The GATE Grind

GATE 2015 EC – Question 27

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

The result of the convolution $x(-t) * \delta(-t - t_0)$ is

  1. $x(t + t_0)$
  2. $x(t - t_0)$
  3. $x(-t + t_0)$
  4. $x(-t - t_0)$

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Correct answer: (D) $x(-t - t_0)$

Explanation

The impulse is even, so $\delta(-t - t_0) = \delta(t + t_0)$. Convolving a signal with $\delta(t + t_0)$ shifts it by $-t_0$, so $x(-t) * \delta(t + t_0) = x(-(t + t_0)) = x(-t - t_0)$.