Analog Modulation
Features
In most communication medium, only a
fixed range of frequencies is available for transmission. One way to
communicate a message signal whose frequency spectrum does not fall within that
fixed frequency range, or one that is otherwise unsuitable for the channel, is
to alter a transmittable signal according to the information in your message
signal. This alteration is called modulation, and it is the
modulated signal that you transmit. The receiver then recovers the original
signal through a process called demodulation. This section
describes how to modulate and demodulate analog signals using blocks.
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Open the Modulation library by
double-clicking its icon in the main Communications Toolbox™ block library.
Then, open the Analog Passband sublibrary by double-clicking its icon in the
Modulation library.
The following figure shows the
modulation techniques that Communications Toolbox supports for analog signals.
As the figure suggests, some categories of techniques include named special
cases.
For a given modulation technique,
two ways to simulate modulation techniques are called baseband and pass
band. This product supports pass band simulation for analog modulation.
The modulation and demodulation
blocks also let you control such features as the initial phase of the modulated
signal and post-demodulation filtering.
Represent Signals for
Analog Modulation
Analog modulation blocks in this
product process only sample-based scalar signals. The input and output of the
analog modulator and demodulator are all real signals.
All analog demodulators in this
product produce discrete-time, not continuous-time, output.
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Representing Analog
Signals Using MATLAB
To modulate an analog signal using
MATLAB®, start with a real message signal and a sampling rate Fs in
hertz. Represent the signal using a vectorx, the entries of which give the
signal's values in time increments of 1/Fs. Alternatively, you can use a matrix
to represent a multichannel signal, where each column of the matrix represents
one channel.
For example, if t measures
time in seconds, then the vector x below is the result of sampling a
sine wave 8000 times per second for 0.1 seconds. The vector y represents
the modulated signal.
Fs = 8000; % Sampling
rate is 8000 samples per second.
Fc = 300; % Carrier frequency
in Hz
t = [0:.1*Fs]'/Fs; %
Sampling times for .1 second
x = sin(20*pi*t); %
Representation of the signal
y = ammod(x,Fc,Fs); %
Modulate x to produce y.
figure;
subplot(2,1,1);
plot(t,x); % Plot x on top.
subplot(2,1,2);
plot(t,y)% Plot y below.
As a multichannel example, the code
below defines a two-channel signal in which one channel is a sinusoid with zero
initial phases and the second channel is a sinusoid with an initial phase
of pi/8.
Fs = 8000;
t = [0:.1*Fs]'/Fs;
x = [sin(20*pi*t),
sin(20*pi*t+pi/8)];
Analog Modulation
with Additive White Gaussian Noise (AWGN) Using MATLAB
This example illustrates the basic
format of the analog modulation and demodulation functions. Although the
example uses phase modulation, most elements of this example apply to other
analog modulation techniques as well.
The example samples an analog signal
and modulates it. Then it simulates an additive white Gaussian noise (AWGN)
channel, demodulates the received signal, and plots the original and
demodulated signals.
% Prepare to sample a
signal for two seconds,
% at a rate of 100
samples per second.
Fs = 100; % Sampling
rate
t = [0:2*Fs+1]'/Fs; %
Time points for sampling
% Create the signal,
a sum of sinusoids.
x = sin(2*pi*t) +
sin(4*pi*t);
Fc = 10; % Carrier
frequency in modulation
phasedev = pi/2; %
Phase deviation for phase modulation
y =
pmmod(x,Fc,Fs,phasedev); % Modulate.
y = awgn(y,10,'measured',103);
% Add noise.
z =
pmdemod(y,Fc,Fs,phasedev); % Demodulate.
% Plot the original
and recovered signals.
figure; plot(t,x,'k-',t,z,'g-');
legend('Original
signal','Recovered signal');
Other examples using analog
modulation functions appear in the reference pages for ammod, amdemod, ssbdemod, and fmmod.
Sampling Issues in
Analog Modulation
The proper simulation of analog
modulation requires that the Nyquist criterion be satisfied, taking into
account the signal bandwidth.
Specifically, the sample rate of the
system must be greater than twice the sum of the carrier frequency and the
signal bandwidth.
Filter Design Issues
After demodulating, you might want
to filter out the carrier signal. The particular filter used, such as butter, cheby1, cheby2, and ellip, can be selected on the mask of the demodulator block.
Different filtering methods have different properties, and you might need to
test your application with several filters before deciding which is most
suitable.
Varying Filter's
Cutoff Frequency Using Simulink
In many situations, a suitable
cutoff frequency is half the carrier frequency. Because the carrier frequency
must be higher than the bandwidth of the message signal, a cutoff frequency
chosen in this way properly filters out unwanted frequency components. If the
cutoff frequency is too high, the unwanted components may not be filtered out.
If the cutoff frequency is too low, it might narrow the bandwidth of the
message signal.
The following example modulates a
sawtooth message signal, demodulates the resulting signal using a Butterworth
filter, and plots the original and recovered signals. The Butterworth filter is
implemented within the SSB AM Demodulator Passband block.
To open this
model , enter doc_filtercutoffs at the MATLAB command
line.
This example generates the following
output:
There is invariably a delay between
a demodulated signal and the original received signal. Both the filter order
and the filter parameters directly affect the length of this delay.
Other Filter Cutoffs. To see the effect of
a lowpass filter with a higher cutoff frequency, set the Cutoff
frequency of the SSB AM Demodulator Passband block to 49, and run the
simulation again. The new result is shown below. The higher cutoff frequency
allows the carrier signal to interfere with the demodulated signal.
To see the effect of a lowpass
filter with a lower cutoff frequency, set the Cutoff
frequency of the SSB AM Demodulator Passband block to 4, and run the
simulation again. The new result is shown in the following figure. The lower
cutoff frequency narrows the bandwidth of the demodulated signal.
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Source: mathworks
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