EE 2170: Design and Analysis of Signals and Systems, Laboratory 1

EE 2170

Design and Analysis of Signals and Systems

Dept. of Electrical Engineering, Southern Methodist University

Double Sideband (DSB) Modulation/Demodulation

In lecture we have been studying the spectrum (both line spectrum for periodic signals and Fourier Transform spectrum for non periodic signals). We have also begun to look at filters and how these affect the frequency distribution of signals which pass through them. In this lab we will apply what we have been studying in lecture to double sideband modulation (DSB). Double sideband and related modulation techniques are used extensively in wireless communications applications such as cell phones. A general modulation system is shown below. The baseband signal (speech, audio, data) is shifted up in frequency to a radio frequency (RF) band by the transmitter. The RF signal is then sent via the transmitting antenna through the wireless channel to the receiving antenna. For example in a cellular phone uplink the transmitter is in the handset and the receiver is the cellular base station (or vice versa for the downlink).

This laboratory will look at modulation using Simulink. As before, things that should be recorded during this lab and put in the lab writeup web page appear highlighted in yellow. Begin by clicking on the Matlab 6 icon to run Matlab. The Matlab interface looks like this:

In the Matlab command window, type "simulink" followed by return. After Simulink loads, you will see a window that looks like this:

Next, click on the blank page icon in the Simulink Library Browser, this opens up an additional window where you can build Simulink models. Click on the "+" sign next to "Simulink" in the Library Browser then click on "Sources", you should see the following:

Scroll down until you see the Sine Wave icon and drag that icon to the blank model window. Next click on "Sinks" in the left part of the Library Browser and drag the "Scope" icon to the model window. The model window should now look like this:

Next, connect a "wire" between the Sine Wave generator and the Scope. This can be done by dragging the mouse from the Sine Wave icon output terminal to the Scope icon input terminal. Double click on the Scope icon, this will cause an oscilloscope screen to appear. An oscilloscope is a device which enables one to view the appearance of a signal. Next go to the model window and from the "Simulation" menu, select "Start". You should then see the following on the Scope screen:

Note the length of the simulation is 10 seconds. The scope can plot multiple channels at one time, in the Scope window, click on the "parameters" icon and set the number of axes to 2. A second plot window should appear and a second input terminal should also appear on the Scope icon. Next go back to the "Sources" pallette and drag the square wave generator to the model window. Then connect the square wave generator to the second input in the Scope icon:

Run the simulation again, how many cycles of the square wave appear in the scope window? What is its period? Include a copy of your plot in your write-up. This can be done by pressing the "Alt" and "Print Scrn" keys simultaneously to copy the active window to the notepad, then paste the image into your Word document.

Next put together the following model. The Signal Generator can be found in the "Simulink/Sources" area of the Simulink Library Browser and the "Power Spectral Density" block can be found under "Simulink Extras/Additional Sinks".

Double click on the "Signal Generator" block and set its parameters as follows:

Similarly, set the parameters of the "Power Spectral Density" block to:

The power spectral density block plots the squared magnitude of the Fourier Transform of the signal connected to its input. It does this by sampling its input every 0.01 seconds, then computing an approximation to the Fourier Transform called the FFT (which we'll discuss later in EE 2370). Next run the simulation and paste the resulting graph in your writeup (you may need to resize it first). How does the graph compare to the theoretical Fourier Transform magnitude for a sine wave? Now set the signal coming from the signal generator to "Square Wave" and rerun the simulation. Paste the graph in your writeup and discuss how the Fourier Transform magnitude computed with Simulink compares to the theoretical value. Now change the sample time of the "power spectral density" plot to 0.001 and rerun the simulation, and paste the resulting plots in your writeup. How does changing the sample time affect the resulting plots? Next, we will investigate the Fourier Transforms of a modulated signal. Add a multiplier (from the "Simulink/Math" area of the Simulink Library Browser) and a "Sine Wave" generator from the "Simulink/Sources" area of the Library Browser:

This is called a Double Sideband Modulator and is the basis for many radio communications systems. The signal being modulated (typically voice, data, or music from a radio station) is the output of the Signal Generator (a square wave here), and the Sine Wave output is the "carrier signal", which is typically at a much higher frequency than the signal being modulated. Set the parameters of the Sine Wave generator to:

and run the simulation (making sure that the "Power Spectral Density" sample time is still set to 0.001). Paste the plots to your writeup and explain the appearance of the Fourier Transform of the modulator output. The modulator output is the signal which is transmitted to a receiver. It is up to the receiver to recover (in this case) the square wave from the modulator output. This can be done by first translating the signal back to its original frequency (baseband) and lowpass filtering the received signal. Add another Sine Wave generator having the same frequency as the carrier frequency as well as a second multiplier and connect them as shown below:

The second Sine Wave and multiplier are a part of the demodulator of a communications system. Run this simulation, record the resulting plots in your writeup and explain your results. To complete the demodulator, we must add a lowpass filter to the output of the multiplier.

A lowpass filter is a filter which passes only low frequencies. Setting the cutoff frequency to one-half the carrier frequency will do the trick. Add a lowpass filter as follows:

The parameters of the "Transfer Fcn" block (found in the “Continuous” library) should be set to:

Now run the simulation. Copy the resulting plot of the receiver output into your writeup and explain your results. To look at the transfer function of the lowpass filter, use the Matlab "freqs(B,A)" command with B = [1] and A = [1/500^2 sqrt(2)/500 1] from the Matlab command window. Add a plot of the lowpass filter transfer function to your write-up and indicate why the filter is lowpass.