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EE 200 – Fall 2009 (Weber)
Homework 3
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Date
EE 200, Homework #
Show intermediate steps whenever possible.
1.
For each of the following systems deﬁned below, indicate whether the sytem is linear, time invariant,
both, or neither. You don’t have to show any proof of your answer, just indicate what type of system it
is.
a.
y
[
n
] =
cos
(2
πn
)
x
[
n
]
e.
y
[
n
] =
x
[
n
] + 0
.
7
y
[
n

1]
b.
y
[
n
] =
cos
(2
πn/
7)
x
[
n
]
f.
y
[
n
] =
x
[
n
] + 0
.
3(
x
[
n

1])
2
c.
y
[
n
] =
cos
(2
πn/
7)(
x
[
n
] +
x
[
n

1])
g.
y
[
n
] = 5
x
[
n
] + 2
d.
y
[
n
] =
x
[
n
] + 0
.
7
x
[
n

1]
h.
y
[
n
] =

x
[
n
]

2.
A sampled signal is given by
x
[
n
] = 4 cos(0
.
3
πn

π/
4)
Find three continuoustime signals,
x
1
(
t
),
x
2
(
t
) and
x
3
(
t
) of the form
x
(
t
) =
A
cos(2
πft
+
φ
) that when
sampled at a sampling rate of
f
s
= 1000 samples/sec. would each give this result. The frequencies of
x
1
(
t
),
x
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 '08
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