Question

A sinusoid x(f) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal low-pass filter with a cut-off 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

• A. 10 Hz
• B. 60 Hz
• C. 30 Hz
• D. 90 Hz

Answer 1

The correct option is C 30 Hz

Given, impulse train of period 20 ms.
$\text{Then, sampling frequency}=\frac{1}{20\times {10}^{-3}}=50\text{Hz}$
If the input signal x(t)$=\cos {\omega }_m\left(t\right)$ having spectrum


The filtered out sinusoidal signal has 20 Hz frequency the sampling must be under sampling. The output signal which is an under sampled signal with sampling frequency 50 Hz is

and $50-f_m=20\text{Hz}$
$f_m=30\text{Hz}$