Question:
A discrete-time signal \( x[n] = \sin(\pi n^2) \), where \( n \) is an integer, is
A discrete-time signal \( x[n] = \sin(\pi n^2) \), where \( n \) is an integer, is
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For a signal to be periodic, the argument of the sinusoidal function must repeat at regular intervals. In this case, the quadratic term causes irregular behavior.
Updated On: May 5, 2025
- Periodic with period \( \pi \)
- Periodic with period \( \pi/2 \)
- Periodic with period \( \pi^2 \)
- Not periodic
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The Correct Option is D
Solution and Explanation
The given discrete-time signal \( x[n] = \sin(\pi n^2) \) is not periodic. For a discrete-time signal to be periodic, there must be a constant period \( N \) such that \( x[n] = x[n + N] \) for all integer values of \( n \). However, the argument \( \pi n^2 \) grows quadratically, which results in no fixed period for the signal. Therefore, the signal is not periodic, and the correct answer is option (4).
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