Digital Signal Processing Reference
In-Depth Information
Response filter. Figure 2.25 shows a typical example, having an arbitrary number of
M
delay stages, each
denoted by the letter
D
. The cascaded delay stages act like a bucket brigade, transporting each sample, as
it enters from the left, one delay stage at a time to the right. As shown, a sample sequence
s
[
]
is passing
through the filter. The output of each delay stage is scaled by a multiplier according to the coefficients
b
i
,
and all products summed yield the output. Any number of delay stages may be used, as few as one stage
being possible. The larger the number of delay stages and multipliers, the greater can be the frequency
selectivity.
The output of an FIR is, in general, computed using convolution. The manner of determining
what an FIR's coefficients
b
i
should be to achieve a certain signal processing purpose is the subject of
FIR design, which is covered extensively in Volume III of the series (see Chapter 1 of this volume for
information on the contents of Volume III).
n
Input
s
s
V>Qí0@
D
D
D
b
1
b
0
b
0
+
\>Q@
Figure 2.25:
A generalized finite impulse response (FIR) filter structure. Note that the filter has
M
delay
stages (each marked with the letter
D
) and
M
+
1 coefficient multipliers.
The IIR
The second type of basic digital filter is the
Infinite Impulse Response (IIR)
filter, which produces
output samples based on the current and possibly previous input samples and previous values of its own
output. This feedback process is usually referred to as a
Recursive Process
,or
Recursion
, and produces,
in general, a unit impulse response which is infinite in extent. When the impulse response decays away
to zero over time, the filter is stable. Figure 2.26 shows the simplest possible such filter, having one stage
of delay and feedback.
A more generalized type of filter using the IIR and FIR in combination is the
M
-th order section,
shown in Fig. 2.27.
Design of IIRs will be covered extensively in Volume III of this series (see Chapter 1 of this volume
for a description of the contents of Volume III).
