GATE 2014 EC (EC3) – Question 27
$x(t)=\cos(10\pi t)+\cos(30\pi t)$ is sampled at 20 Hz and reconstructed using an ideal low-pass filter with cutoff 20 Hz. Which frequencies are present?
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Correct answer: (A) 5 Hz and 15 Hz only
Explanation
The original tones are5and15Hz, and sampling at20Hz creates spectral replicas separated by20Hz. Within a low-pass cutoff of20Hz, both±5and±15remain; the aliased copies reinforce the same frequencies. Therefore **5Hz and15Hz only,A**. A10Hzcutoff would instead retain only5Hz.