ECE 421, Spring 2006, HW Assignment #1
Signals and Systems Review Problems
Due Tuesday, January 31
1. Determine the Laplace transform for the following timedomain signal. Express the answer in the
normal transfer function format, that is, as a ratio of polynomials.
x
1
(
t
)=
½
0
,t
<
0
t
2
−
4
e
−
3
t
+3
e
2
t
≥
0
¾
(1)
2. Determine the timedomain expressions for each of the Laplace transforms shown below.
X
2
a
(
s
1
s
(4
s
+1)
=
0
.
25
s
(
s
+0
.
25)
(2)
X
2
b
(
s
12
s
2
(4
s
=
3
s
2
(
s
.
25)
(3)
X
2
c
(
s
13
s
(
s
2
+4
s
+ 13)
=
13
s
(
s
+2+
j
3) (
s
+2
−
j
3)
(4)
3. Without computing inverse Laplace transforms, determine the output signals for each of the following
three systems for the given sinusoidal inputs. The system transfer functions are given by the
G
i
(
s
)
,
and the input signals are
x
i
(
t
)
.
G
3
a
(
s
20 (
s
+3)
(
s
.
2) (
s
+6)(
s
+ 10)
,x
3
a
(
t
)=5cos(2
t
−
π/
6)
(5)
G
3
b
(
s
10 (
s
+2)
2
(
s
+5)(
s
+7)
3
b
(
t
)=2cos(2
t
+
3) + 10 cos (6
t
+
3)
(6)
G
3
c
(
s
10
(
s
.
3)
3
3
c
(
t
)=4cos(0
.
5
t
)+10cos(2
t
+
3)
(7)
4. For each of the transfer functions below, determine the poles and zeros and indicate whether the system
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This note was uploaded on 10/25/2010 for the course ECE 421 taught by Professor Cook,g during the Spring '08 term at George Mason.
 Spring '08
 Cook,G

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