July 2010
Intermediate to advanced
576 pages
17h 29m
English
Content preview from Microscope Image Processing
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Another solution, known as conjugate quadrature filters (CQFs) [10], is
H
1
(z) ¼ z
1
H
0
(z
1
)
G
0
(z) ¼ H
0
(z
1
)
G
1
(z) ¼ H
1
(z
1
) ¼ zH
0
(z)
(7:53)
which implements the orthogonal FIR filters. Again, using Eq. 7.53, the alias
term, Eq. 7.50, becomes zero, and the distortion term, Eq. 7.49, becomes
H
0
(z)H
0
(z
1
) þ H
0
(z)H
0
(z
1
) ¼ 2z
l
(7:54)
Since the filters have real values, using H(e
jv
) ¼ H(e
jv
), Eq. 7.54 can be
written as
H
0
(e
jv
)
2
þ H
0
(e
jv
)
2
¼ H
0
(v)
2
þ H
0
(v þ p)
2
¼ 2(7:55)
In this case, there do exist filters h
0
(n) that satisfy Eq. 7.55, and thus perfect
reconstruction can be realized using two-channel filter banks. It is apparent
from Eq. 7.53 that h
1
(n) ¼ (1)
n
h
0
(1 n), since H(z
1
) implies time reversal
h(n), while H(z) implies sign alternation ...
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