Image Processing Reference
In-Depth Information
Fig. 14. Decimating allpass-based minimum-phase IIR HT: (a) optimum block structure (b)
SFG of the 1st (2nd) order allpass sections
Fig. 15. Block structure of decimating minimum-phase IIR CHBF
Dec:
R
→
C
Int:
C
→
R
Dec:
C
→
C
Int:
C
→
C
n
mc
(
n
+
1
)
/2
n
+
1
(
−
)
−
N
M
n
1
/2
n
1
N
A
3
(
n
−
1
)
/2
3
(
n
−
1
)+
2
3
(
n
−
1
)
N
Op
2
n
−
2
4
n
−
2
4
n
−
4
Table 4. Expenditure of minimum-phase IIR CHBF;
n
:order,
n
mc
: McMillan degree,
N
M
(
N
A
)
: number of multipliers (adders), operational clock frequency:
f
Op
=
f
n
/2
doubling this structure, as depicted in Fig. 15, the IIR CHBF for decimating a complex signal
by two is obtained. Multirate transposition [Göckler & Groth (2004)] can again be applied to
derive the corresponding dual structures for interpolation.
The expenditure of the half- (
C
→
C
) CHBF decimators and
their transposes is listed in Table 4. A comparison of Tables 2 and 4 shows that, basically,
the half-complex IIR CHBF sample rate converters (cf. Fig. 14) require almost the same
expenditure as the real IIR HBF systems depicted in Fig. 9.
R
C
) and the full-complex (
2.2.3 Comparison of FIR and IIR CHBF
As it is obvious from the similarity of the corresponding expenditure tables of the previous
subsections, the expenditure chart Fig. 10 can likewise be used for the comparison of CHBF
