This preview shows pages 1–2. Sign up to view the full content.
ECE 301, Homework #3, due date: 2/01/2012
https://engineering.purdue.edu/
∼
chihw/12ECE301S/12ECE301S.html
Question 1:
[Advanced] Consider two functions
f
(
t
) and
g
(
t
) described as follows.
f
(
t
) =
{
1
if

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

s
)
ds
. Plot
h
(
t
) as a function of
t
.
Question 2:
[Basic] 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:
[Basic] Let
x
1
(
t
) =
e

t

2
j
,
x
2
(
t
) = sin(
t
+ 3
π/
4), and
x
3
[
n
] =
e

n

1

. Find
the total energy and the average power of
x
1
(
t
),
x
2
(
t
), and
x
3
[
n
].
Question 4:
[Basic] p. 59, Problem 1.22 (g) and p. 60, Problem 1.24 (a) and (b).
Question 5:
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 '06
 V."Ragu"Balakrishnan

Click to edit the document details