Digital Signal Processing Reference
In-Depth Information
'The DSB/SC modulated signal at carrier frequency 100pi (rad/s) is:'
c = m.*cos(100*pi*t)
% use the symbolic “fourier” function to calculate the Fourier
% transform of the modulated signal.
'The Fourier transform of the DSB/SC signal is:'
Cw = fourier(c)
The following MATLAB program generates and plots a DSB/SC-AM signal and its frequency
spectrum numerically:
% This MATLAB program generates and plots a DSB/SC-AM signal and
% its frequency spectrum numerically
.
% generate a time vector of 256 elements in .01s steps.
t = .01*(1:256);
% generate the message signal m(t)=2cos(20pit)+sin(4pit)
m= 2*cos(20*pi*t) + sin(4*pi*t);
%Display the message signal
subplot(3,1,1), plot(t,m), title('The message signal m(t)'),grid
% modulate a carrier signal, cos(200pit), with m(t).
c = m.*cos(100*pi*t);
%Display the message signal
subplot(3,1,2), plot(t,c), title('DSB/SC-AM Signal'), grid
% use the fft function to approximate the Fourier
% transform of the modulated signal.
CF = fft(c,256);
%generate a frequency vector of 256 elements.
f = 2*pi*(1:256)/(256*.01);
% plot the magnitude spectrum of the modulated signal
%Display the message signal
subplot(3,1,3), plot(f, abs(Cf)), title('DSB/SC-AM Frequency
Spectrum'), grid, grid
■
To make the message suitable for human ears on the receiving end of the com-
munication link, the modulation process must be reversed. This process is called
demodulation
.
Demodulation can be accomplished in much the same way that the modula-
tion was done. First, the received signal, which we assume to be the same as the
transmitted signal, is multiplied by a “local oscillator” signal. The local oscilla-
tor is tuned to produce a sinusoidal wave at the same frequency as the carrier wave
in the transmitter. Because of this requirement to match the local-oscillator fre-
quency to the carrier frequency, this demodulation technique is classified as
synchronous detection
. As shown in Figure 6.34(a),
x(t),
y(t) = x(t)cos(v
c
t).
Again using Euler's identity and the frequency-shifting property of the Fourier
transform, we find that
1
2
[X(v - v
c
) + X(v + v
c
)].
Y(v) =
