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
F
1
EE179 Spring 2016-17
Introduction to Communications
Pauly
Problem Set #1
Due: Friday April 21, 2017 at 5 PM.
1. In Lecture 3, slides 28-29, we said that if we want to estimate a signal vector cx giv
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
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
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.
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 Di
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 va
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 associa
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
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, an
1
EE179 Spring 2016-17
Introduction to Communications
Pauly
Problem Set #2
Due: Friday April 28, 2017 at 5 PM.
1. We have an input signal m(t) that is band limited to B (its full bandwidth is 2B). We
Angle Modulation, III
Lecture topics
I
FM Modulation
I
FM Demodulation
I
Spectral pre-emphasis and de-emphasis to improve SNR
Based on lecture notes from John Gill
US Broadcast FM
I
US FM bandwidth sp
Signals and Systems: Part 2
I
Parsevals thereom for the Fourier Series
I
The Fourier transform in 2f
I
Some important Fourier transforms
I
Some important Fourier transform theorems
I
Convolution and M
Signals and Systems, Part 1
I
A signal is a real (or complex) valued function of one or more real
variables.
I
I
I
I
I
voltage across a resistor or current through inductor
pressure at a point in the
Communication Channels
I
wires (PCD trace or conductor on IC)
I
optical fiber (attenuation 4dB/km)
I
broadcast TV (50 kW transmit)
I
voice telephone line (under -9 dbm or 110 W)
I
walkie-talkie: 500 m
Communication Systems Overview
L&D Chapter 1
I
Information representation
I
Communication system block diagrams
I
Analog versus digital systems
I
Performance metrics
I
Data rate limits
Next week: sign
Digital Carrier Modulation
Lecture topics
I
Eye diagrams
I
Pulse amplitude modulation (PAM)
I
Binary digital modulation
I
I
Amplitude shift keying (ASK)
I
Frequency shift keying (FSK)
I
Phase shift ke
Sampling and Pulse Trains
I
Sampling and interpolation
I
Practical interpolation
I
Pulse trains
I
Analog multiplexing
Based on lecture notes from John Gill
Sampling Theorem
Sampling theorem: a signal
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 narrow
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 infor
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
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 rand
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)|
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
!
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
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 p
Unit Impulse Response (t)
(Dirac Delta Function)
! Defined
by two properties
1. (t ) = 0
(t)
2.
(t )dt = 1
0
! Also
limit of unit area pulse with vanishing width
! Properties: 1. (t ) (t ) = (0) (t )
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 modu
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 Le