3.9 Determine the Inverse DTFT (Discrete time Fourier Transform)

Find $x[n]$, give its DTFT $X(\mathrm{\Omega })$

$$\begin{array}{rl}x[n]& =\frac{1}{2\pi }{\int }_{-\pi }^{\pi }X(\mathrm{\Omega })e^{i\mathrm{\Omega }n}d\mathrm{\Omega }\end{array}$$

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]