LECTURE on September 11, 2009
The perfect reconstruction of $ {x(t)} $ from $ x_s(t) $ is possible if $ X(f) = 0 $ when $ |f| \ge \frac{1}{|2T|} $
PROOF: Look at the graph of $ X_s(f) $
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To avoid aliasing,
$ \frac{1}{T}\ - f_M \ge f_M $ $ \iff $ $ \frac{1}{T}\ \ge 2f_M $
To recover the signal, we will require a low pass filter with gain $ T $ and cutoff, $ \frac{1}{2T} $
