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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.
Using
AMlarge.m
, plot the spectrum of the message
$w\left(t\right)$ , the
spectrum of the carrier
$c\left(t\right)$ , and the spectrum of the received
signal
$v\left(t\right)$ . What is the spectrum of the envelope?
How close are your results to the theoretical predictions in
[link] ?
One of the advantages of transmissions using
AM with large carrier is that there is no needto know the (exact) phase or frequency of the transmitted signal.
Verify this using
AMlarge.m
.
c=cos(2*pi* fc*t+phase)
with
phase=0.1, 0.5, pi/3, pi/2, pi
, and verify that
the recovered envelope remains unchanged.c=cos(2* pi*(fc+g)*t)
with
g=10, -10, 100, -100
, and verify that
the recovered envelope remains unchanged.Can
g
be too large?Create your own message signal
$w\left(t\right)$ , and rerun
AMlarge.m
.
Repeat Exercise
[link] with this new message. What differences do you see?
In
AMlarge.m
, verify that the original message
w
and the recovered envelope
envv
are offset by 1, except at the
end points where the filter does not have enough data.Hint: the delay induced by the linear filter is approximately
fl
/2.
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.
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] .
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