exercise chapter 3
TRANSCRIPT
Page 88-89
Q#3.21 – Q#3.25
Q#3.21
• Plot the following signals
a. x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
b. x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
-5 -4 -3 -2 -1 0 1 2 3 4 5
0
0.5
1
1.5
2
time (seconds)
2u(t
+2)
x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
time (seconds)
-u(t
-0.5
)
x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
-5 -4 -3 -2 -1 0 1 2 3 4 50
1
2
3
4
time
r(t-
0.5)
x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-3
-2.5
-2
-1.5
-1
-0.5
0
time (seconds)
-r(t
-2)
x(t)=2u(t+2) –u(t-0.5)+r(t-0.5)-r(t-2)
012
2u(t
+2)
-1-0.5
0
-u(t
-0.5
)
-5 -4 -3 -2 -1 0 1 2 3 4 5024
-3-2-10
-r(t
-2)
-5 -4 -3 -2 -1 0 1 2 3 4 50
1
2
time (seconds)
x(t
)
Part b
• x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
-6 -4 -2 0 2 4 60
5
10
15
time (seconds)
2r(
t+1)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
-6 -4 -2 0 2 4 6
-20
-15
-10
-5
0
time (seconds)
-4r(
t-1)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
-6 -4 -2 0 2 4 6
0
0.2
0.4
0.6
0.8
1
time (seconds)
u(t
-2)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
-6 -4 -2 0 2 4 60
2
4
6
8
time (seconds)
2r(
t-3)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
-1
-0.5
0
-u(t
-4)
0
0.5
1
u(5
-t)
-6 -4 -2 0 2 4 6
-1
-0.5
0
time (seconds)
-u(t
-4)u
(5-t
)
x(t)=2r(t+1)-4r(t-1)+u(t-2)+2r(t-3)-u(t-4)u(5-t)
0
5
10
15
2r(t+
1)
-20
-10
0
-4r(t
-1)
0
0.5
1
u(t-2
)
-1
-0.5
0
-u(t
-4)u
(5-t
)
0
4
8
2r(t-
3)
-6 -4 -2 0 2 4 60
2
4
time (seconds)
x(t)
Q#3.23 Page 89
• Plot the following signalsa.
b.
c.
d. x(t)=r(t) π[(t-3)/2]+2u(2-t)+4u(t-4)
x(t)=r(t) π[(t-3)/2]+2u(2-t)+4u(t-4)
0
0.2
0.4
0.6
0.8
1
rect[(t
-3)/
2]
0
2
4
6
r(t)
-6 -4 -2 0 2 4 60
2
4
time (seconds)
r(t)
rect[
(t-3
)/2]
x(t)=r(t) π[(t-3)/2]+2u(2-t)+4u(t-4)
-6 -4 -2 0 2 4 60
0.5
1
1.5
2
time (seconds)
u(2-
t)
x(t)=r(t) π[(t-3)/2]+2u(2-t)+4u(t-4)
-6 -4 -2 0 2 4 6
0
0.5
1
1.5
2
2.5
3
3.5
4
time (seconds)
4u(t-
4)
x(t)=r(t) π[(t-3)/2]+2u(2-t)+4u(t-4)
0
2
4
r(t)
rect[
(t-3
)/4]
0
1
2
2u
(2-t
)
0
2
4
4u(t
-4)
-2 0 2 4 6 8 100
2
4
time (seconds)
x(t
)
Q#3.24
• Write equations for the test signals shownbelow
(a)
-2 -5/3 -4/3 -1 -2/3 -1/3 -0 1/3 2/3 1 4/3 5/3 2-2
-1
0
1
2
3
4
time (seconds)
x(t)
• x(t)=6r(t+1)-6r(t+1/3)-18r(t)+18r(t-1/3)+2u(t-2/3)