Analog Modulation
Representing Analog Signals
To modulate an analog signal using this toolbox, start with
a real message signal and a sampling rate Fs in
hertz. Represent the signal using a vector x, 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 phase
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)];
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Analog Modulation Example
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.
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