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Due to economic reasons, only the upper side band of an AM wave is transmitted, but at the receiving station, there is a facility for generating the carrier. Show that if device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station. |
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Answer» Let `omega_c and omega_m` be the angular frequency of carrier waves and message signal wave respectively. For simplicity, let the signal received at the receiving station be `e = E_1 cos (omega_c + omega_m)t` Let the instantaneous voltage of carrier waves `(e_c)` given by `e_c = E_c cos omega_ct ` be avialable at the receiving station, Now, `e xx e_c = E_1E_c cos (omega_c + omega_m) t cos omega_ct` `(E_1E_c)/2 [ cos {(omega_c + omega_m) t + omega_ct} + cos { (omega_c + omega_m) t - omega_ct}]` `= (E_1E_c)/2[cos(2omega_c+omega_m) t + cos omega_mt]` At the receiving station, when the signal is passed through low-by pass filter, it will pass the high frequency signals `(2omega_c + omega_m)` but obstruct the low frequency signal `omega_m`. Therefore, we can record the modulating signal `= (E_1E_c)/2 cos omega_mt`, which is a signal of angular frequency `omega_m`. |
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