Synchronous and Asynchronous Demodulation of AM, Carrier Frequency Offsets

Objective

The objective of this lab is to deepen students understanding of synchronous and asynchronous demodulation principles for amplitude modulation.

AM-DSB/SC, Synchronous Demodulation, Sinusoideal Carrier

1. Build a Simulink model for synchronous amplitude demodulation of a sinusoidally modulated signal.  (You built the modulator part of this in Lab 1.)  A block diagram of the modulator and demodulator looks like



2. Download the MAT-file sig1.mat to your Lab 2 working directory.
3. At the Matlab prompt type

>> load sig1

This will load the variable x into the Matlab workspace.  Use this as the modulating signal in your simulation.
4. Use a carrier frequency of w_c=2(pi)0.3
5. Before you add the low pass filter to the simulation, export the signals  (y(t), z(t)) to the Matlab workspace using To Workspace blocks.  (Note that x(t) already exists in the workspace.)
6. Use the function that you wrote in Lab 1 to plot the spectra of these three signals.  For example code, see sigspec.m .  You should see something like this.




7. Note that the "double frequency" terms show up at normalized frequency 0.4 instead of 0.6 where they should be.  This is due to aliasing and we will talk about it later.  For now, the important thing to realize is that we have to design the low pass filter to pass the baseband component of z(t) and remove the component at 0.4.
   
8. An FIR equiripple filter that will do the job can be designed using the Matlab code

   >> B = remez(30,[0 0.1 0.3 0.5]*2,[1 1 0 0]);
   

   The first argument in the remez function is the filter order.  The length of the filter is one more than the order.  In this case, the resulting filter is a 31 tap FIR filter.  The second arguement is a vector containing the frequencies of the filter bands.  The pass band extends from [0 to 0.1] and the stop band extends from [0.3 to 0.5].  Notice these two bands in the figure below.  When using remez, don't forget to multiply the desired band frequencies by 2.  The last arguement is a vector that says the desired response should be [1 and 1] at the frequencies [0 and 0.1].  The response should be [0 and 0] at the frequencies [0.3 and 0.5].  You can change the response of filters designed with the remez function by changing the filter and changing the filter band edge frequencies.  For more information see the help for the remez function.
9. Use your spectrum plotting function to plot the magnitude response of the filter on top of the spectrum of y(t).  The plot should look something like this



10. Add the low pass filter to you model.  The easies block to use is the Discrete Filter block in the Discrete block library.  The interface for this block is simple.  If you called the filter filter you designed B, then put B in the numerator of the discrete filter.  Let the denominator be 1.
11. Add a To Workspace block to capture the signal w(t).  Plot the spectra of the signals x(t), y(t), z(t), and w(t) in the same figure window but in different axes.  Your plot may look something like this



12. Write an explanation of the signal spectra at each point.  Is the scaling appropriate.
13. Turn in the spectral plots and the explanation to the lab TA.

AM-DSB/SC, Carrier Frequency Offset, Sinusoidal Carrier

1. Modify the previous experiment by introducing a carrier frequency offset during demodulation.  Leave the modulation carrier at 0.3 but make the demodulation carrier 0.3001.  Run the simulation and display the signals x(t) and w(t).  When I did this, I got the following picture.



2. Plot x(t) and w(t) and write an explanation of why w(t) does not look like x(t).  How important is accurate carrier frequency synchronization?  Turn all of this into the lab TA.