A continuous time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period $T_{s}$ . In which one of the following cases, the sampled signal is periodic?

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Solution

A signal is said to be periodic if $\frac{T}{T_{s}}$ is a rational number.

$In the case, T = \sqrt{2} T_{s}$
$\sqrt{2}$ is not a rational number. So it is not periodic.

$In the case, T = 1.2 T_{s}$

$\Rightarrow \frac{T}{T_{s}} = \frac{6}{5}$ which is a rational number and this is periodic.

A sampled signal is not always periodic for all type of signals. So option (c) and (d) are not valid here.

Hence, Only option (b) is correct.

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