Digital Signal Processing Reference
In-Depth Information
Figure 5.4
System diagram of general discrete-time system.
From this description, we can determine the transfer function
H
(
z
) to be
M
∑
−
k
a
⋅
z
k
Y
(
z
)
k
=
0
H
(
z
)
=
=
N
X
(
z
)
∑
−
k
1
−
b
⋅
z
k
k
=
1
(5.28)
We can represent (5.28) in a slightly different way to allow for further
development:
M
∑
−
k
a
⋅
z
k
Y
(
z
)
W
(
z
)
1
k
=
0
⋅
=
⋅
W
(
z
)
X
(
z
)
1
N
∑
−
k
1
−
b
⋅
z
k
k
=
1
(5.29)
This representation leads to two separate relationships, as shown below:
M
∑
=
−
k
Y
(
z
)
=
W
(
z
)
⋅
a
⋅
z
k
k
0
(5.30)
N
∑
=
−
k
W
(
z
)
=
X
(
z
)
+
W
(
z
)
⋅
b
⋅
z
k
k
1
(5.31)
