Question

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 cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) is
1. 10 Hz
2. 60 Hz
3. 30 Hz
4. 90 Hz

Answer 1

Correct Answer - Option 3 : 30 Hz

Period of sampling train, T_s = 20 ms

\(\therefore {f_s} = \frac{1}{{20 \times {{10}^{ - 3}}}} = 50{\rm{Hz}}\)

If frequency of x(t) is f_x, then after sampling the signal, the sampled signal has the frequency,

f_s - f_x = 50 - f_x and f_s + f_x = 50 + f_s

 Now, the sampled signal is applied to and ideal low pass filter with cut off frequency.

f_c = 25 Hz

Now, the o/p of filter carried a single frequency component of 20 Hz

∴, only \(\left( {{f_s} - {f_x}} \right)\) component passes through the filter, ie.

f_s - f_x < 25

and f_s - f_x = 20

50 - f_x­ = 20

f_x = 50 - 20 = 30 Hz