For the modulated signal {x}( {t})= {m}( {t}) \cos (2 \pi {f}_{ {c}} {t}), the message signal {m}( {t})=4 \cos (1000 \pi {t}) and the carrier frequency {f}_{ {c}} is 1 {MHz}. The signal {x}( {t}) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is

Correct Answer is : cos(920πt)

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 38 of 65

Marks: +1, -0

For the modulated signal

{x}( {t})= {m}( {t}) \cos (2 π {f}_{ {c}} {t})

, the message signal

{m}( {t})=4 \cos (1000 π {t})

and the carrier frequency

{f}_{ {c}}

1 {MHz}

. The signal

{x}( {t})

is passed through a demodulator, as shown in the figure below. The output

y(t)

of the demodulator is

Solution:

x(t)=m(t) \cos (2 π f c t)

m^{'}(t)=4 \cos (1000 n t)

f_{c}=1 \;\text " MHz "\;

Z(t)=m(t) \cos (2 π f c t) \cos [2 n(f_{c}+40) t]

=\;{m(t)}/{2} \cos [2 π 2 f_{c}+40]++\cos (π × 40) t

=\cos (1080 π t)+\cos (920 π t)

=f_{m 1}=540 \;\; {Hz}, \;\; f_{m 2}=460 {Hz}

y(t)=\cos 920 π t

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