The GATE Grind

GATE 2026 EC – Question 13

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

The Laplace Transform of the signal $x(t) = u(t-2) * (t\,u(t))$ is given by which of the following expressions? [“$*$” represents convolution operator]

  1. $\frac{e^{-2s}}{s^2(s-2)}$
  2. $\frac{e^{-2(s-2)}}{s^3}$
  3. $\frac{s\,e^{-2s}}{(s-2)^2}$
  4. $\frac{e^{-2s}}{s^3}$

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Correct answer: (D) $\frac{e^{-2s}}{s^3}$

Explanation

Convolution in time becomes a product in the s-domain. $\mathcal L\{u(t-2)\}=e^{-2s}/s$ and $\mathcal L\{tu(t)\}=1/s^2$, so $X(s)=e^{-2s}/s^3$.