Image Processing Reference
In-Depth Information
e j π /2
1
2 ,(b)
Fig. 21. DF operations: (a) Real HBF prototype centrosymmetric about H 0 (
)=
Two selected DF filter functions, (c,d) Spectra of decimated DF output signals
by (38), o
defined by (9). According to (39),
highest efficiency is obtained by additionally introducing a suitable complex scaling factor of
unity magnitude:
∈{
0, 1, 2, 3
}
, with the RHBF impulse response h
(
k
)
e j a 4 h
e j 4 [ k ( 2 o + 1 )+ a ] =
1
2
a
2 ,
z o =
j k ( o +
)+
h k , o , a =
(
k
)
h
(
k
)
h
(
k
)
(39)
N
1
N
1
where
. By directly equating (39), and relating the result
to (9) with a suitable choice of the constant a
k
and o
∈{
0, 1, 2, 3
}
2
2
=
2 o
+
1 compliant with (29), we get :
2 j o +
1
2
k
=
0
h k , o =
0
k
=
2 l
l
=
1,...,
(
N
3
)
/4
(40)
j ( k + 1 )( o +
1
2
) h k k
=
2 l
1 l
=
1,...,
(
N
+
1
)
/4
with the symmetry property:
j ( 2 o + 1 ) k h k , o
h
=
k
>
0,
o
∈{
0, 1, 2, 3
}
.
(41)
k , o
The respective COHBF centre coefficient
) 4 ]+
) 4 ] }
1
2 {
h 0, o =
[(
+
[(
+
∈{
}
cos
2 o
1
jsin
2 o
1
, o
0, 1, 2, 3
,
(42)
Search WWH ::




Custom Search