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Old Exam with Solution - Signals and Systems - Fall 2000 | ECE 350, Exams of Signals and Systems

Material Type: Exam; Professor: Smith; Class: Signals and Systems; Subject: Electrical & Computer Engineer; University: Boise State University; Term: Spring 2000;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Name: __SOLUTIONS__
EE 222 Signals & Transforms
Exam #3
Fall 2000
1) (40 points) You are given a system that relates the input and output voltages of following circuit
y(t)=Vout(t)x(t)=Vin(t) R=1/5
L=1/20 H
C=1/5F
+
-
+
-
(a) (10 points) What is the transfer function )(
)(
)(
1sV
sV
sH
in
out
= as a ratio of polynomials?
1
1
1)(
1
)(
1
)(
1
)( 2
1
1
1
1++
=
++
=
+
+
+
=
sLCs
CsLs
Cs
Ls
Cs
sH
R
L
R
R
R
(b) (10 points) Draw the Bode Plot for this system Use the attached semilog paper and label the
plot fully.
)1)(1(
1
125.001.0
1
1
1
)(
520
22
1++
=
++
=
++
=ss
R
LsssLCs
sH
Frequency (rad/sec)
Phase (deg); Magnitude (dB)
Bode Diagram H1(j
ω
)
-50
-40
-30
-20
-10
0
100101102
(c) (5 points) Draw a pole/zero diagram for this system. Label the diagram fully.
Im
Re
x
-5
x
-20
(d) (5 points) Is this a low pass filter, a high pass filter or a band pass filter? State why you chose
your answer.
Low Pass Filter. It has a maximum value of 0dB which occurs for ω<5.
(e) (10 points) A continuous-time LTI system with frequency response H(jω) is constructed by
cascading another continuous-time LTI systems with frequency response H2(jω), after H1(jω).
pf3
pf4

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Name: __ SOLUTIONS __

EE 222 Signals & Transforms

Exam

Fall 2000

  1. (40 points) You are given a system that relates the input and output voltages of following circuit

x(t)=V (^) in (t) R=1/5Ω y(t)=V (^) out (t)

L=1/20 H

C=1/5F

(a) (10 points) What is the transfer function

V s

V s

H s

in

= out as a ratio of polynomials?

1

1 1

LsCs LCs s

Cs

Ls

Cs

H s

R

L R R

R

(b) (10 points) Draw the Bode Plot for this system Use the attached semilog paper and label the plot fully.

20 5

1 =^2 + + = 2 + + = s + s +

R

H s LCs L s s s

Frequency (rad/sec)

Phase (deg); Magnitude (dB)

Bode Diagram H 1 (jω)

0

100 101 102

(c) (5 points) Draw a pole/zero diagram for this system. Label the diagram fully. Im

x Re

x

(d) (5 points) Is this a low pass filter, a high pass filter or a band pass filter? State why you chose your answer. Low Pass Filter. It has a maximum value of 0dB which occurs for ω<5. (e) (10 points) A continuous-time LTI system with frequency response H(jω) is constructed by cascading another continuous-time LTI systems with frequency response H2(jω), after H 1 (jω).

x(t)=V (^) in (t) R=1/5Ω y2(t)=Vout 2(t)

L=1/20 H

C=1/5F

H 2 (s)

H 1 (s)

The straight-line approximations of the Bode Magnitude plots of H(j ω ) should be as follows.

Frequency (rad/sec)

Phase (deg); Magnitude (dB)

Bode Diagram H(jω)

0

100 101 102

Specify the equation and Bode diagram for H (^) 2(s).

Frequency (rad/sec)

Phase (deg); Magnitude (dB)

Bode Diagram H 2 (jω)

0

100 101 102

20

5 2

s

s

H s

  1. (20 points) A signal is

50

10 sin( 100 ) ( ) 2 cos( 50 ) + 

t

t xt t

(a) (7 points) What is the equation describing X(j ω)?

( ) 2 [ ( 50 ) ( 50 )]^10 | |^100 πδ ω

X j = − + + + <

(b) (7 points) Sketch and fully label X(j ω).

X(jω)

ω -100 -50 50 100

2π 2π

100π (^10) π

(c) (6 points) According to Nyquist, what is the smallest sampling frequency, ωs, that may be

used to sample x(t) so that full reconstruction is possible? Explain how you arrived at your answer.

Frequency ω (rad/sec)

Magnitude (dB)

Bode Diagram H(jω)

0

20

40

10 0 10 1 10 2 10 3 10 4