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 6 of the Kamen/Heck text.
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 given below. Make sure that you understand what these commands are doing - you will have some homework exercises next week 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? (The imzoom command is useful to zoom-in on a figure.) Do harmonics appear to be present? Can you guess what produced this sound?
Download the sound file chirp.au to your account, and read it into MATLAB with the commands:
x = auread('chirp.au');
The sampling rate for this data is 8192 samples per second. Listen to the sound, then view the FFT of the signal (with the frequency axis labeled in Hertz), and then view the spectrogram in MATLAB with the command:
specgram(x, 512, 8192, 256, 1);
(You may have to exit Netscape to properly view the colors in the spectrogram.)
What is different between the FFT results and the spectrogram results? Use the help command in Matlab for more details about the arguments to the specgram command. Try to relate the spectrogram to the sound that you hear.
The spectrogram is computed by performing the FFT on subsets of the data. The intent of this exercise is to show you an application of the FFT in signal analysis.