Assignment #4
Tue 09/13/05
1(15).
Suppose the step
response of a discretetime, LTI system is
≤
<
≤
<
=
n
n
n
n
n
y
step
2
,
3
2
0
,
0
,
0
]
[
.
(a)
Sketch
]
[
n
y
step
.
(b)
Suppose the input to this system is
{
}
,...
0
...,
0
,
1
,
1
,
1
,
1
]
[
1
=
n
x
.
First, express
]
[
1
n
x
in terms of step
functions and then use the linearity and timeinvariance properties to express the output,
]
[
1
n
y
, in
terms of
]
[
n
y
, and sketch.
(c) Suppose the input is
{
}
,...
0
,
1
,
1
,
1
,
1
,
1
,
1
,
1
,
1
]
[
2




=
n
x
.
Express the output,
]
[
2
n
y
, in terms of
]
[
1
n
y
, and sketch.
2(20).
Suppose the impulse response of a discretetime, LTI system is
{
}
1
,
1
,
1
,
1
]
[
=
n
h
.
(a) Find (expressed in sequence form) and sketch the output
]
[
n
y
when the input is
{
}
1
,
1
,
1
,
1
]
[
=
n
x
.
(b)
Find (in sequence form) and sketch the output
]
[
1
n
y
when the input is
]
1
[
]
[
]
[
1


=
n
x
n
x
n
x
.
(c) Find (in sequence form) and sketch the output signal,