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Spring 2009
EE 341
Lab 4: The FFT and Digital Filtering
Due: In your discussion section June 25
When using a digital computer, frequency analysis means using a Fast Fourier Transform
(FFT). This necessitates we spend some time becoming familiar with using the FFT to study
the frequency content of a discretetime signal.
1.
MATLAB function FFT
In this problem you will learn how to use the MATLAB command
fft
. First, use the
help
feature in MATLAB to learn the syntax of the
fft
function. The FFT function computes the
Discrete Fourier Transform (DFT) of a sequence. In general the FFT of a sequence will be a
complex function so you will need to look at the magnitude and phase separately. The
MATLAB commands
abs
and
angle
are useful for obtaining the magnitude and phase of a
complex valued sequence. Also, since the FFT only has values at discrete frequencies, it may
be useful to do the plots with
stem
to reinforce that idea, but continuous frequency plots (i.e.
using
plot
) are often used since they are closer to the DTFT that you are ultimately
interested in.
The FFT outputs a sequence that corresponds to the range
π
2
0
≤
Ω
≤
, where
is the
discrete frequency (or
Ω
1
0
≤
≤
f
for normalized discrete frequency
f
;
2
/
Ω
=
f
). You are
probably more familiar with seeing the spectrum plotted over the range
≤
Ω
≤
−
(or
5
.
0
5
.
0
≤
≤
−
f
). The
fftshift
function can be used for this purpose.
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 Fall '09
 Chizeck
 Frequency

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