The GATE Grind

GATE 2016 EC (EC2) – Question 20

Networks, Signals and Systems · Continuous-time Signals · 1 mark · Numerical answer

The energy of the signal $x(t)=\sin(4\pi t)/(4\pi t)$ is ________.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.24 to 0.26

Explanation

Use the transform convention $X(f)=\int x(t)e^{-j2\pi ft}\,dt$. Since $x(t)=\operatorname{sinc}(4t)$, its transform is $X(f)=\tfrac14\operatorname{rect}(f/4)$.

The rectangle has width 4 Hz and squared height 1/16. Parseval therefore gives $E=\int|X(f)|^2df=4/16=$ **0.25**.

More Continuous-time Signals questions

All Continuous-time Signals questions →