FFT Lab

In this lab you will use the freeware program Audacity to sample a sound source and do a Fast Fourier Transform (FFT) spectrum and also a spectrogram of a sound sample. Bring a musical instrument to class (or you will have to sing).

Directions:

1. Audacity is installed in all the computers in PS100.
2. Plug the microphone into the computer, log in and turn the microphone on.
3. Play an instrument and record a few seconds of sound: Click on the red circle at the top to start taking data; Yellow square to stop. Try to make this a constant pitch of constant volume for this part.
4. Select an interesting portion of the graph by dragging the cursor over it (it will be shaded). Use the magnifying glass button to zoom in until you can see the waveform. Sketch or print the waveform. Does it look like a sine wave? Or some other kind of wave? Compare with your neighbors.
5. Now choose ‘Plot Spectrum’ from the Analyze menu (the data must be selected to use this option). The graph is the Fourier Spectrum of the data. Use the cursor to find the frequency of the first 5 or 6 peaks in the graph. Write down these frequencies and the approximate amplitude (in dB) of each.
6. Compare with your neighbors or with different instruments (try to compare instruments playing the same note for at least three different instruments, use your voice if you don't have three instruments). How is the Fourier spectrum different from those of other instruments, even when they are playing the same note?
7. Choose “enhanced autocorrelation” instead of “spectrum”. The autocorrelation looks for the strongest signals in the data. What do are the strongest frequencies in your sample? Are these the same as the highest peaks when you choose “spectrum”?
8. Set the program back to “spectrum” and change the numbers in the next selection (it should have 512 to start with). How do different choices affect the spectrum?
9. The number you just changed is the number of samples per second used to do the Fourier analysis. Why do you get different pictures for different data sampling? What would happen to the Fourier spectrum if the choosen sample rate was slower than the frequency of the sound source?
10. Go back to a sample rate of 512 and view the spectrum for different windows. What do the various choices of windows do to the graph? Wikipedia the names of these different windows to see what they are and explain them in your report.
11. Close the spectrum window, use the magnifying glass with the minus sign to zoom out until you see the whole sample. Select the whole sample with the cursor. Click on ‘audio track’ (on the left) and select ‘spectrum’ from the menu. This is a wavelet transform or spectrograph of the data. Notice that it plots frequency along the y-axis and time along the x-axis. How does this graph compare to a Fourier spectrum?
12. If the pitch did not change during the sample, take another sound sample with a changing pitch. The spectrogram will now have lines that go up or down. Describe this spectrogram and state how it relates to the sound you heard.

Other Questions:

• What is a Fourier series?
• What are harmonics? How are they different from overtones?
• Suppose you have the FFT from two different sources playing the same note in front of you.
• What would be the same and what would be different between the two spectra?
• How would you change the first one to sound like the second one?
• If you had a device which could replicate all the frequencies of the FFT spectra for the first instrument in the amounts proportional to those on the graph, what would it sound like?
• Explain why we only examined the sine and cosine solutions to the wave equation in class. Why didn't we worry about more complicated waves such as square waves or triangle waves?