[7] x(t) is a band-limited signal with bandwidth B=3000 rad/sec. Its spectrum is assumed to have a square shape with unity amplitude. We sample x(t) at a rate of one sample every Ts second. (a) What is the minimum sampling rate @s=2rTs required to avoid the Aliasing effect? (b) Draw the spectrum of the sampled signal, when the sampling frequency is 1500, 3000 and 7500 rad/sec. (c) If we pass the sampled signal through an ideal LPF with bandwidth equals B, draw the spectrum of the reconstructed signal in each of the three cases described in (b).

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[7] x(t) is a band-limited signal with bandwidth
B=3000 rad/sec. Its spectrum is assumed to
have a square shape with unity amplitude. We
sample x(t) at a rate of one sample every Ts
second.
(a) What is the minimum sampling rate
@s=2rTs required to avoid the Aliasing effect?
(b) Draw the spectrum of the sampled signal,
when the sampling frequency is 1500, 3000
and 7500 rad/sec.
(c) If we pass the sampled signal through an
ideal LPF with bandwidth equals B, draw the
spectrum of the reconstructed signal in each
of the three cases described in (b).
Transcribed Image Text:[7] x(t) is a band-limited signal with bandwidth B=3000 rad/sec. Its spectrum is assumed to have a square shape with unity amplitude. We sample x(t) at a rate of one sample every Ts second. (a) What is the minimum sampling rate @s=2rTs required to avoid the Aliasing effect? (b) Draw the spectrum of the sampled signal, when the sampling frequency is 1500, 3000 and 7500 rad/sec. (c) If we pass the sampled signal through an ideal LPF with bandwidth equals B, draw the spectrum of the reconstructed signal in each of the three cases described in (b).
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