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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.
Asked by K Last Modified
Answer 
Tasneem
Let ωc and ωs be the respective frequencies of the carrier and signal waves.
Signal received at the receiving station, V = V1 cos (ωc + ωs)t
Instantaneous voltage of the carrier wave, Vin = Vc cos ωct
At the receiving station, the low-pass filter allows only high frequency signals to pass through it. It obstructs the low frequency signal ωs. Thus, at the receiving station, one can record the modulating signal 
, which is the signal frequency.
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