ECE 2200: Section IX Problems
(Week 10 / Spring 2009)
Note: In this section, we have ﬁve problems. Majority of the problems are taken
from the ”Signal Processing First CD”, but
they may have been slightly changed
or may have some extra parts
. Please read this handout carefully. Answers to all
of the problems will be provided.
1. Use linearity and timeinvariance to convolve the following two rectangular pulses:
x
(
t
) = 2
u
(
t
)

2
u
(
t

2)
h
(
t
) = 3
u
(
t

5)

3
u
(
t

1)
.
(a) Expand the convolution
y
(
t
) =
x
(
t
)
*
h
(
t
) into four terms and exploit the result
from Example 9

9 from McClellan, Schafer and Yoder,
Signal Processing
First
textbook to get
y
(
t
).
(b) Write the answer for
y
(
t
) as separate cases over ﬁve diﬀerent regions.
(c) Plot
x
(
t
) versus
t
, and
y
(
t
) versus
t
.
2. Signal Processing First CD: ”Chapter 9/Homework/Evaluating a Convolution In
tegral”
A linear timeinvariant system has impulse response:
h
(
t
) =
(
e

2
t

1
≤
t
≤
1
0
otherwise
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 Spring '05
 JOHNSON
 Digital Signal Processing, Signal Processing, LTI system theory, Impulse response

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