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 (ωc + ω_s)t 

Instantaneous voltage of the carrier wave, V_in = 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 ω_s.

 Thus, at the receiving station, one can record the modulating signal , (V₁V_c)/2cosω_st which is the signal frequency.