Image Processing Reference
In-Depth Information
Fig. 17. Optimum SFG of linear-phase FIR COHBF decimating by two
R C
C R
C C
C C
Dec:
Int:
Dec:
Int:
+
n mc
n
n
2
N M
(
n
+
6
)
/4
(
n
+
6
)
/2
N A
n /2
+
1
n
+
4
n
+
2
+
+
+
N Op
3 n /4
5/2
3 n /2
7
3 n /2
5
Table 5. Expenditure of linear-phase FIR COHBF; n :order, n mc : McMillan degree, N M (
N A )
:
number of multipliers (adders), operational clock frequency: f Op =
f n /2
operations over that of a classical HT (CHBF), respectively (cf. Figs. 12 and 13). This is due
to the fact that, as a result of the transition from CHBF to COHBF, only the centre coefficient
changes from trivially real ( h 0 =
j
2 2 ) calling for only one extra
multiplication. The number n mc of delays is, however, of the order of n , since a (nearly) full
delay line is needed both for the real and imaginary parts of the respective signals. Note that
the shimming delays are always included in the delay count. (The number of delays required
for a monorate COHBF corresponding to Fig. 17 is 2 n .)
1
+
1
2 ) to simple complex ( h 0 =
2.3.2 Minimum-Phase (MP) IIR filters
In the IIR COHBF case the frequency shift operation (3) is again applied in the z -domain. This
is achieved by substituting the complex z -domain variable in the respective transfer functions
H
(
)
z
and all corresponding SFG according to:
z
z 1 =
z 1
j
2 .
ze j 4
z :
=
=
(34)
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