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NCERT Class XII Chapter
Communication Systems
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Question : 8 of 8
Marks: +1, -0
Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the receiving station, there is a facility for generating the carrier. Show that if a device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station.
Solution:  
Let, the received signal be A1A_1 cos (ωc+ωm)t(\omega_c+\omega_m)t
The carrier signal available at the receiving station is AcA_c cos ωc\omega_c t
Multiplying the two signals, we get A1AcA_1A_c cos (ωc+ωm)(\omega_c+\omega_m) t cos ωc\omega_c t
= A1A22\frac{A_1A_2}{2} [cos⁡(2ωc+ωm)t+cos⁡ωmt][\cos(2\omega_c+\omega_m)t+\cos\omega_m t]
If this signal is passed through a low pass filter, we can recover the modulating signal A1A22\frac{A_1A_2}{2} cos ωmt\omega_m t
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