Digital Signal Processing Reference
In-Depth Information
x
(
t
)
w
(
t
)
w
(
t
)
y
(
t
)
b
2
1/
a
2
x
(
1)
(
t
)
y
(
1)
(
t
)
b
1
a
1
x
(
2)
(
t
)
y
(
2)
(
t
)
b
0
a
0
(a)
(b)
x
(
t
)
w
(
t
)
y
(
t
)
b
2
1/
a
2
x
(
1)
(
t
)
y
(
1)
(
t
)
b
1
a
1
x
(
2)
(
t
)
y
(
2)
(
t
)
b
0
a
0
(c)
Figure 3.26
Direct form I realization of a second-order system.
To derive an integrator form of the simulation diagram, each side is integrated
n
times, resulting in the equation
n
m
a
k
y
(k-n)
(t) =
a
b
k
x
(k-n)
(t).
a
k= 0
k= 0
Solving this equation for
y(t)
yields
m
n- 1
1
a
n
B
R
y(t) =
b
x
x
(k-n)
(t) -
a
a
k
y
(k-n)
(t)
.
(3.84)
a
k= 0
k= 0
