GATE 2024 EE – Question 53

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

If the energy of a continuous-time signal $x(t)$ is $E$ and the energy of the signal $2x(2t-1)$ is $cE$, then $c$ is _____ (rounded off to 1 decimal place).

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Correct answer: 1.99 to 2.01

Explanation

Scaling the amplitude by 2 multiplies the energy by $2^2=4$. Compressing time by a factor 2 (replacing $t$ by $2t$) divides the energy by 2, and the shift by 1 does not change it. So the energy is $4E/2=2E$ and $c=2.0$.