Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
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X<br />
( e<br />
⎡<br />
⎢<br />
⎣<br />
jω 1<br />
+ ∞ ω 2<br />
) = ∑ X<br />
⎜<br />
a<br />
j −<br />
Ts<br />
l=<br />
−∞ Ts<br />
Ts<br />
⎛<br />
⎝<br />
π ⎞⎤<br />
l<br />
⎟⎥<br />
⎠⎦<br />
The discrete signal is an aliased<br />
version <strong>of</strong> the corresponding<br />
analog signal<br />
It is possible to recover X a<br />
(jΩ)<br />
from X(e jω ), or x a<br />
(t) from x(n)<br />
if the infinite replicas <strong>of</strong> X a<br />
(jΩ)<br />
do not overlap with each other<br />
to form X(ejw).<br />
This is true for b<strong>and</strong>-limited<br />
analog signals.
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