Image Processing Reference
In-Depth Information
Fig. 6. Polyphase representation of a decimator (a,b) and an interpolator (c) for sample rate
alteration by two; shimming delay:
z
−
1/2
d
z
−
1
:
=
=
Fig. 7. Optimum SFG of LP FIR HBF decimator (a) and interpolator (b) of order
n
10
=
=
=
MoR:
f
Op
f
n
Dec:
f
Op
f
n
/2 Int:
f
Op
f
n
/2
+
n
mc
n
n
/2
1
N
M
(
n
+
2
)
/4
+
N
A
n
/2
1
n
/2
+
+
N
Op
3
n
/4
3/2
3
n
/4
1/2
Table 1. Expenditure of real linear-phase FIR HBF;
n
:order,
n
mc
: McMillan degree,
N
M
(
N
A
)
:
number of multipliers (adders),
f
Op
: operational clock frequency
concurrently
exploited. (Note that this concurrent exploitation of coefficient symmetry
and
minimum memory property is not possible for Nyquist(
M
)filters with
M
>
2. As shown in
[Göckler & Groth (2004)], for Nyquist(
M
)filters with
M
>
2only
either
coefficient symmetry
or
the minimum memory property can be exploited.)
The application of the multirate transposition rules on the optimum decimator according to
Fig. 7(a), as detailed in Section 3 and [Göckler & Groth (2004)], yields the optimum LP FIR
HBF interpolator, as depicted in Fig. 6(c) and Fig. 7(b), respectively. Table 1 shows that the
interpolator obtained by transposition requires less memory than that published in [Bellanger
(1989); Bellanger et al. (1974)].