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Band Pass Sampling Statement and Problems

A band limite...

Question

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 $f_{s} (i n k H z)$ for perfect reconstruction of x(t) is

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Solution

Let us assume an arbitary spectrum for x(t) as shown below:

The spectrum of the sampled signal can be given as,

For proper reconstruction of the signal,

$f_{s} - 5 \geq 8$

$f_{s} \geq 8 + 5 = 13 k H z$

$S o, f_{s (m i n)} = 13 k H z$

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