Use MATLAB environment to create a message signal and a carrier signal and apply

Question

Use MATLAB environment to create a message signal and a carrier signal and apply a simplified amplitude modulation (DSB-SC-AM) to see the modulated signal in time domain. Later using the Fourier transform you will see how modulation affects the signal in the frequency domain.

To do this analysis, in the time domain:

1. Create a 1 second long message signal. The message signal is a rectangular pulse between 450 and 550 milliseconds with magnitude 1. (Hint: Create the signal using millisecond units ((t=0:0:001:1));

2. Create carrier signal of the same duration with frequency f0 = 400 Hz. You can either use sin or cos waveforms as a carrier with magnitude 1. (i.e. C = cos(2?f0t))

3. Modulate signal by multiplying the message signal and the carrier. Plot all 3 signals in the time domain and explain what you observe in the modulated signal.

In the frequency domain:

4. Take the Fourier transform of the message and carrier and modulated signal and plot the magnitude spectrum of all of the 3 signals. (Hint: Use fft, fftshift, abs, plot and other commands for his part; Apply 1000-point fft for clear results. To understand this better look up information on fft command by typing help fft in the command window).

Explanation / Answer

%%1
t= 0:0.001:1;
rectpulse=zeros(1, 1001);
rectpulse(451:550)=1;
%%2
f0=450;
C = cos(2*pi*f0*t);
%%3
Modulated_signal= rectpulse.*C;
figure(1)
plot(rectpulse);
figure(2)
plot(C);
figure(3)
plot(Modulated_signal);
%we observe that after modulation carrier signal carries information of
%rect pulse and modulated signal is zero otherwise. Nonzero only at rect
%pulse.
%%4
rectpulse_shifted_fft= fftshift(fft(rectpulse, 1000));
C_shifted_fft= fftshift(fft(C, 1000));
Modulated_signal_shifted_fft=fftshift(fft(Modulated_signal, 1000));

figure(4)
plot(abs(rectpulse_shifted_fft));
figure(5)
plot(abs(C_shifted_fft));
figure(6)
plot(abs(Modulated_signal_shifted_fft));

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