Question: Which of the following signals can be down sampled by a factor of 2 using the system in Figure without any loss of information? (a)

Which of the following signals can be down sampled by a factor of 2 using the system in Figure without any loss of information?

(a) x[n] = ?[n ? n0], for n0 some unknown integer?

(b) x[n] = cos(? n/4)

(c) x[n] = cos(? n/4) + cos(3? n/4)

(d) x[n] = sin(? n/3) / (? n/3)?

(e) x[n] = (?1)n sin(? n/3) / (? n/3)

xn| = x[nM] x{n] Sampling period I Sampling period T= MT

xn| = x[nM] x{n] Sampling period I Sampling period T= MT

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