Digital Signal Processing Reference
In-Depth Information
x
[
n
]
y
[
n
]
1/
a
0
b
0
D
D
1
1
a
1
b
1
D
D
2
2
a
2
b
2
(a)
x
[
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y
[
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]
1/
a
0
b
0
D
a
1
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1
D
a
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b
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Figure 10.15
Direct form II realization of
a second-order system.
(b)
with Using the procedure illustrated with the second-order systems, we con-
struct the block diagrams for the direct form I and the direct form II. The block dia-
grams are given in Figures 10.16 and 10.17, for
a
0
Z 0.
M = N.
For
M Z N,
the appropriate
coefficients in the figures are set to zero.
EXAMPLE 10.13
A low-pass digital filter
We consider again the of Example 9.8, Section 9.5. Two applications of this filter are
in radar-signal processing and in automatic aircraft-landing systems. The purpose of the filter
is to remove high-frequency noise from the input signal, while passing the lower-frequency
information in that signal. The filter equation is given by
a-filter
y[n] - (1 - a)y[n - 1] = ax[n].
