Digital Signal Processing Reference
In-Depth Information
2.46
Find the total response
y(n)
of the LTI-DT system defined by the fol-
lowing difference equation
(
0
.
5
)
n
u(n)
y(n)
+
0
.
25
y(n
−
1
)
+
y(n
−
2
)
=
where
y(
−
1
)
=
1and
y(
−
2
)
=−
1
2.47
Find the total response
y(n)
for the LTI system given by
y(n)
+
1
.
4
y(n
−
1
)
+
0
.
44
y(n
−
2
)
=
0
.
5
δ(n
−
2
)
,where
y(
−
1
)
=
1and
y(
−
2
)
=
0
.
5
are the initial states.
2.48
Repeat Problem 2.47 for the system described by the difference equation
y(n)
+
0
.
5
y(n
−
1
)
+
0
.
04
y(n
−
2
)
=
x(n)
where
y(
−
1
)
=
0
,y(
−
2
)
=
0, and
x(n)
={
1
.
0
↑
0
.
5
−
1
.
0
}
.
2.49
Solve the following difference equation for
y(n), n
≥
0
y(n)
+
0
.
6
y(n
−
1
)
−
0
.
4
y(n
−
2
)
=
2
x(n
−
2
)
(
0
.
1
)
n
u(n)
.
where
y(
−
1
)
=
1
,y(
−
2
)
=
0
.
5, and
x(n)
=
2.50
Given an LTI, discrete-time system described by the difference equation
y(n)
+
0
.
4
y(n
−
1
)
+
0
.
04
y(n
−
2
)
=
x(n)
−
0
.
5
x(n
−
1
)
(e
−
0
.
1
n
)u(n)
, find its unit pulse
where
y(
−
1
)
=
2
,y(
−
2
)
=
2, and
x(n)
=
response
h(n)
.
2.51
The difference equation describing an LTI discrete-time system is given
below. Solve for
y(n)
y(n)
+
0
.
4
y(n
−
1
)
+
0
.
03
y(n
−
2
)
=
x(n
−
2
)
(
0
.
5
)
n
u(n)
.
where
y(
−
1
)
=
1,
y(
−
2
)
=
1, and
x(n)
=
2.52
Find the total response
y(n)
of the discrete-time system described by the
following difference equation
y(n)
−
0
.
3
y(n
−
1
)
+
0
.
02
y(n
−
2
)
=
x(n)
−
0
.
1
x(n
−
1
)
0
.
2
)
n
u(n)
.
where
y(
−
1
)
=
0,
y(
−
2
)
=
0, and
x(n)
=
(
−
2.53
Repeat Problem 2.52, assuming that the system is described by the dif-
ference equation
y(n)
−
0
.
04
y(n
−
2
)
=
x(n
−
1
)
(
0
.
2
)
n
u(n)
.
where
y(
−
1
)
=−
0
.
2
,y(
−
2
)
=
1
.
0, and
x(n)
=
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