ECE 301, Homework #3, due date: 2/3/2010
http://cobweb.ecn.purdue.edu/
∼
chihw/10ECE301S/10ECE301S.html
Question 1:
Consider two functions
f
(
t
) and
g
(
t
) described as follows.
f
(
t
) =
(
1
if

1
≤
t <
1
0
otherwise
(1)
g
(
t
) =
(
cos(
πt
)
if
t <
3
0
otherwise
.
(2)
Define a new function
h
(
t
) =
R
∞
∞
f
(
s
)
g
(
t

s
)
ds
. Plot
h
(
t
) as a function of
t
.
Question 2:
Following the previous question, what are the “total energies” of the three
signals
f
(
t
),
g
(
t
), and
h
(
t
)? Are they of finite energies? What are the “(overall) average
powers” of
f
(
t
) and
h
(
t
)? Are
f
(
t
) and
h
(
t
) of finite powers?
Question 3:
Let
x
1
(
t
) =
e

1

2
jt
,
x
2
(
t
) = cos(
t
+
π/
4), and
x
3
(
t
) =
e

t

1

. Find the total
energy and the average power of
x
1
(
t
),
x
2
(
t
), and
x
3
(
t
).
Question 4:
p. 59, Problem 1.21 (e) and (f), and p. 59, Problem 1.22 (f) and (h).
Question 5:
p. 61, Problem 1.25 (e) and (f).
Question 6:
p. 61, Problem 1.26 (a,c,e)
Question 7:
Write down the expression of the continuoustime harmonically related
complex (HRCE) for a given fundamental frequency
ω
=
2
π
5
.
How many distinct CT
HRCEs do we have? What is the common period of all HRCEs?
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 Spring '06
 V."Ragu"Balakrishnan
 following discretetime signals, common period

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