Digital Signal Processing Reference
In-Depth Information
x
[
n
]
w
[
n
]
w
[
n
]
y
[
n
]
b
0
1/
a
0
D
D
x
[
n
1]
y
[
n
1]
b
1
a
1
D
D
x
[
n
2]
y
[
n
2]
b
2
a
2
(a)
(b)
x
[
n
]
w
[
n
]
y
[
n
]
b
0
1/
a
0
D
D
x
[
n
1]
y
[
n
1]
b
1
a
1
D
D
x
[
n
1]
y
[
n
1]
b
2
a
2
(c)
Figure 10.14
Direct form I realization of a second-order system.
Consider now the
N
th-order difference equation
N
M
[eq(10.48)]
a
k
y[n - k] =
a
b
k
x[n - k].
a
k= 0
k= 0
Solving this equation for
y
[
n
] yields
M
N
1
a
0
B
R
y[n] =
b
k
x[n - k] -
a
a
k
y[n - k]
,
(10.68)
a
k= 0
k= 1
