Question

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.

Answer 1

Let ω_c and ω_s be the respective frequencies of the carrier and signal waves.

Signal received at the receiving station, V = V₁ cos (ω_c + ω_s)t

Instantaneous voltage of the carrier wave, V_in = V_c cos ω_ct

At the receiving station, the low-pass filter allows only high frequency signals to pass through it. It obstructs the low frequency signal ω_s. Thus, at the receiving station, one can record the modulating signal , which is the signal frequency.