1.

A discrete-time signal x[n] = sin(π2n), n being an integer, is(A) periodic with period π.(B) periodic with period π2.(C) periodic with period π/2.(D) not periodic 

Answer»

Correct option (D) not periodic

Explanation:

Assume x [n] to be periodic, (with period N)

⇒ x[n] = x [n + N]

⇒ sin(π2n) = sin(π2(n + N))

Every frigonometric function repeate after 2π interval.

⇒ 2πk = π2N ⇒ N = (2k/π)

Since ‘k’ is any integer, there is no possible value of ‘k’ for which ‘N’ can be an integer, thus non-periodic.



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