3.9 Determine the Inverse DTFT (Discrete time Fourier Transform)

Find \(x[n]\), give its DTFT \(X(\Omega )\)

\begin{align*} x[n] &= \frac {1}{2 \pi } \int _{-\pi }^{\pi } X(\Omega ) e^{i\Omega n} \mathop {d\Omega } \end{align*}

Mathematica

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

Which gives

Sin[(Pi*n)/8]