ECE220
Signals and Information
Spring 2008
Homework 5: Due Monday, March 10,
at 10:08am
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 1216 and Chapters 9 and 10 in the textbook.
Problem 1
Consider narrow pulses
δ
Δ
(
t
) and
δ
Δ
(2
t
) depicted in ±igure 1.
δ
∆
(2
t
29
2∆
1
t
∆
2
∆
2
δ
∆
(
t
29
∆
2∆
1
t
∆
±igure 1.
We argued inFormaly in class that
lim
Δ
→
0
δ
Δ
(
t
) =
δ
(
t
)
(a)
What is lim
Δ
→
0
δ
Δ
(2
t
)?
(b)
What is lim
Δ
→
0
δ
Δ
(
αt
) For
α
n
= 0?
Problem 2
Consider the Function
x
(
t
) =
e

2
t
u
(
t
−
3). On the same graph plot Functions
(a)
x
(
−
t
)
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x
(2
−
t
)
(c)
x
(
T
−
t
) where
T
is some nonzero number.
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 Spring '05
 JOHNSON
 Digital Signal Processing, LTI system theory, Impulse response, Consider narrow pulses

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