October 2015
Beginner
551 pages
17h 46m
English
Content preview from A Computational Introduction to Digital Image Processing, 2nd Edition
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Appendix C
The Fast Fourier Transform
We have discussed the Fourier transform and its uses in Chapter 7. However, as we know,
the Fourier transform gains much of its usefulness by the existence of a fast algorithm to
compute it. We look briefly at one version of the fast Fourier transform here. More details
can be found in [13] or [54].
To start, we shall look at the very simple DFT for a two-element vector, where for
convenience we shall omit the scaling factor:
X
0
X
1
=
1 1
1 −1
x
0
x
1
=
x
0
+ x
1
x
0
− x
1
.
We can express this combination with a “butterfly diagram” as shown in Figure C.1. We
x
1
X
1
x
0
X
0
−1
FIGURE C.1: A butterfly diagram
shall see how this butterfly ...
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