ECE 3614: Introduction to
Communication Systems
Generalized Fourier
Transform
Spring 2016
Generalized Fourier Transform
Example : g(t)=1
Consider the Fourier Transform of a constant:
Unfortunately this integral does not converge
Does its Fourier Transform
ECE 3304
Introduction to Power Systems
Lecture 6
Power System Basics
Fall 2016
Per Unit System
September 8
Reference : Book, Chapter 3
ECE 3304
6.1 Per Unit System:
18 kV
Generator
230 kV
Y
Transmission
Line
14 kV
Y
Distribution
Line
4 kV
YY
Load
To solve
ECE 3304
Introduction to Power Systems
Lecture 1
Power System Basics
Motivation
Components of Electric Energy Systems
August 23th 2016
ECE 3304
ECE 3304 Motivation
1
2003 Blackout:
61,800 MW of load
50 million people
8 states, 1 province
Cost:
$6 billions
ECE 2534
Test 2
April 22, 2015
1. On the scope trace of an I2C transaction on the following page:
a. Indicate where the start condition occurs.
b. Determine the slave address.
c. Specify whether we
ECE 3304
Introduction to Power Systems
Lecture 5
Transformer Model from Testing
September 6
Fall 2016
Transformer Model from Testing
Reference : Book, Chapter 3
ECE 3304
5.1 Derivation of Transformer Model Parameter from Tests
If you are given a transform
ECE 3304
Introduction to Power Systems
Lecture 3
Power System Basics
Fall 2016
August 30
Three Phase Circuits
Reference : Book, Chapter 1 & 2
ECE 3304
3.1 Review Example for Single Phase Circuits:
In the following circuit, find the Phasor currents
I, IA,
ECE 3304
Introduction to Power Systems
Lecture 4
Power System Basics
Fall 2016
September 1
Transformer Modeling
Reference : Book, Chapter 1 & 3
ECE 3304
4.1 Motivation for Transformer Modeling
Transformers are key for the efficient transmission of
AC elec
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 5 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
1. Frequency Modulation vs. Amplitude Modulation (10 pts)
A message signal m(t) = Am cos(
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 4 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
1. Selection of analog modulation formats: AM system design (10 pts)
In this problem, we
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 3 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
In this quiz, we will revisit the concept of Linear Time Invariant (LTI) Systems.
1. (10
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 2 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
1. In this quiz, we will revisit the concepts of Fourier Series and Fourier Transform.
(a
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 1 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
1. In this quiz, we will revisit the concept of energy and power signals.
(a) (4 pts) Is
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 7 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
Choose the most suitable answer for each question.
1. Which of the following two systems
ECE 3304
Introduction to Power Systems
Lecture 7
Power System Basics
Fall 2016
AutoTransformers
Instrument Transformers
September 15th
Reference : Book, Chapters 3
ECE 3304
7.1 Autotransformers
IH
+
VH

NSE
IHIL
NC
IL
+
VL

Cost effective special pur
ECE 2534
Test #2
April 23, 2014
1. For the serial peripheral interface timing diagram shown on the next page:
a. Determine the values of CKP and CKE that must be used for
initialization. Justify yo
ECE 3614: Introduction to
Communication Systems
LTI Systems Additional
Examples and Filtering
Spring 2016
Magnitude/Phase Response
The transfer function H(f) is a characteristic property of
an LTI system
We are interested both in the amplitude response o
ECE 3614: Introduction to
Communication Systems
Double sideband AM
Transmitted Carrier
Spring 2016
Analog Modulation
Double Sideband Transmitted Carrier AM (DSBTC AM)
Let m(t) denote the analog message signal
Typically m(t) represents voice or music
Tr
ECE 3614: Introduction to
Communication Systems
Fourier Transform:
Definition
Spring 2016
Unit Step Function
Definition:
Sometimes defined with:
2
Dirac Delta Function (Impulse)
Notes:
Several ways to define
Here is one
While magnitude is infinite, area i
ECE 3614: Introduction to
Communication Systems
Fourier Series
Spring 2016
Continuous Time Fourier Series
We can represent a periodic signal x(t) with period T0 exactly by the
sum of complex sinusoids
where
Note that f0 = 1/T0
The above integral must conv
ECE 3614: Introduction to
Communication Systems
Fourier Transform
Properties
Spring 2016
Continuous Time Fourier Transform
Table of Transform Pairs
2
Fourier Transform
What we are measuring with the Fourier Transform is not the
amplitude of a component wi
ECE 3614: Introduction to
Communication Systems
Review of Signals and
Systems
Spring 2016
Signals and Systems
Signal:
set of information of some quantity
function of independent variable: usually time or
frequency
examples: speech, wave radiated by an ant
ECE 3614: Introduction to
Communication Systems
LTI Systems
Spring 2016
Linear Timeinvariant Systems
Importance
Why study LTI systems?
Several parts of a communication system can be
modeled as LTI
Filters
Equalizers
Channel
Pulse shaping (special type of
ECE 3614: Introduction to
Communication Systems
Double sideband AM
 Suppressed Carrier
Spring 2016
Introduction to Modulation
A communication system:
Definition: Communications is the transfer of information at one
time or location to another time or loc
ECE 3614: Introduction to
Communication Systems
Energy Spectral Density
and Power Spectral Density
Spring 2016
Classification of Signals
Energy and Power
Energy:
Power:
2
Energy and Power Spectral Densities
Overview
The Fourier Transform provides frequenc
ECE 2534
Test 2
April 24, 2013
1. The SPI timing diagram below is for an external digital to analog converter.
a. The slave requires only that data be read in on a rising edge. There
are t
ECE 3304
Introduction to Power Systems
Lecture 2
Review of Magnetic Circuits and
Single Phase AC
Fall 2016
August 25th
Reference : Book, Chapter 1
ECE 3304
2.1 Magnetic Fields Review
a) Amperes Circuital Law:
D
H dl S J t ds
Where:
J = Current Density
D
ECE 3614: Introduction to Communication Systems
Spring 2017 Quiz 8 10 points
Note: This is a closed book and closed notes quiz.
Name:
Instructor: Prof. H. S. Dhillon
Suppose that an analog music signal is found to have a bandwidth of 15 kHz and that sampl