GATE 2023 EE – Question 63
A signal $x(t)=2\cos(180\pi t)\cos(60\pi t)$ is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz.
The maximum frequency present in the filtered signal in Hz is _____________ (Round off to the nearest integer).
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Correct answer: 80
Explanation
$x(t)=\cos(240\pi t)+\cos(120\pi t)$, with components at 120 Hz and 60 Hz. Sampling at 200 Hz aliases the 120 Hz tone to $|120-200|=80$ Hz, which lies inside the 100 Hz cutoff, and the 60 Hz tone stays at 60 Hz. (The images at $200\pm60$ and $200\pm120$ are above 100 Hz and are removed.) The highest frequency in the output is 80 Hz.