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
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
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
EE3210 Signals and Systems
Tutorial 1
Problem 1: A continuous-time signal x(t) is shown in the gure below.
x(t)
2
1
-2
0 1
-1
2
-1
t
Sketch and label carefully the signal x(4 t/2).
Problem 2: Determine and sketch the even and odd parts of the signal depic
Solutions to EE3210 Tutorial 1 Problems
Problem 1: The signal x(4 t/2) is obtained from x(t) as below:
x(t)
2
1
-2
0 1
-1
2
-1
t
Time shift
x(4 t)
x(t + 4)
Time reversal
2
x(4 t / 2)
Time scaling
2
1
1
1
6
-6
-5
-1
2
-4
-3
-2
t
2
3
4
12
5
-1
1
t
4
6
8 10
EE3210 Signals and Systems
Tutorial 2
Problem 1: Determine if each of the following two signals is periodic. If the signal is
periodic, determine its fundamental period.
(a) x(t) = [cos(2t )]2
3
(b) x[n] = cos( n) cos( n)
2
4
Problem 2: Determine if each
Solutions to EE3210 Tutorial 2 Problems
Problem 1:
(a) Using the trigonometric identity
cos2 =
1 + cos(2)
2
we obtain
2 1 + cos(4t 2 )
3
=
.
3
2
Thus, the signal is periodic with T0 = 2/ = 2/4 = /2.
cos 2t
(b) Using the trigonometric identity
1
cos cos
Solutions to EE3210 Tutorial 3 Problems
Problem 1:
(a) The system is not causal. For example, when n = 1, we have y[1] = x[2].
(b) The system is stable. For 0 < B < , given |x[n]| B for all n, we have |x[2n]| B
for all n, and therefore |y[n]| B for all n.
EE3210 Signals and Systems
Tutorial 3
Problem 1: Consider the discrete-time system whose input x[n] and output y[n] are
related by
y[n] = x[2n].
Determine which of the following properties hold for this system:
(a) Causal
(b) Stable
(c) Time invariant
(d)
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)
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
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
Solutions to EE3210 Quiz 2 Problems
Problem 1:
(a) Given that h[n] = [n + 1] [n], we have
1,
n = 1
h[n] = 1, n = 0
0,
elsewhere.
Thus:
System A is not memoryless, because h[n] = 1 for n = 1 = 0.
System A is not causal, because h[n] = 1 for n = 1 < 0.
S
8&(Vbll04 (SC MFJ+FM
Name:
Student Number #:
City University of Hong Kong E
Department of Electronic Engineering if:
EE 3210 Systems and Signals
Midterm Quiz 2
NOTE: 1.
1. This is a 1.5-hour, open book, open notes midterm test.
2. There are 4 proble
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
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 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
Tutorial 4
Problem 1: Consider a discrete-time LTI system with unit impulse response h[n] =
4n u[2 n]. Use the convolution sum to nd the response y[n] of the system to the input
x[n] = ( 1 )n u[n 4].
2
Problem 2: Consider a cont
Fourier Series
Systems
2-1
Outline
3.1 LTI Systems: System
Characterizations
3.2 Exponential Fourier Series
3.4 Properties of Fourier Series
Systems
2-2
Input-Output Relationship of LTI Systems
Continuous-Time
Systems
h
x(t)
y(t)
y (t ) x( )h(t )d
Disc