GATE EC 2016 Set 1 — Question 17
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Signals & Systems → Continuous-Time Signals → DT Signal Representation
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Question
A continuous-time function is periodic with period . The function is sampled uniformly with a sampling period . In which one of the following cases is the sampled signal periodic?
Correct answer
(B) T = 1.2 Tₛ
Solution
A sampled signal is periodic if there exists an integer such that for all . This implies . For a continuous-time signal with period , this condition is satisfied if is an integer multiple of , i.e., for some integer . This simplifies to . Thus, the ratio of the signal period to the sampling period must be a rational number.
(A) is irrational.
(B) is rational. This satisfies the condition.
(C) and (D) are incorrect as it depends on the rationality of the ratio.
(A) is irrational.
(B) is rational. This satisfies the condition.
(C) and (D) are incorrect as it depends on the rationality of the ratio.
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