GATE 2024 IN – Question 27
The Nyquist sampling frequency for $x(t)=10\sin^2(200\pi t)$ is ______ Hz (nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 400 to 400
Explanation
Using $\sin^2\theta=(1-\cos2\theta)/2$ gives $x(t)=5-5\cos(400\pi t)$. The highest frequency is $400\pi/(2\pi)=200$ Hz. Twice this is the Nyquist rate: **400 Hz**.