Databases Reference
In-Depth Information
T A B L E 16 . 1
Filter coefficients for the
reversible transform.
Low-Pass Filter
k
h
k
3
4
0
1
4
±
1
1
8
±
2
−
High-Pass Filter
k
h
k
0
1
1
2
±
1
−
T A B L E 16 . 2
Filter coefficients for the 9/7
ireversible transform.
Low-Pass Filter
k
h
k
0
0
.
602949018236
±
1
0
.
266864118443
±
2
−
0
.
078223266529
±
3
−
0
.
016864118443
±
4
0
.
026748757411
High-pass filter
k
h
k
0
0
.
557543526229
±
1
−
0
.
29635881557
±
2
−
0
.
028771763114
±
3
0
.
045635881557
contains three nonzero coefficients. Because of this the filter is also referred to as the (5,3)
filter. The coefficients are given in Table
16.1
. Notice that the filters are symmetric, which
means they have linear phase. This in turn means that we can use them without any coefficient
expansion. This filter can be implemented using lifting. The lifting procedure consists of one
prediction and one update step. Using the terminology of the previous chapter, these are given
by
x
2
k
+
x
2
k
+
2
2
d
k
=
x
2
k
+
1
−
and
d
k
−
1
+
d
k
+
2
s
k
=
x
2
k
+
2
+
4
The irreversible wavelet transform is the CDF(4,4) transform described in the previous
chapter. We have already given the lifting implementation of this wavelet. The corresponding
filters are given in Table
16.2
. The filter again is symmetric and because the analysis filters
contain nine and seven coefficients it is known as the 9/7 transform.
