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EE 200 – Fall 2009 (Weber)
Homework 4
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Date
EE 200, Homework #
Show intermediate steps whenever possible.
1.
Three systems are connected in cascade: the output of
S
1
goes to the input of
S
2
, the output of
S
2
is
the input to
S
3
. The systems are speci±ed as follows.
S
1
:
y
1
[
n
] =
x
1
[
n
]

x
1
[
n

1]
S
2
:
y
2
[
n
] =
x
2
[
n
] +
x
2
[
n

2]
S
3
:
y
3
[
n
] =
x
3
[
n

1] +
x
3
[
n

2]
a.
What is the frequency response of the overall system,
S
, with input
x
[
n
] =
x
1
[
n
] and output
y
[
n
] =
y
3
[
n
]?
b.
Based on your result in part a, Write a di²erence equation similar to the ones above that describes
the system
S
in terms of
x
[
n
] and
y
[
n
].
2.
A system has an impulse response of
h
[
n
] =
δ
[
n
]

δ
[
n

3].
a.
What is the frequency response of the system?
b.
Determine the output of the system when the input is
x
[
n
] = cos(2
πn/
3)
c.
Determine the output of the system when the input is
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This note was uploaded on 02/26/2010 for the course EE 30446 at USC.
 '08
 ZADEH

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