Biomedical Engineering Reference
In-Depth Information
11.2.2 Infinite Impulse Response (IIR) Digital Filters
The Pole-zero transfer function of an
L
th
-
order direct form Infinite Impulse Response
Filter (IIR-filter) has the
z
-transform transfer function described by (11.11).
b
−1
b
−
L
B
(
z
)
A
(
z
)
=
b
o
+
+···+
1
Z
LZ
H
(
z
)
=
(11.11)
a
−1
a
−
L
1
+
+···+
1
Z
LZ
where the
z
s are the “
z
-transformation.”
General characteristics of the infinite impulse response filters are as follows:
a.
Very sharp cutoff
b.
Narrow transition band
c.
Low-order structure
d.
Low-processing time
There are several designs that can be used to implement (11.11), such as the direct, paral-
lel, or cascade design. The “Direct” design is shown in Fig. 11.10, whereas a “Symmetric
Lattice” of the IIR design is shown in Fig. 11.11.
x
k—
1
x
k—
2
x
k—L
x
k
z
-1
z
-1
z
-1
b
0
b
1
b
L—
1
b
L
+
+
+
+
+
y
k
+
+
-
-
-
a
L
a
L—
1
a
1
y
k—L
y
k—
1
z
-1
z
-1
z
-1
FIGURE 11.10
:
Direct-form IIR digital filter. Note the numerator coefficients are the
b
L
terms
and the denominator coefficients are the
a
L
terms
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