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A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period Tₛ. In which one of the following cases is the sampled signal periodic?
- (A) T = √(2) Tₛ
- (B) T = 1.2 Tₛ
- (C) Always
- (D) Never
Correct answer: (B) T = 1.2 Tₛ
Solution
A uniformly sampled periodic signal is itself periodic (in n) iff the ratio T/Ts is rational. T=sqrt(2)Ts is irrational (not periodic); T=1.2Ts=6/5 is rational, so the sampled sequence is periodic. Answer is (B), not 'Never'.
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