Question

The signal x(t) = sin (200 πt) + 2 sin (400 πt) is modulated to produce a signal g(t) = x(t) sin (400 πt). This is passed through a low pass filter having a cut-off frequency of 400 π rad/sec and passband gain of 2. Then the output signal after the filter is

Answer 1

Correct Answer - Option 3 : cos (200 πt) 

x(t) = sin 200 πt + 2 sin (400 πt)

g(t) = x(t) sin 400 πt

g(t) = [sin 200 πt + 2 sin 400 πt] sin 400 πt

\(= 12\;\left[ {\cos 200\;\pi t - \cos 600\pi t} \right] + \cos 0\pi t - \cos 800\pi t\)

Now, this signal is passed through LPF having a cut-off frequency of 400 π Hz and passband gain of 2.

So output signal = cos 200 πt.     

Option 3 is correct.