One objective in this lab is to learn how to use the Fast Fourier Transform (FFT) capabilities of the oscilloscope to analyze the frequency content of signals. The other objective is to begin using the dSPACE units that are on the lab benches in room 129. The dSPACE units contain A/D and D/A circuits as well as a digital signal processing (DSP) chip. The FFT and the dSPACE units will be useful tools for the lab project in this course, which we will begin very soon.

A formal report is not required for this lab. However, there are some calculations related to FFT measurements that I would like you to submit before you leave lab today. I would expect the calculations to take approximately one page per group.

1. Using the FFT on the Oscilloscope

Begin by connecting the function generator to the oscilloscope. Set the function generator to produce a sine wave with amplitude 100 mV and frequency 1 kHz. Display the sine wave on the oscilloscope, and save this "time-domain" view of the signal as setup 1 using the SETUP key on the scope.

Now we can display the sine wave in the "frequency domain" using the FFT as follows. First, press the 1 key and turn the time-domain display of the sine wave OFF. Press the +/- key, then turn FUNCTION 2 to ON, then choose the FFT operation. (Note that the scope will also perform differentiation and integration operations.) Familiarize yourself with the various items that can be specified for the FFT display. Settings that work for the 100 mV, 1 kHz sine wave are as follows: 10 dB Units/div, 10 dBV Reference Level, and on the FFT MENU: Hanning Window, Frequency Span 9.766 kHz (change with Time/Div knob and the knob next to SETUP button), and Move 0 Hz to left. Save this "frequency-domain" view of the signal as setup 2. Now you can view signals in the time-domain by recalling setup 1, and setup 2 will produce a frequency-domain view of the signal.

Please do the following exercises.

• Understand the effects of each setting in the FFT menu. See what happens if you change these settings to other values.
• Change the amplitude of the sine wave (try 50 mV and 200 mV). What happens to the FFT display? Does something unusual happen as the sine wave amplitude is increased further?
• Change the frequency of the sine wave (try 500 Hz, 2 kHz, and other values). What happens to the FFT display? Be sure that you can interpret the scale along the horizontal axis (in hertz).
• SUBMIT A SOLUTION FOR THE FOLLOWING:
  Determine how to convert the vertical axis of the FFT display to an amplitude in volts. The "Reference Level" of 10dBV is the RMS sine wave amplitude relative to a sine wave with 1 volt RMS amplitude, and this level is at the top of the oscilloscope display.
• Change the function generator to generate a square wave. View the square wave on the scope in both the time-domain (setup 1) and the frequency domain (setup 2). Can you relate the FFT of the square wave to our discussion of the Fourier series? What are the amplitudes of the various sine wave components?
• SUBMIT A SOLUTION FOR THE FOLLOWING:
  Verify that the amplitudes of the harmonics for the square wave decay at (1/n), where n is the harmonic number, as we derived in class.
• Look at the FFT for other signal shapes, such as triangle, ramp, noise, and "sinc". What is different about the FFTs of these signals? Can you relate the properties of the FFT to the shape of the signals in the time domain?
• Connect a microphone to the scope, and analyze the frequency content of speech, whistling, music, and any other signals that you would like. (If you had ENR 100 lab with me, then this should be familiar.)
• Use the FFT to determine the frequencies that are used in telephone touch-tones. The touch-tone signals are called dual-tone, multi-frequency (DTMF) signals. Can you see why this name is appropriate? You should be able to verify the following table.

  Frequency (Hz)	1209	1336	1477
  697	1	2	3
  770	4	5	6
  852	7	8	9
  941	*	0	#

The FFT is an important and useful tool to analyze the frequency content of signals. You should now be able to use the oscilloscope to perform the FFT operation.

2. Getting Started with the dSPACE Units

It is best to access this section of the notes on the Web at
http://www.eg.bucknell.edu/~kozick/elec32098/lab5.html
in order to easily follow some links to other pages.

The dSPACE boxes contain four analog-to-digital converters (ADCs), four digital-to-analog converters (DACs), and a digital signal processing (DSP) chip. The boxes allow us to write DSP programs that process real signals. The boxes can be programmed in two ways: through Simulink and through C programming. (You can also program them in assembly language!) This section will show you the steps required to program the dSPACE boxes using both methods. You can then use the dSPACE boxes to perform a project for this course. I will give you more details about the lab project next week.

Some projects that students completed in 1994 and 1995 for the Signals and Systems course are described at
http://www.eg.bucknell.edu/~kozick/ili/ili.html
Please browse through these links to get an overview of the dSPACE box and the types of projects that students have performed in the past.

In order to set up your Sun account so that it can access the software for the dSPACE boxes, please perform the following steps. Every student should perform these steps today, so that all accounts are set up to access the dSPACE boxes.

1. ** SKIP STEP 1 FOR TODAY **
   We need to use "tcsh" rather than "csh" as the shell so that UNIX commands can be executed from MATLAB. You can do this as follows.
   • Type the command:

     nispasswd -s

   • Then answer the prompt for "New shell:" as follows:

     /usr/local/bin/tcsh

2. Edit the file named .cshrc that is located in your home directory when you log in. Add the following line at the end of the .cshrc file, and then save the file:

   source /home/charcoal/local/dsp_cit/bin/dspace.sh

   Please type carefully and check your typing before saving the file. Note that there is a space after source, and an underscore in dsp_cit. Also, you must type Return at the end of this line.
3. Make a new directory citfiles under your home directory by typing:

   cd
   mkdir citfiles

4. Log out, and then log back in.
5. To verify that you can access the dSPACE software, type

   down31

   You should see an error message "Wrong number of arguments ...".

2.1. Programming with Simulink

The easiest way to program the dSPACE boxes is through Simulink. However, we need to upgrade the software for the dSPACE boxes in order for them to work with the latest version of Simulink that is running on the Suns. If and when this software is upgraded, I will provide instructions to you.

As an example of what you can do with Simulink and the dSPACE boxes, the following block diagrams implement a low-pass filter with a cutoff frequency that can be varied in real-time from the computer.

More advanced activities which I will show you later for your projects (if needed):

• It is possible to transfer sampled data to the Suns using a tool called trace31. A detailed description is available at the dSPACE Instructions Link. For example, you might want to sample speech, music, or other signals with the dSPACE box, and then process the samples on the Sun with MATLAB.

2.2. Programming with C

Important: The first time that you use the dSPACE box, save the file dspace.ini in the directory citfiles in your account.

An example C program is provided at lab1.c. Download this program to your directory, and look at the code. Ask for an explanation of the code, and then run the program on a dSPACE box, following the steps described at dSPACE Instructions.

Input a sine wave signal to the dSPACE box and view the output on an oscilloscope.

• Verify that the signal is sampled at the rate specified in the C program.
• View the input and output signals on an oscilloscope for a sine wave input. Can you see the effects of the ADC and DAC? What happens to the output sine wave when the input sine wave frequency gets "too high"?
• Modify the program in two ways: (1) output a value that is the average of the current and previous samples, and (2) output a value that is the difference between the current and previous samples. (These can be two separate programs, or you can output one result on DAC channel 1 and the other result on DAC channel 2.) Try processing sine waves, square waves, speech, or other signals. How would you describe the operation of these two programs? Are they performing some type of filtering? What is the difference equation that relates the output values y[n] to the input values x[n]?
  You have just implemented a real-time digital filter!
• You can perform processing that is more interesting than merely adding or subtracting adjacent samples. The "other things" that you can do are referred to as digital signal processing (DSP) algorithms. Many interesting projects of this type are possible.

Thank you.