GATE 2018 EC – Question 64
A band limited low-pass signal $x(t)$ of bandwidth 5 kHz is sampled at a sampling rate $f_s$. The signal $x(t)$ is reconstructed using the reconstruction filter $H(f)$ whose magnitude response is shown below.
The minimum sampling rate $f_s$ (in kHz) for perfect reconstruction of $x(t)$ is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 13
Explanation
The filter is flat up to 6 kHz and falls to zero at 8 kHz. The first image of the signal spectrum extends down to $f_s-5$ kHz, and this must lie beyond the filter's cut-off at 8 kHz, so $f_s-5\ge8$ and $f_s\ge13$ kHz.