ELEC 320, Fall 2006
Profs. Wismer & Kozick
Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
The development of the FFT algorithm for computing the DFT
is one of the primary reasons that digital signal processing (DSP)
is so common today.
This lab provides a brief introduction to the DFT and FFT.
The DFT and FFT are discussed in Chapter 5 of the Lathi text.
What are the DFT and FFT?
The DFT provides the Fourier transform of sampled
Similar to the continuous-time Fourier transform that we will study
in class, the DFT describes the frequency content
of discrete-time signals.
The FFT is a fast way to compute the DFT:
the FFT and DFT produce identical results, but the FFT
requires less computation.
Further details about the DFT and FFT are available in notes
at the following link:
Notes on the DFT and FFT
Please download the sound file
hw1data.au to your directory from the Web page for this
Read the file into Matlab, listen to it, and take
the FFT with the commands:
x = auread('hw1data.au');
X = fft(x);
The sampling rate for this signal is 8192 samples per second.
You can plot the FFT magnitude versus Hertz with the MATLAB commands
Make sure that you understand what these commands are doing - you
will have some homework exercises to do in a few weeks that will use MATLAB
and the FFT.
Fs = 8192;
N = length(X);
f = (0:N-1)'/N*Fs;
Which frequency (in hertz) appears to be dominant?
Do harmonics appear to be present?
Can you guess what produced this sound?
Generate a periodic signal of pulses using the function
Try several (at least three) different frequencies and a several pulse
shapes (e.g., square, triangle, etc.).
- Observe the time signal on the oscilloscope.
Which frequency components do you expect to see in the
frequency spectrum of the signal?
- Use the FFT on the oscilloscope to observe the frequency spectrum
of the signal.
Does it agree with your prediction?
For the square wave, verify that the frequency spectrum contains
odd harmonics with amplitudes proportional to (1/n) for n=1, 3, 5,
- Use the Keithley A/D board to record digital samples of the
Do the same for a pulse signal with duty cycle 20%.
Be sure to choose the sampling rate larger than twice the highest
significant frequency component in the signal!
Use the FFT in Matlab to plot the spectrum of the signal.
Use subplot to put the time-domain and frequency-domain
graphs on the same figure.
Are the amplitudes of the harmonics correct relative to the
amplitude of the fundamental?
Print your plots, and identify the fundamental frequency,
the harmonics, and their relative amplitudes.
- Please submit answers to these questions before you leave lab
on November 8 or 13.
Continue to work on your design project during each of the lab
meetings on November 1, 6, 8, and 13.