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(2πf0t))
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).
5. Explain what you see in the spectrum of the modulated signal and how it relates to the spectrum of the message and carrier.
6. Solve this modulation problem by hand (i.e. take the Fourier transform of the modulate signal)
7. Plot the magnitude spectrum of the modulated signal as you computed by hand in part 6.
8. What are the similarities between your hand computed result vs. the MATLAB result from part 4?
9. What are the differences between your hand computed result vs. the MATLAB result from part 4? What causes these differences?
10. In MATLAB, show that by modulation we can have more than one user on the spectrum. For this you can create another message and put in on the different carrier and show that the spectrum of the 2 massage signals do not interfere. Explain how the receiver should be designed.