A sinusoid x(t) of unknown frequency is sampled by an impulse

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A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) has a frequency of

1. 10 Hz
2. 60 Hz
3. 30 Hz
4. 90 Hz

Correct Option: C

Sampling rate 50 Hz
Let x(t) has a frequency of f_x Hz,

After sampling with 50 Hz spectrum will be LPF of cut off = 25 Hz
output = 20 Hz
⇒ 50 – f_x = 20
⇒ f_x = 30 Hz