Solutions to EE3210 Tutorial 2 Problems
Problem 1:
t
(a) The signal x(4 2 ) is obtained from x(t) as below:
x(t)
2
1
-2
0 1
-1
t
2
-1
Time shift
x(4 t)
x(t + 4)
Time reversal
2
x(4 t / 2)
Time scaling
2
2
1
1
1
6
-6
-5
-4
-3
t
-2
-1
2
3
4
12
t
5
-1
4
6
8
EE3210
Signals and Systems
Part 11: Laplace Transform
Instructor: Dr. Jun Guo
D EPARTMENT OF E LECTRONIC E NGINEERING
Changes of Part1 v1 Lecture Notes
Pages 1424: Add an overview of partial fraction
expansion for rational functions.
Page 1
Changes of Par
EE3009 Tutorial 2
(Internet Structure, Delay)
Review Question
What are the three components of the Internet structure?
What are the four most important types of delay in a computer network?
Problem
1. Consider two hosts, A and B, connected by a single lin
EE3009
Data Communications & Networking
Course Overview
0-1
Contact Information
Lecturer
Dr. Albert Sung
Office: G6518, Email: [email protected]
Tutors
Name
Email
FU Yaru
[email protected]
LI Yuming
[email protected]
LOU Yang, Fel
Unit 4
Network Layer and IP Networks
Network Layer & IP Networks
4-1
Unit 4: Outline
4.1 Network Layer: Overview
4.2 Virtual Circuit & Datagram Networks
4.3 IP: Internet Protocol
application
transport
4.4 IP Forwarding and DHCP
4.5 Network Address Tr
Unit 3
HTTP, UDP and TCP
HTTP, UDP and TCP
3-1
Unit 3: Outline
application
3.1 Principles of Network Applications
3.2 Application Layer: Web and HTTP
transport
3.3 Security: HTTPS
3.4 Connectionless Transport: UDP
network
3.5 Connection-oriented Tran
Unit 1
Transmission Media and
Networking
Transmission Media & Networking
1-1
Outline of Unit 1
1.1 Transmission Media
1.2 Network Topology and Classification
1.3 Circuit Switching vs. Packet Switching
Transmission Media & Networking
1-2
Unit 1.1
Transmiss
ECE 301 Fall 2011 Division 1
Homework 2 Solutions
Reading: textbook Chapter 1.
Problem 1. Determine whether or not each of the following signals is periodic. If the signal is
periodic, determine its fundamental period. Note that the signals in Parts (a)-(
EE3210
Signals and Systems
Part 7: Discrete-Time Fourier Series
Dr. GUO, Jun
D EPARTMENT OF E LECTRONIC E NGINEERING
Discrete-Time Periodic Complex Exponentials
In contrast to continuous-time complex exponentials, a
discrete-time complex exponential of th
EE3210 Signals and Systems
Tutorial 7
Problem 1: Let x1 (t) be a continuous-time periodic signal with fundamental period T
and Fourier series coecients ak . Consider
x2 (t) = x1 (1 t).
Find a relationship between the Fourier series coecients bk of x2 (t)
Solutions to EE3210 Tutorial 7 Problems
Problem 1: Recall pages 13 and 14 of Part 1 lecture notes. The signal x2 (t) = x1 (1 t)
can be obtained from x1 (t) in two alternative ways:
(a) Time shift rst followed by time reversal, i.e.:
x1 (t) y(t) = x1 (t +
Part 2. LTI SYSTEMS
the output of the system for x[n] is given by
2.1. THE IMPULSE RESPONSE AND
CONVOLUTION
x[k]hk [n]
y[n] =
k=
LTI systems & impulse response
If in addition, the system is time-invariant(LTI), then
if we let h0 [n] = h[n] to be the respo
3. Continuous and discrete time Fourier series
Quick overview:
Continuous time Fourier series
The signal x(t) can be decomposed into a Fourier series
The Fourier transform is defined by
where x(t) is the c.t. signal.
Then the coefficients of the exponenti
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.003: Signals and SystemsSpring 2007
Tutorial for the week of Febuary 26
In these notes, the following materials are covered:
Eigenfunctions of linear system
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.003: Signals and SystemsSpring 2007
Solutions to tutorial problems for the week of Febuary 26
Eigenfunctions of LTI systems O&W 3.64
(a) We know that each k
EE3009 Tutorial 1
(Circuit Switching vs. Packet Switching, Internet Basics)
Review Questions:
What is the major difference between LAN and WAN?
What is multiplexing? List some common multiplexing techniques.
Problem:
1.
Suppose there are four employees wo
EE3009
Tutorial 1
(Solution)
Question 1
a) Four telephone lines are needed.
b)
i.
4 n 4 n
0.2 0.8
n
N
0
Probability
ii.
0.4096
1
2
3
4
0.4096
0.1536
0.0256
0.0016
Two telephone lines are enough because the probability that more than two
users want to
1.(a)
is a periodic signal.
Solution
1.(b)
It is clear that the signal has a fundamental period of
.
Moreover, the squared magnitude is
As
is periodic, we can find the power first. The power
can be computed from each of the above terms and then
sum togeth
Solutions to EE3210 Tutorial 13 Problems
Problem 1:
(a) No. From Property 3 of ROC, we know that, if x[n] is of nite duration, then the
ROC is the entire z-plane, except possibly z = 0 and/or z = . However, in this
case, X[z] has a pole at z = 1/2. Theref
Laplace Transform
Fourier Analysis
4-1
Laplace Transform
Laplace transform is a useful technique
for analyzing systems described by
differential equations.
Two types of Laplace transform:
1.
2.
Bilateral Laplace transform
Unilateral Laplace transform
a
Introduction to Signals
Signals
1-1
What is a signal?
A signal is a physical phenomenon, a physical
process, or a set of data, represented
mathematically as a function of one or more
independent variables. For this reason, we
typically write a signal as
EE 3210 Summary of Coverage
Signals
1-1
Signals
Continuous-time vs discrete-time signals
Periodic signals: general periodic signals, real
and complex sinusoids
Polynomial signals: unit impulse, unit step
Operation of signals: scaling, shift
Signals
1-
Introduction to Systems
Systems
2-1
Outline
2.1 Introduction
2.2 Classification of Systems
2.3 Convolution Sum for Discrete-Time
LTI Systems
2.4 Convolution Integral for ContinuousTime LTI Systems
2.5 Properties and Characterizations of
LTI Systems
S
Introduction to Signals
Signals
1-1
What is a signal?
A signal is a physical phenomenon, a physical
process, or a set of data, represented
mathematically as a function of one or more
independent variables. For this reason, we
typically write a signal as
Appendix A list of possibly relevant equations
Complex number:
Eulers formula: ej = cos + j sin
Fundamental period of a periodic signal:
Continuous-time sinusoidal: T0 = 2/0
Discrete-time sinusoidal: N0 = 2k/0 if N0 and k have no factors in common.
Solutions to EE3210 Quiz 1 Problems
Problem 1: Note that
cos[(n 1)] = (1)n1 .
Thus, the input x[n] and output y[n] of this system are also related by
y[n] = (1)n1 x[n].
(a) The system is memoryless. Only the current value of the input x[n] inuences the
cu
Name: _
Student ID: _
Signature: _
CITY UNIVERSITY OF HONG KONG
Semester B 2013/2014
EE3210: Signals and Systems
Quiz 2
1.
2.
3.
4.
Time allowed: One hour
Total number of problems: 4
Total marks available: 35
This paper may not be retained by candidates
S
Name: _
Student ID: _
Signature: _
CITY UNIVERSITY OF HONG KONG
Semester B 2013/2014
EE3210: Signals and Systems
Quiz 1
1.
2.
3.
4.
Time allowed: One hour
Total number of problems: 3
Total marks available: 25
This paper may not be retained by candidates
S
Appendix A list of possibly relevant equations
Complex number:
Eulers formula: ej = cos + j sin
Fundamental period of a periodic signal:
Continuous-time sinusoidal of the form x(t) = A cos(t + ): T0 = 2/
Discrete-time sinusoidal of the form x[n] = A
Systems in Time Domain
Chapter Intended Learning Outcomes:
(i)
Classify different types of systems
(ii)
Understand the property of convolution and
relationship with linear time-invariant system
(iii)
Understand the relationship between differential
equati
Fourier Series
Chapter Intended Learning Outcomes:
(i)
Represent continuous-time
Fourier series
(ii)
Understand the properties of Fourier series
(iii)
Understand the relationship between Fourier series
and linear time-invariant system
H. C. So
Page 1
peri
Discrete-Time Fourier Transform
Chapter Intended Learning Outcomes:
(i)
Represent discrete-time signals using discrete-time
Fourier transform
(ii)
Understand the properties of discrete-time Fourier
transform
(iii)
Understand the relationship between discr
Tutorial 3 on Week 4
1. Compute the output
if the input is
and
the linear time-invariant system impulse response is
with
. Is the system stable? Why? Is
the system causal? Why?
2. Determine
where
and
are
and
H. C. So
Page 1
Semester B 2016-17
3. Compute
t
Fourier Transform
Chapter Intended Learning Outcomes:
(i)
Represent continuous-time aperiodic signals using
Fourier transform
(ii)
Understand the properties of Fourier transform
(iii)
Understand
the
relationship
between
transform and linear time-invariant