GATE EC 2014 Set 1 — Question 27
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Question
A discrete-time signal , being an integer, is
Correct answer
(D) not periodic.
Solution
A discrete-time sinusoidal signal is periodic if and only if the ratio of its angular frequency to is a rational number.where and are integers.
In this case, . Since is an irrational number, is also irrational. Therefore, the signal is not periodic. Furthermore, in discrete-time, a period must be an integer, making options A, B, and C conceptually incorrect regardless of the value of .
In this case, . Since is an irrational number, is also irrational. Therefore, the signal is not periodic. Furthermore, in discrete-time, a period must be an integer, making options A, B, and C conceptually incorrect regardless of the value of .
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