Correct Answer - Option 1 : 14 sample / sec
Nyquist Sampling Theorem:
A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to twice the highest frequency component of the message signal, i.e.
fs ≥ 2 fm
Where,
fs is the sampling frequency
fm is the highest frequency component of the message signal
Therefore to convert continuous signals to discrete signals, the sampling must be done at the Nyquist rate.
Calculation:
Given: f(t) = 2 sin 9πt + sin 12 πt + sin 14 πt,
ωm = 14π rad/sec
fm = 14π/2π = 7 Hz
For getting minimum sampling frequency,
fs = 2 fm
= 2 × 7
= 14 Hz
= 14 samples/sec
Therefore, The minimum sampling frequency is 14 Hz