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A discrete-time signal x[n] = sin(π² n), n being an integer, is

1. periodic with period π
2. periodic with period π²
3. periodic with period π/2
4. not periodic

Correct answer: not periodic

Solution

The signal x[n] = sin(π² n) is not periodic because the frequency π² is an irrational multiple of π, which means that the signal does not repeat at regular intervals for integer values of n.

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