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Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are

1. 5 Hz and 15 Hz only
2. 10 Hz and 15 Hz only
3. 5 Hz, 10 Hz and 15 Hz only
4. 5 Hz only

Correct answer: 5 Hz and 15 Hz only

Solution

The original signal contains frequency components at 5 Hz (from cos(10πt)) and 15 Hz (from cos(30πt)). Sampling at 20 Hz allows these frequencies to be preserved, while the ideal low-pass filter with a cut-off at 20 Hz effectively removes any higher frequency components, confirming that only 5 Hz and 15 Hz are present in the reconstructed signal.

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