Correct Answer - Option 2 : T = 1.2 T
s
Consider x(t) = cos (ω0t)
If x(t) is sampled with a sampling period Ts
x(n) = cos Ω0n is obtained
\(\frac{{{{\rm{\Omega }}_0}}}{{{T_s}}} = {\omega _0}\)
Here \(\frac{{2\pi \;m}}{{{N_0}\;{T_s}}} = \frac{{2\pi }}{{{T_0}}}\)
\(\therefore \frac{{{T_0}}}{{{T_s}}} = \frac{{{N_0}}}{m}\)
For the sampled signal to be periodic, ‘m’ should be such that an above expression is a rational number.
Thus \(\frac{T}{{{T_s}}} = \frac{{12}}{{10}} = \frac{6}{5}\)
T = 1.2 Ts