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GATE 2014 EC (EC1) – Question 27

Networks, Signals and Systems · Discrete-time Signals · 1 mark · Multiple choice

For integer n, the discrete-time signal $x[n]=\sin(\pi^2n)$ is ______.

  1. periodic with period $\pi$
  2. periodic with period $\pi^2$
  3. periodic with period $\pi/2$
  4. not periodic

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Correct answer: (D) not periodic

Explanation

A discrete-time sinusoid has an integer period N only if its angular frequency satisfies ω0N=2πm for integers N>0 and m. Here π²N=2πm would require N=2m/π, impossible for a nonzero integer N because π is irrational. The sequence is **not periodic,D**.