w)/(16*Pi)] - DiracComb[(Pi + 8*w)/(16*Pi)])