This preview shows pages 1–2. Sign up to view the full content.
ECE220
Signals and Information
Spring 2008
Homework 7: Due Monday, April 7,
at 10:08pm
Drop your homework in the collection box marked
”ECE220 Spring 2008, homework”
, located
on the second foor oF Phillips at the south entrance to 219 Phillips.
Print your
name, NetId, and lab section
in the top right corner on all pages.
NOTE: This homework is based on lectures 2066 and Chapter 12 in the textbook.
Problem 1
Consider the system in ±igure 1.
LTI system
H(j
ω
)
x(t)
w(t)
y(t)
m(t)
±igure 1.
Assume that the input signal
x
(
t
) has a bandlimited ±ourier transForm
X
(
jω
) as graphed in
±igure 2.
X(j
ω
)
5π
10π
15π
5π
10π
15π
ω
±igure 2.
(a)
The signal
w
(
t
) is de²ned by
w
(
t
) =
x
(
t
) cos(5
πt
), that is
m
(
t
) = cos(5
πt
). Make a sketch
oF the ±ourier transForm
W
(
jω
) oF
w
(
t
).
(b)
The Frequency response oF the LTI ²lter in ±igure 1 is
H
(
jω
) =
b
1

ω

<
5
π
0

ω

>
5
π
Plot the ±ourier transForm
Y
(
jω
) oF the output
y
(
t
).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '05
 JOHNSON

Click to edit the document details