Questions for DSP Midterm I
1. Why is digital signal processing so popular? Why, on the other hand, is
it not used everywhere? What are its limitations?
2. Explain the process of A/D conversion.
3. Draw a Venn diagram (set diagram) which shows the set rel
Expectation Values
Consider a quantum ensemble characterized by ( .x )
P ( x0 ) = ( x0 )
2
is the probability a measurement
of position for any member of the ensemble will
x0 .
yield the result _
What is the average of position measurements over
the ensem
Early Quantum Theory
Classical background:
light is a wave
electrons are particles
Planck
Black-body radiation
Energy transfer in units of hv
v : frequency of light
h : Plancks constant
Einstein
Light itself is quantized
quanta of light photon
Photoelectr
University of Notre Dame
Department of Electrical Engineering
Course EE 40471 Digital Signal Processing
Dr. M. Haenggi
March 30, 2011 mh
Project: E-Music
Due: Monday, May 2, 2011 (in class)
Remarks:
Files:
- All files can be found at http:/www.nd.edu/~mha
Infinite Square Well
V ( x)
V 0
V
0
I
We choose to solve with
coordinate system which
does not exploit symmetry.
V
L
II
x
2 2
( x) V ( x) ( x) E ( x)
2
2m x
III
In regions I and III, 0.
In region II, V ( x) 0.
2 2
E
2
2m x
2mE
2
let k
2mE
k 2
Ge
Finite Potential Well
V ( x)
a
a
0
V0
x
Find bound states
(E
V ( x)
0
x a
V0
x a
Region
I
Region
II
a
0
a
Region
III
x
Strategy: Find general solutions to S.E. in each
region.
Find acceptable solutions in each
region.
Match and at boundaries to
determ
Time independent Schrdinger Equation
2 2
(
x
,
t
)
V
(
x
,
t
)
(
x
,
t
)
i
+
=
( x, t )
2
2m x
t
(TDSE)
Look for separable solution
( x, t ) =
( x) (t )
2
2 ( x)
(
,
)
(
)
(
)
(
)
V
x
t
x
t
i
x
(t )
+
=
(t )
2
2m
t
x
divide by (t ) ( x)
2 1 2
1 (
Quantum statics
Quantum dynamics
Motion
Since a QM particle does not have a position,
what does motion mean?
P ( x, t0 )
x
P ( x, t1 )
x
P ( x, t 2 )
x
Motion is described by change in the state
function.
Fifth Postulate of Quantum Mechanics
The time deve
Is Probability Conserved?
Suppose we prepare a particle in a state ( x, t = 0).
We normalize the state so that
P ([ , ] ,=
t 0=
)
*( x, 0) ( x, 0)dx
= 1
Its subsequent time development is governed by
TDSE:
2 2
+
=
(
x
,
t
)
V
(
x
,
t
)
(
x
,
t
)
i
( x,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Homewrok set # 1 solution
posted on 9/11/02
Problem 1) Take A = cfw_0,1,2,3,4,5
a) S = cfw_( x, y, z ) / x A, y A, z A, x + y + z = 5
2) [GAR] 2.3
a) S = cfw_2,3,4,5,6,7,8,9,10,11,12
b) A = cfw_2,4,6,8,10,12
c) if sum = 2 S = cfw_(1,1)
sum = 3 S = cfw_(1,
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
Probability Homework #1 Solution
1.9 V 2 n =
cfw_
1 n
X ( j) X
n j =1
1
n
2
()
1.12
.
.
.
queue
n machines
system
(repairman)
Each time a machine breaks down corresponds to a terminal submitting a
job to the system (repairman).
2
changes were instituted after the intervention
by the Berkeley president, an indication that
the story pressed against key ideological
boundaries. MEDIA AND SOCIAL CONTROL As
Stuart Hall indicated, it is the media's ability to
"define" the situation that
By taking decisional "events," pluralists have
guaranteed diversity by focusing only on those
issues on which elites agree. Lukes (1974)
argues that the most effective power prevents
conflict from arising in the first place. This,
according to Hall (1982)
gave little coverage to the anarchists' own
stated beliefs, but considerable attention to
official and police statements, and comments
bystanders. Official statements emphasized the
deviance of the anarchists, who contrasted
themselves to an apathetic soc
direct communication of a government official
to a (generally high-level) manager of a media
organization. The more sources and interest
groups criticize the mass media, the more the
government will try to control the media. The
characteristics of the com