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.
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. The received signal is given by,
A1 cos (ωc + ωm) t
Carrier signal is given by,
Ac cos ωc t
where,
ωc and ωm are the angular frequency of the carrier wave and message signal wave. ωc and ωm are the angular frequency of the carrier wave and message signal wave.
The carrier Ac cos ωct is available at the receiving station.
On multiplying the two signals, we get
A1 Ac cos (ωc + ωm) t cos ωctA1 Ac cos (ωc + ωm) t cos ωct
= A1Ac2[2 cos (ωc + ωm) t. cos ωct]= A1Ac2[2 cos (ωc + ωm) t. cos ωct]
= A1 Ac2[cos (2 ωc + ωm) t + cos ωmt]= A1 Ac2[cos (2 ωc + ωm) t + cos ωmt]
If this signal is passed through a low-pass filter, it will pass through the high frequency signals and block the low frequency signals.
Thus, modulating signal, is given by A1 Ac2cos ωmt.A1 Ac2cos ωmt.
of a single frequency ωmωm .
The received signal is given by,
A1 cos (ωc + ωm) t
Carrier signal is given by,
Ac cos ωc t
where,
ωc and ωm are the angular frequency of the carrier wave and message signal wave. ωc and ωm are the angular frequency of the carrier wave and message signal wave.
The carrier Ac cos ωct is available at the receiving station.
On multiplying the two signals, we get
A1 Ac cos (ωc + ωm) t cos ωctA1 Ac cos (ωc + ωm) t cos ωct
= A1Ac2[2 cos (ωc + ωm) t. cos ωct]= A1Ac2[2 cos (ωc + ωm) t. cos ωct]
= A1 Ac2[cos (2 ωc + ωm) t + cos ωmt]= A1 Ac2[cos (2 ωc + ωm) t + cos ωmt]
If this signal is passed through a low-pass filter, it will pass through the high frequency signals and block the low frequency signals.
Thus, modulating signal, is given by A1 Ac2cos ωmt.A1 Ac2cos ωmt.
of a single frequency ωmωm .
