Signals and Systems MAE 143A
Midterm Exam Spring Quarter 2009 a
Student name and number K C
The material allowed in the midterm: copy of the slides, class notes, and the textbook. No
copy of previous exam solutions or practice exams are allowed. No c
Practice Questions for Final, 2009
The material for the Final will be based on all the homework (Homework 1 through Homework 4),
the slides (signalsCT.pdf systemsCT.pdf, ImpulseResponse.pdf, systemsFD.pdf) and the text book
(this is the material included
Signals and Systems - MAE 143A
Quiz 1 - Winter Quarter 2009
Student name and number
PLEASE READ:
You have 45 minutes. Please mark your papers with your name and surname, and student number.
Read the questions very carefully. Answer the questions asked and
Signals and Systems - MAE 143A - Quiz 2, 2009
Student name and number
NOTE: For all the questions you need to REASON/EXPLAIN your answer.
1. (5 points) Find an ODE model for the mechanical system shown in Figure 1.
Figure 1: Multibody system for Problem 1
Signals and Systems - MAE 143A
Midterm Exam - Winter Quarter 2010
Student name and number
The material ALLOWED in the midterm: a clean copy of the slides, and 1 page *front
only* of your handwritten notes. Material NOT ALLOWED: previous exam solutions,
pr
Signals and Systems - MAE 143A Midterm Exam - Winter Quarter 2008
Student name and number For all the questions you need to show ALL your work to get to the answer. 1. (10 points) The circuit in Figure 1 (left graph) represents a practical passive lter. T
Signals and Systems - MAE 143A Final Exam - Winter Quarter 2008
Student name and number For all the questions you need to show ALL your work to get to the answer. 1. (7 points) Consider the system x1 = x2 + u cos x2 3 x 2 = x 1 x 1 + x 2 4 where u is the
Signals and Systems - MAE 143A Final Exam - Winter Quarter 2007
Student name and number For all the questions you need to show ALL your work to get to the answer. 1. (4 points) For the time function
t
f (t) =
0
e3 (t )e2(t ) d,
t 0.
(i) (2 points) Find th
Signals and Systems - MAE 143A
Final Exam - Spring Quarter 2009
Student name and number
The material allowed in the midterm: copy of the slides, class notes, homework solutions,
and the textbook. No copy of previous exam solutions or practice exams are al
Signals and Systems - MAE 143A Midterm Exam - Winter Quarter 2007
Student name and number For all the questions you need to show ALL your work to get to the answer. 1. (4.5 points) Consider the set of dierential equations: x = x + 2z + u z = z + 3x y = 3z
Signals and Systems - MAE 143A
Final Exam - Winter Quarter 2010
Student name and number
The material ALLOWED in the nal: a clean copy of the slides, the table of FT pairs, and
1 page of your handwritten notes. Material NOT ALLOWED: previous exam solutions
MAE143 A - Signals and Systems - Winter 11
Final
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including
your class notes and textbook. You may use a hand calculator with no communication
capabilities
(ii) You
Signals and Systems - MAE 143A Practice Final Exam- Winter Quarter 2007
Student name and number For all the questions you need to show ALL your work to get to the answer. 1. (4 points) For the time function
t
f (t) =
0
sin(2(t ) d,
t0
(ii) (2 points) Usi
MAE143 A - Signals and Systems - Winter 11
Midterm, February 2nd
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including
your class notes and textbook. You may use a hand calculator with no communication
capab
MAE143 A - Signals and Systems - Winter 11
Final
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including
your class notes and textbook. You may use a hand calculator with no communication
capabilities
(ii) You
2.
i(t ) = is (t ) + ic (t )
ic (t ) = C
d
(Vc (t )
dt
is (t ) =
Vs
R1
Vc (t ) + ic (t ) R2 = 0
d
(V (t ) R2 = 0
dt c
, Vc (t ) + C
t
1
The eigenvalue of the solution is =
, so the solution is Ket = Ke CR2 ,
CR2
where K is a constant we will get from
Homework 3
18a. We set ( )
( ) to get the impulse response of the system:
()
()
( ).
Following the algorithm on Page 166, we get that
like
. Therefore our solution looks
()
The homogeneous solution
() ()
( ) should satisfy
()
()
()
(
) ()
Now we need to d
MAE 143A Homework 4
Chapter 4
12.
a)
"
(1)
When car is at rest, set all derivates in (1) equal to zero which yields
0
.
0.6
0.404 m
b) Rearrange (1) as
"
0
(2)
Define new variable as
"
"
"
Substitute into (2) which yields
"
"
0
"
"
"
"
(3)
Case 2: m=n, ad
Homework 6
Problem 33. Excitation of the system and its response are given
()
(
)
()
(
(
)
)(
)
(
(
)
)(
)
We know that response is equal to the convolution of excitation and impulse response
()
( ) ( ) or in Fourier space ( )
( ) ( ), where convolution i
Homework 7 Solutions
( )=
Problem 25:
(1000 )
( ) where
.
= 11000 ,
= 0.002 ,
=
= 500
Fourier transform the input signal and multiple with the frequency response of the ideal filter. The
inverse of the product yields the output signal.
( ) = ( ) (
Homework 8
Solutions
Chapter 14
25. Over a time range of 0 < t < 400ms , signal x(t ) = 3cos(20 t ) 2sin(30 t ) is
shown in following figures (dashed line), together with sampled by different sampling
intervals: 1/120s, 1/60s, 1/30s, 1/15s.
Ts =1/120s
x(t
MAE 143 A: Signals and Systems.
Homework #1.
Assigned Jan 6. Due Jan 13
1. Sketch the following continuous-time signals. You should draw by hand (do not use MATLAB or a
calculator) after reasoning how the signals look like.
(a) g (t) = u(t + 1) 2u(t 1) +
MAE 143 A: Signals and Systems.
Homework #3.
Assigned Jan 20. Due Jan 27.
1. For dierent systems, we observe the following input-output experiments:
(a) System 1: x(t) cos2 (2f0 t) and 2x(t) 1 + cos(4f0 t), for some constant f0 . Is the system
homogeneous
MAE 143 A: Signals and Systems.
Homework #4.
Assigned Jan 27. Due Feb 3.
1. A circuit with two resistors, an inductor and a capacitor element, is modeled by the following linear
ODE:
dV
1/3 0 V
1/3
dt
+
i
diL =
1/3 0 iL
1/3 S
dt
Here, V is the potential d
MAE143 A - Signals and Systems - Winter 11
Midterm, February 2nd
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including
your class notes and textbook. You may use a hand calculator with no communication
capab
Signals and Systems - MAE 143A
Final Exam - Winter Quarter 2009
Student name and number
For all the questions you need to show ALL your work to get to the answer. Please
justify your answers (a yes/no answer is not enough.)
List of allowed materials: Book