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ECE 483 Quiz # 1 Solution
Problem 1. (6 points)
For each of the following
z
transforms, determine the ±nal value of the
corresponding signal
f
(
k
) as
k
→ ∞
. If the ±nal value theorem does not apply, state the reason
that this is so and no further computation is needed.
(a)
(1.5 points)
F
(
z
) =
z
+2
(
z
+1)(
z

0
.
5)
.
Solution:
FVT does not apply as
F
(
z
) has a pole at

1, which is on the unit circle but not
at 1.
(b)
(1.5 points)
F
(
z
) =
z
(
z
2

0
.
25)(
z

1)
.
Solution:
FVT applies, and
f
(
∞
) = 1
/
0
.
75 = 1
.
3333.
(c)
(1.5 points)
F
(
z
) =
z

4
+ 3
z

7
.
Solution:
FVT applies, and
f
(
∞
) = 0.
(d)
(1.5 points)
F
(
z
) =
2
z
2
+3
(
z

0
.
3)(
z
2
+2
z
+2)
.
Solution:
FVT does not apply as
F
(
z
) has poles at 1
±
j
which are outside the unit circle.
Problem 2. (6 points)
Given
F
(
z
) =
2
z
2
+1
z
4

z
3
+3
z

1
, ±nd the corresponding
f
(
k
) for
k
= 0
,
1
,
2
,
3.
Solution:
Using the long division method, we have
f
(0) =
f
(1) = 0,
f
(2) =
f
(3) = 2.
Problem 3. (8 points)
For the following
F
(
z
), ±nd its inverse
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This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 evens

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