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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
5.3 Fourier, Hadamard, and Cosine Transform Compression
155
The discrete cosine transform may be implemented by using a double
sized fast Fourier algorithm. To show this, consider the one-dimensional
transform in (134). We first zero-pad the data to make it IN elements long:
f
p
(m)=f(ml
m = 0, 1,..., Ν - 1
= 0, m = Ν, Ν +
1,...,2N
- 1 (140)
We can rewrite (134) as
F(u) = ψ Rejexp(; ^) f
p
(m) exp^m ^)},
u = 0, Ι,.,.,Λί - 1 (141)
The summation is clearly a 2N-element discrete Fourier transform, which
may be implented with an FFT algorithm.
As was shown recently by Chen et al. [10], it is also possible to directly
write a fast algorithm for the
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Publisher Resources

ISBN: 9780323139915