Digital Signal Processing Reference
In-Depth Information
Input
Output
s[n]
y[n]
+
a
1
D
Figure 2.26:
A simple recursive filter structure having a summing junction and a single feedback stage
comprised of a one-sample delay element and a scaler.
I
n
O
t
b
0
x[n]
+
+
y[n]
b
1
a
1
D
b
M
a
M
D
Figure 2.27:
A generalized
M
-th order digital filter utilizing both recursive and nonrecursive computa-
tion.
2.5.7 DIFFERENCE EQUATIONS
LTI systems can also be represented by a constant-coefficient equation that permits sequential computa-
tion of the system's output. If
x
[
n
]
represents an input sequence and
y
[
n
]
represents the output sequence
of the system, an FIR can be represented by the difference equation
M
y
[
n
]=
b
m
x
[
n
−
m
]
m
=
0
Example 2.11.
Compute the response to the sequence
x
[
n
]
=
ones(
1
,
4
)
of the FIR represented by the
difference equation given below (assume that
x
[
n
]
= 0 for
n<
0).
