Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
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X ( 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 />
• Suppose signal b<strong>and</strong> is<br />
limited to ±Ώ 0 ,<br />
• If T s is small, Ώ 0 T s π, or<br />
<br />
<br />
F 0<br />
= Ώ 0<br />
/2 π > Fs/2=1/2T s<br />
Then the freq. Resp. <strong>of</strong> x(t)<br />
is a overlaped replica <strong>of</strong> its<br />
analog signal x a<br />
(t), so<br />
cannot be reconstructed
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