The GATE Grind

GATE 2016 EC – Question 17

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

A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the sampled signal periodic?

  1. $T = \sqrt{2} T_s$
  2. $T = 1.2 T_s$
  3. Always
  4. Never

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Show answer and explanation

Correct answer: (B) $T = 1.2 T_s$

Explanation

The sampled sequence repeats only when the period $T$ is a rational multiple of the sampling period $T_s$, so that a whole number of samples fits in whole periods. $1.2 = \frac{6}{5}$ is rational, so it is periodic, while $\sqrt{2}$ is irrational.