0.4 Analog (de)modulation  (Page 3/9)

The output of this program is shown in [link] . The slowly increasing sinusoidal “message” $w\left(t\right)$ is modulated by the carrier $c\left(t\right)$ at $f_c=1000$ Hz. The heart of the modulation is the point-by-point multiplication of the message and the carrierin the fifth line. This product $v\left(t\right)$ is shown in [link] (c). The enveloping operation is accomplished byapplying a lowpass filter to the real part of $2v\left(t\right)e^{j2\pi f_{c}t}$ . This recovers the original message signal, though it is offset by 1 and delayedby the linear filter.

The principal advantage of transmission systems that use AM with a large carrier is that exact synchronization is not needed;the phase and frequency of the transmitter need not be known at the receiver, as was demonstratedin Exercise  [link] . This means that the receiver can be simplerthan when synchronization circuitry is required. The main disadvantage is thatadding the carrier into the signal increases the power needed for transmission but does not increase the amount ofuseful information transmitted.Here is a clear engineering tradeoff; the value of the wasted signal strength must be balanced againstthe cost of the receiver.

Amplitude modulation with suppressed carrier

It is also possible to use AM without adding the carrier.Consider the transmitted/modulated signal

diagrammed in [link] (a), in which the message $w\left(t\right)$ is mixed with the cosine carrier. Direct application of the frequency shift property of Fouriertransforms [link] shows that the spectrum of the received signal is

As with AM with large carrier, the upconverted signal $v\left(t\right)$ for AM with suppressed carrier has twice the bandwidth of the original message signal. If the original messageoccupies the frequencies between $\pm B$ Hz, then the modulated messagehas support between $f_c-B$ and $f_c+B$ , a bandwidth of $2B$ . See [link] .