Todays Lecture
Review of signals and spectral analysis
Signal representation
Introduction of linear time-invariant (LTI)
system
Fourier series and Fourier transform
ENGG2310A Principle of Commun. Systems
1
Introduction
Information: Voice, data, image, vid
1
Analog Communications
Amplitude Modulation (AM)
Frequency Modulation (FM)
Lecture 3
Principles of Communications
2
Radio broadcasting
30-300M Hz
SOURCE
Source
Transmitter
Analog baseband signal
Lecture 3
Transmitted
signal
Channel
Received
signal
Rec
1
Lecture 8. Digital Communications
Part III. Digital Demodulation
Binary Detection
M-ary Detection
Lecture 8
Principles of Communications
2
Digital Communications
Analog Signal
Bit sequence
0001101110
t
Source
SOURCE
A-D
Conversion
Digital
Baseband
Mod
EE 3008. Fourier Transform Tutorial Questions
Q1) The Fourier transform (also called the spectrum) of x(t) is defined
as
x(t )e
X( f )
j 2ft
dt
Find the Fourier transform of the following function. Draw its
magnitude.
A g(t)
t
0
-T/2
T/2
T
Q2) Draw the
2.C. Fourier Transform
1
Formal Definition of Spectrum
Given a time-domain signal s(t), its Fourier transform is defined as follows.
S( f )
Fourier transform:
s t e j 2 ft dt
S(f) is referred to as the Fourier spectrum (or simply spectrum) of s(t).
Somet
2.B. Fourier Series
1
Fourier Series
We start our discussion with Fourier series analysis. Please review your notes on
this topic. (I presume that you have learned it before.) The different between a
Fourier series and a Fourier transform is as follows:
Communication Systems
Chapter 1
Introduction
1
Contacts and Notes
Professor Ping Li
Telephone: 3442 9574
Office: G6417
Email: [email protected]
EE3008 has co-requisites:
EE3210 Signals & Systems or
EE3118 Linear Systems and Signal Analysis
Linear syst
Q1)
EE 3008. Random Process Tutorial Solutions
All possible outcomes are listed below,
HHH HHT HTH HTT THH THT TTH TTT
There three events with two heads and one tail, i.e.,
HHT HTH THH
Therefore the probability is 3/8.
3/4
2
3/4
0.5
Prcfw_0.5 x 3 / 4
Prc
Chapter 5
Digital Bandpass Modulation and
Demodulation Techniques
1
Motivations and Goals
In a radio system, the signals are often modulated to radio frequency (typically
at very high frequency range). For this reason, we will study the modulation
and dem
EE3008 Principles of Communications: Quiz Questions
1) Consider a delta function d(t). What is d(t-5)?
a)
A signal that is zero at t=5.
b)
A signal that is nonzero at t>5.
c)
A signal that is nonzero at t=5 and zero everywhere else.
d)
A signal that is no
EE3008 Quiz 3
(12:05-1:35pm, Apr. 12, 2017)
Question 1 (30 marks)
An audio signal with bandwidth 10kHz is sampled at the Nyquist rate, quantized into 1024 levels, and
transmitted by using 4-ary PAM with transmission power 10 W over an AWGN channel with 90
EE3008 Assignment
Due Date: Apr. 13, 2017
Q1. Consider a binary PAM system with a probability of p to transmit a 1 and probability of 1p to transmit a 0.
1. Derive the optimal threshold as a function of p.
2. Discuss the optimal threshold when p<1/2, p>1/
Q1. Consider a binary PAM system with a probability of p to transmit a 1 and probability of 1p to transmit a 0.
1. Derive the optimal threshold as a function of p.
2. Discuss the optimal threshold when p<1/2, p>1/2 and p=1/2.
Solution
In the lecture notes
EE3008 Quiz 3
X
(12:05-1:35pm, Apr. 12, 2017)
Question 1 (30 marks)
An audio signal with bandwidth 10kHz is sampled at the Nyquist rate, quantized into 1024 levels, and
transmitted by using 4-ary PAM with transmission power 10 W over an AWGN channel with
EE3008 Quiz 2
(12:05-1:35pm, Mar. 22, 2017)
Question 1 (24 marks)
Consider the following two random signals:
a. X(t)=X, and X is a Gaussian random variable with mean 0 and variance 1.
b. X (t ) n Z n v(t nT0 ) , which is shown in Fig. 1, where Z n Z is a
1.
A (parallel) B (direct) C (pilot) D (phased)
2. Class BIP
A 140.128.5.255 B 140.128.5.128 C 140.128.5.254 D 140.128.5.1
3. RSA
A B C D
4.
A B C D
5. (recursion)
A (tree) B (queue) C (linked list) D (stack)
6. C
EE 3008. Baseband Modulation Tutorial Questions
Q1) A sequence 01 is represented by the following signal. Find the
energy spectrum of this signal.
s01(t)
A
-A
2
t
Q2) A sequence 11 is represented by the following signal. Find the
energy spectrum of this s
Q1)
EE 3008. Random Process Tutorial Questions
A coin is tossed three times. What is the probability of two heads and one tail?
Q2)
Given that the random variable X has density function
0 < x <1
2x
f ( x)
otherwise
0
Find Pr(0.5<x<3/4) and Pr(-0.5<x<0.5)
EE 3008. Fourier Transform Tutorial Solutions
Q1) This is already given in the notes. We repeat the result below.
G( f )
g (t )e
j 2 ft
T /2
dt
Ae j 2 ft dt
T / 2
e j 2 ft
A
j 2 f
t T / 2
t T / 2
e j fT e j fT
A
j 2 f
e j fT e j fT 1
A
j2
f
A sin(
EE3008 Principles of Communications: Quiz Questions
1)
Consider a rectangular pulse of duration 0.001s. We use its first zero in the
spectrum as the bandwidth. We design a filter to process the signal before transmission.
What is the type of filter requir
Chapter 8
Analog-to-Digital and Digital-to-Analog
Conversion
1
8.A Overview
2
Introduction
Most digital systems, such as phones and TV, are actually used to deliver
analogue signals. (After all, we are human beings and we can only see and
listen to analog
CHAPTER 2
1.
(a)
Find the correct values of
0, cos(0.5) and
(b)
cos(0.5)
(t ) cos tdt , (t 0.5) cos tdt
1, cos(0.5) and
(c)
cos(-0.5)
2
2.
Find the correct values of
(t
3
and
(t ) cos(t 0.5)dt
, cos(0.5) and
(d)
cos(0.5)
3) (t 2)dt and
1
3
(t
3
0, co
EE 3008. AD-DA Conversion Tutorial Questions
Q1) Consider a multi-user PCM system. For circuit speed limitation, a pulse requires a minimum
duration of 1s. If the input bandwidth of each user (before sampling) is 3kHz and the
quantization level is 16, cal
Chapter 5
Digital Bandpass Modulation and
Demodulation Techniques
1
Motivations and Goals
In a radio system, the signals are often modulated to radio frequency (typically
at very high frequency range). For this reason, we will study the modulation
and dem
Chapter 3
Digital Baseband Modulation Techniques
1
Outline
In a modern communication system, the basic unit of information is bit.
Mathematically, a bit represents either 0 or 1. The goal of a communication
system is to tell the receiver which one, i.e.,
Supplementary Material to Chapter 4
Probability and Random Process
1
Outline
Due to the presence of random noise during transmission, any digital
communication system is subject to errors. Such errors are random in nature.
Probability theory is an useful
Chapter 4
Receiver Design
1
Overview
So far we have considered the frequency domain properties of digital systems.
In this chapter we consider transmitting such signals through a noisy channel.
We first focus on the baseband, which refers to the transmiss
Chapter 2
Frequency Domain Analysis
1
2.A. Basic Concepts
2
Frequency Domain Analysis
Frequency domain analysis can also be called spectrum analysis. It is a
basic tool for engineering. However, it is not a subject of this course. Rather,
you will learn t
EE 3008. Chapter 6 Analog Modulation Tutorials
AM Questions
Q1. A modulating signal f(t) (with Fourier transform F(f) is applied to a double-sideband suppressedcarrier modulator operating at a carrier frequency of 200 Hz. Sketch the spectral density of th
EE 3008. Baseband Modulation Tutorial Solutions
These are two delay factors.
Q1) Using the shift property, we have
S01 ( f ) A sin c( f ) e j f e j 3 f
2
2
Common factor =1.
2
A2 2sinc2 ( f ) e j f e j f e 2 j f
This is the spectrum
of
A
2
A2 2sinc2 (