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GATE 2018 EE – Question 49

Signals and Systems · Representation of continuous and discrete time signals, shifting and scaling properties · 2 marks · Multiple choice

The signal energy of the continuous-time signal $x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is

  1. 11/3
  2. 7/3
  3. 1/3
  4. 5/3

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Correct answer: (D) 5/3

Explanation

The signal is a ramp rising from 0 to 1 on $[1,2]$, equal to 1 on $[2,3]$ and a ramp falling from 1 to 0 on $[3,4]$. The energy is $\frac13+1+\frac13=\frac53$.