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dual wavelet functions. Hence the scaling and wavelet functions and their
respective dual are given by
φ
(
t
)=
k
h
[
k
]
√
2
φ
(2
t
−
k
)
,
(8.43)
φ
(
t
)=
k
h
[
k
]
√
2
φ
(2
t
−
k
)
,
(8.44)
with
h
[
k
]=
k
h
[
k
]
,
=
√
2
.
k
And,
ψ
(
t
)=
k
g
[
k
]
√
2
φ
(2
t
−
k
)
,
=
k
k
]
√
2
φ
(2
t
(8.45)
1)
k
h
[1
(
−
−
−
k
)
.
Its dual is
ψ
(
t
)=
k
g
[
k
]
√
2
φ
(2
t
−
k
)
,
=
k
k
]
√
2
φ
(2
t
(8.46)
1)
k
h
[1
−
−
−
k
)
.
(
We list below the filter coecients for some members of the Cohen-Daubechies-
Feauveau (CDF) family of biorthogonal spline wavelets. It is easy to observe
from Table 8.2 that they are symmetric.
Table 8.2.
Coecients for some members of Cohen-Daubechies-Feauveau family of
biorthogonal spline wavelets [14].
h/
√
2
h/
√
2
1/2,1/2
-1/16,1/16,1/2,1/16,-1/16
1/4,1/2,1/4
-1/8,1/4,3/4,1/4,-1/8
1/8,3/8,3/8,1/8
−
5
/
512
,
15
/
512
,
19
/
512
, −
97
/
512
, −
13
/
256
,
175
,
256
, ···
8.8 Concluding Remarks
Spline wavelets have been discussed in a simple way so that one can get some
idea about them without any di
culty. A brief background for wavelets may
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