Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
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<strong>Reconstruction</strong><br />
Impulse train<br />
conversion<br />
Ideal lowpass<br />
filter<br />
x (n)<br />
(t)<br />
x a<br />
L<br />
∑ +∞<br />
n=<br />
−∞<br />
x( n)<br />
δ ( t − nTs<br />
) = L + x(<br />
−1)<br />
δ ( t + Ts<br />
) + x(0)<br />
δ ( t)<br />
+ x(1)<br />
δ ( t −Ts<br />
) +<br />
∑ +∞<br />
n=<br />
−∞<br />
x ( t)<br />
= x(<br />
n)sinc[<br />
F ( t − nT )]<br />
a<br />
s<br />
s<br />
Interpolating formula<br />
sinc(x) = sin(πx)/πx<br />
Lowpass filter b<strong>and</strong>-limited to the [-Fs/2,Fs/2] b<strong>and</strong><br />
The ideal interpolation is not practically feasible because the entire<br />
system is noncausal <strong>and</strong> hence not realizable.
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