Solution:
$
x(t)=\pi(t)=A \quad ; \frac{-T}{2} \leq t \leq \frac{T}{2}\\
$
$
F[\pi(t)]=\int_{-\frac{T}{2}}^{\frac{T}{2}} A e^{-j \Omega t} d t\\
$
$
=A\left[\frac{e^{-j \Omega t}}{-j \Omega}\right]_{-\frac{T}{2}}^{\frac{T}{2}}\\
$
$
=\frac{A}{-j \Omega}\left[e^{-j \Omega \frac{T}{2}}-e^{j \Omega \frac{T}{2}}\right]\\
$
$
=\frac{2 A}{j \Omega}\left[\frac{e^{j \Omega \frac{T}{2}}-e^{-j \Omega \frac{T}{2}}}{2}\right]=\frac{2 A}{\Omega} \sin \Omega \frac{T}{2}\\
$
$
=\frac{2 A}{\Omega …
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