Lecture topics
Narrowband FM modulation
Wideband FM modulation
Demodulation of FM signals (FM detection)
Properties of FM
EE 179
May 21, 2012
Page 1
Review of last lecture
Review of previous lecture
Frequency deviation of FM signal:
mp
mmax mmin
= kf
f =
Lecture topics
Introduction to angle modulation
Relationship between FM and PM
FM bandwidth and Carsons rule
EE 179
May 14, 2012
Page 1
Time-varying frequency
Many signals have time-varying frequency distributions (music,
speech, video).
Visualizations of
Lecture topics
FM bandwidth and Carsons rule
Spectral analysis of FM
Narrowband FM Modulation
Wideband FM Modulation
EE 179
May 18, 2012
Page 1
Review of last lecture
Angle modulation:
EM (t) = A cos c t + (t) = A cos c t + h(t) m(t)
PM: (t) = kp m(t)
FM:
Sampling theorem
Every band-limited signal g(t) can be reconstructed from samples
g(kT ) for small enough T
Precise statement: if G(f ) = 0 when f > B , then
g(2Bk ) sinc(t 2Bk )
g(t) =
k =
=
g
k =
k
k
sinc t
T
T
where T = 1/2B . This is a sinc interpola
Lecture topics
Line coding
PSD of line codes
Intersymbol interference
EE 179
June 1, 2012
Page 1
Line coding
Goal is to transmit binary data (e.g., PCM encoded voice, MPEG
encoded video, nancial information)
Transmission distance is large enough that comm
Lecture topics
PSD of line codes
Intersymbol interference
Pulse shaping
Eye patterns
EE 179
June 4, 2012
Page 1
PSD of line codes (review)
Input PSD depends on
pulse shape (smoother pulses have narrower PSD)
pulse rate (spectrum stretches with pulse rate)
EE 179: Introduction to Analog and
Digital Communications
Professor Andrea Goldsmith
Next-generation Cellular
Wireless Internet Access
Wireless Multimedia
Sensor Networks
Smart Homes/Spaces
Automated Highways
In-Body Networks
All this and more
Lecture #1
EE 178/278A Probabilistic Systems Analysis
Spring 2014
Tse/Hussami
Sample Final
Give yourself 3 hours to work on this sample final.
The last page of your exam contains a table of probabilities associated with the standard normal distribution.
EE 178/278A,
EE 178/278A Probabilistic Systems Analysis
Spring 2014
Final Exam
,
P RINT your name:
(last)
(first)
All answers should be justified unless stated otherwise.
Please define all events and all random variables before using them in your solutions to the ques
EE 178
Probabilistic Systems Analysis
Autumn 2016-17 Tse
Sample Midterm
Give yourself 3 hours to work on this sample midterm.
EE 178, Autumn 2016-17, Sample Midterm
1
Problem 1: Rolling Tetrahedral Dice
You have a fair tetrahedral die with 4 sides. You ro
EE 178
Probabilistic Systems Analysis
Spring 2015
Tse
Final Exam
There are 6 questions with a total of 100 points.
All answers have to be justified.
Please do not consult with any others on the exam.
You have 24 hours to do the exam.
If you have any quest
Final Solutions Spring 2014-2015
Problem 1: Short Questions
(a) The rectangle below represents the entire event space. We have depicted two events, A and B as portions of
the event space. Notice that events A and B do not overlap. Assume they are not empt
Sample Midterm Solutions Autumn 2016-17
Problem 1: Rolling Tetrahedral Dice
You have a fair tetrahedral die with 4 sides. You roll it three times. Consider the following events:
A = first roll is a 3
B = second roll is a 2
C = second roll is a 3
D = the f
EE 178
Probabilistic Systems Analysis
Autumn 2016 Tse
Final solutions
There is a total of 7 questions with a total of 100 points. You have a total of 3 hours.
Please write all your answers in the exam booklet.
The exam is closed book but you are allowed t
Midterm Coverage/Review:
Overview and Signals
!
Overview of Communication Systems (Ch. 1.1-1.3)
! Analog
and digital signals
! Channel effects, SNR, and capacity
! Bit times and data rates
! Communication system block diagram
!
Signals (Ch. 2.1-2.4, 2.6,
Lecture topics
Single sideband modulation (SSB) (review)
Vestigial sideband modulation (VSB)
Quadrature modulation
Implementation issues
EE 179
May 9, 2012
Page 1
Single Sideband (SSB) in frequency domain
EE 179
May 9, 2012
Page 2
SSB in time domain
The o
Lecture 2 Outline
l Review
of last lecture
l Information
representation
l Communication
l Analog
versus digital systems
l Performance
l Data
system block diagrams
metrics
rate limits
Review of Last Lecture
l
Communication systems exchange multimedia data
Lecture 3 Outline
! Data
Rate Limits (cont.)
! Signals
and Systems
! Energy
and Power in Signals
! Impulse
! Signal
and Unit Step Signals
Operations
Review of Last Lecture
!
Communication systems modulate analog signals or
digital signals (bits) for trans
Review of last lecture
Unit impulse (generalized) function
Unit step function
Denition of Fourier series:
Dn e2if0 nt
g(t) =
n=
where
a+T0
Dn =
a
g(t)e2if0 nt dt
g(t)e2if0 nt dt =
T0
where T0 is the period and f0 is the fundamental frequency
EE 179
April
Rectangular Pulse Example
A
-.5#
Infinite Frequency Content
A(t/)
.5#
t
-1/#
1/#
f
g (t ) = A(t / ) G( f ) = Asinc(f )
!
!
!
!
Rectangular pulse is a time window
Shrinking time axis causes stretching of frequency axis
Signals cannot be both time-limited a
Lecture 7 Outline
! Examples
! Channel
! Ideal
of Communication Channels
Distortion and Equalization
Filters
! Energy
! Power
Spectral Density and its Properties
Spectral Density and its Properties
! Filtering
and Modulation based on PSD
Examples of Chann
Review: energy/power spectral density
Instantaneous power of a signal (real or complex valued): |g(t)|2
Total energy:
|g(t)|2 dt
provided the integral is nite.
By Parsevals theorem,
|G(f )|2 df
|g(t)|2 dt =
Energy spectral density is |G(f )|2 .
If g(t) is
Random signals
A random signal is a signal chosen randomly from a set of
possible realizations
Noise signals are random (we could subtract the deterministic
part)
An important characterization of random signals is the PSD
Filtering and modulation of rando
Lecture 10 Outline
l
Random Variables
l
Cumulative Distribution Function (cdf)
l
Probability Density Function (pdf)
l
Means, Moments, and Variance
l
Gaussian Random Variables
l
Several Random Variables
Review of Last Lecture
l
Probability theory, probabil
Lecture 11 Outline
Gaussian Random Variables
1
[( x )
p X ( x) =
e
2
2
2
/ ]
Z~N(0.1)
N(,2)
Tails decrease
exponentially
x
x
1
Q( y ) =
2
e
x2 / 2
dx
y
& x #
p( X x) = FX ( x) = 1 Q$
!, Q( x) = .5erfc x / 2
%"
(
)
Several Random Variables
yx
p XY ( x, y
Lecture 12 Outline
Random binary waveform
We can model random binary data (such as output of compression
or encryption) by discrete time random process:
Pcfw_Xn = +1 = Pcfw_Xn = 1 = 1/2
. . . , X1 , X2 , X3 , . . . are independent
A continuous-time random
Amplitude modulation review
Amplitude modulation:
s(t) = Ac (1 + ka m(t) cos(2fc t)
with ka > 0. Alternatively,
s(t)(A + m(t) cos(c t)
Bandwidth of m(t) is than fc
Spectrum of modulated signal:
S (f ) = 1 Ac (f + fc ) + (f fc ) +
2
1
2 ka Ac
M (f + fc ) +
EE 178/278A Probabilistic Systems Analysis
Spring 2014
Tse/Hussami
Final Soln
Final exam sample solutions
EE 178/278A, Spring 2014, Final Soln
1
(a) For any events A and B, if P(A) 6= 0, P(B) 6= 0, and A and B disjoint, then A and B are dependent.
True. 0