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Digital Picture Processing, 2nd Edition
book

Digital Picture Processing, 2nd Edition

by Azriel Rosenfeld, Avinash C. Kak
January 2014
Intermediate to advanced content levelIntermediate to advanced
435 pages
18h 42m
English
Morgan Kaufmann
Content preview from Digital Picture Processing, 2nd Edition
2.2
Discrete
Picture
Transforms
25
where the last equality
is
obtained
by
making use
of
the orthogonality relation-
ship (39). This proves that
the
discrete Fourier transform
of [#] in (43) is
[F]
χ
[D].
§
One can similarly show that the discrete Fourier transform of the
"circular" convolution
of
two
Μ χ Ν
arrays
in the
frequency domain
is
equal
to
the
product
of the
inverse transforms
of the two
arrays. That
is, if we
construct
the
following circular convolution
in the
frequency domain:
M-l
N-1 M-L N-1
G(u,v)
= Χ Σ
F(w,z)D(u-w,v-z)
= £ £
F(u-w,v-z)D(w,z)
w = 0 ζ = 0 w = 0 z = 0
for
u =
0,1,2,
...,M— 1, ν =
0,1,2,
...,N— 1,
then
its
inverse discret ...
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Publisher Resources

ISBN: 9780323139915