Biomedical Engineering Reference
In-Depth Information
y
(
n
)
+
+
+
h
(0)
h
(2)
h
(1)
h
(
N
1)
−
x
(
n
)
z
−
1
FIGURE 2.17
A direct FIR filter configuration.
2.6.3.1
Direct FIR Filter
This filter configuration (Figure 2.17) is very similar to the IIR system and
has the difference equation
M
y
(
n
)=
h
(
j
)
x
(
n
−
j
)
(2.148)
j
=0
where
h
(
j
) is the impulse response for a given input
x
(
n
) and output
y
(
n
).
2.6.3.2
Cascaded FIR Filter
This system can be obtained if the transfer function is factored into
L-subsystems, each subsystem may be a first- or second-ordered system. The
cascaded FIR filter in Figure 2.18 has the following transfer function:
H
(
z
)=
1
2
z
−
1
1
3
z
−
1
+
z
−
2
1
2
−
−
(2.149)
FIR filters are sometimes preferred over the IIR types due to their stability
and ease of implementation, FIR filters also possess linear-phase character-
istics where the impulse response
h
(
n
) is symmetric about the length of the
response. This means that
h
(
n
)=
h
(
N
n
), where
N
represents the total
number of sequences or the length of the response. Unfortunately, FIR filters
require long sequences to implement sharper cutoffs in the attenuation region.
In the next section, we examine two methods for FIR filter design.
−
1
−
2.6.4 Design of FIR Digital Filters
There are several well-known methods for designing FIR filters such as win-
dow, frequency sampling, minmax, and optimal design techniques. We will
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