ESE563

Digital Signal Processing

Course Overview
Course Information
Course : Digital Signal Processing
Code : ESE563
Credit Hour : 3
Semester : 6
Status : Elective
Contact Hour : 3 hours lecture, 1 hour tutorial
Synopsis : This subject introduces the principles of digital signal
processing. The students will be exposed to MATLAB software
to generate computer implementations of the techniques.
Teaching : Theories are covered through lectures, discussions, tutorials
Methodology and quizzes. Computer simulations via MATLAB will be used
when required.
Evaluation : 60% (Final examination)
40% (Test and quizzes)
Course Information
Course Outcomes (CO)
CO1 Able to illustrate computations and deduce conclusion in solving
difference equations using impulse response and z-transformation
method.
CO2 Able to apply DFT and FFT to any discrete signals formation for
frequency analysis observations.
CO3 Able to deduce system response from given specifications when
designing FIR and IIR filters.
Course Information
Programme Outcomes (PO)
PO1 Fundamental Apply knowledge of mathematics, science and
engineering fundamentals to the solution of
complex electrical engineering problems.
PO2 Problem Solving / Identify, formulate, research literature and
Specialisation analyse complex electrical engineering problems
reaching substantiated conclusions.
PO3 Design Ability to design solutions for complex electrical
engineering problems with appropriate
consideration for public health and safety,
culture, society, and environment.
Course Information
CO-PO Matrix
PO1 PO2 PO3
CO1 √
CO2 √
CO3 √

Recommended Textbook
• John G. Proakis, Digital Signal Processing: Principles, Algorithms &
Applications, 4th Ed., Prentice-Hall, 2007.
Course Information
Course Coordinator / Lecturer
(September 2018 – January 2019)

Dr. Megat Syahirul Amin Megat Ali MIET, AAE

Senior Lecturer
Centre for System Engineering Studies
Faculty of Electrical Engineering
Universiti Teknologi MARA

Room : T2-A16-13A
Telephone : 03-55436080
Email : megatsyahirul@salam.uitm.edu.my
ESE563
Digital Signal Processing
Concepts
Learning Outcomes (Week 1)
The students should be able to:
• Define CT and DT signals.
• Demonstrate the understanding on sampling and quantisation
concepts.
• Sketch and manipulate discrete signals.

(Slides were based on the original notes by Dr. Hadzli Hashim)

Introduction
• Continuous-Time (CT) Signal
A signal where its amplitudes are being represented at all time.
Usually, representation denoted by (.).

x(t)

Continuous signal
Introduction
• Discrete-Time (DT) Signal
A signal where its amplitudes are being represented only at certain
interval of time. Usually, representation denoted by [.].

x[n]

Discrete signal
Introduction
• Sampling
A process of measuring the amplitude of a CT signal at specific time
intervals, T which results in its conversion to DT signal.

x[n]

n
-4 0 14

Sampling of CT signal
Introduction
• Sampling
 Most common sampling is periodic

x[n]  x[nT ], -  n  

where T is the sampling period in second and n is number of

sequence.
 fs = 1/T is the sampling frequency in Hz.
 Sampling frequency can also be represented in rad/s where

 s  2f s
Introduction
• Sampling
Example:
What would happen if we chose the wrong sampling time as shown
in the figure below?

x(n)

1 Answer:
0.5 The original signal will
not be reconstructed
0 n
20 40 60 80 correctly.
-0.5

Discrete-time signal
Introduction
• Quantisation
A process of mapping different ranking levels of amplitudes with
either a continuous or discrete signal and provide opportunity for
encoding to binary digital signal.
x[n]
11111111

256 levels

000000000
Quantisation of discrete signal
Introduction
• Quantisation
 This process, also known as analogue-to-digital conversion, loses
information (by truncating or rounding the sample values). That
is, discrete-valued signals are always an approximation to the
original continuous-valued signal.
 Common practical digital signals are represented as 8-bit (256
levels), 16-bit (65,536 levels), 24-bit (16.8 million levels), 32-bit
(4.3 billion levels) and so on. Although any number of
quantisation levels is possible, not just powers of two.
Introduction
• Example:
Based on the figure below, describe the 4-bit binary representations
for amplitudes at y(0), y(4), y(7) and y(10).
Discrete-Time Signal
• Introduction
 The mathematical techniques for the analysis of linear time-
invariant systems for discrete-time systems are usually classified
as sequence domain method. It is because the input, output and
system model are all described using sequences of numbers.
 The output sequence is the response of the system to some
input sequence of values. We usually interpret these sequences
of numbers as indexed in time, although not necessary to do so.
 Discrete-time signal can be represented by x[n] where n is an
integer. Basic discrete-time signal can be written in two types of
sequences; unit impulse sequence and unit step sequence.
Discrete-Time Signal
• Unit Impulse
The unit impulse sequence δ[n] is defined as

1, n0
 [ n]  
0, n0

δ[n]

... ...
n
-3 -2 -1 0 1 2 3 4 5
Unit impulse
Discrete-Time Signal
• Unit Impulse
The unit impulse sequence δ[n]can also be represented as δ[n] = {…,
0, 0, 1, 0, 0, …}. Similarly, the shifted unit step sequence is defined as

1, nm
 [ n  m]  
0, nm

δ[n-m]

... ...
n
-3 -2 -1 0 1 2 m
Shifted unit impulse
Discrete-Time Signal
• Unit Step
The unit step sequence u[n] is defined as

1, n0
u[n]  
0, n0

u[n]

... ...
n
-3 -2 -1 0 1 2 3 4 5
Unit step
Discrete-Time Signal
• Unit Step
The unit step sequence u[n]can also be represented as u[n] = {…, 0,
0, 1, 1, 1, …}. Similarly, the shifted unit step sequence is defined as

1, nm
u[n  m]  
0, nm

u[n-m]

... ...
n
-3 -2 -1 0 1 m
Shifted unit step
Discrete-Time Signal
• Relationship between unit impulse and unit step
The unit step sequence u[n] and unit impulse sequence δ[n] by

 [n]  u[n]  u[n  1]

Preceding elaborations have also highlighted that

x[n] [n]  x[0] [n]

x[n] [n  m]  x[m] [n  m]

Hence, any sequence x[n] can be expressed as


x[n]   x[m] [n  m]
m  
Discrete-Time Signal
• Relationship between unit impulse and unit step
In general, x[n] can be expressed as

x[n]  f ( [n])

For example,

x[n]  {2,2,3,1,2}

x[n]  2 [n  2]  2 [n  1]  3 [n]   [n 1]  2 [n  2]

Discrete-Time Signal
• Relationship between unit impulse and unit step
Graphically, x[n] can also be shown as the figure below.

x[n]

n
-2 -1 0 1 2

x[n] = 2δ[n+2] - 2δ[n+1] + 3δ[n] - δ[n-1] + 2δ[n-2]

DT Signal Manipulations
• The basic concept of discrete-time signal manipulations is
similar to the continuous-time signal manipulations
Example:
Given a sequence of x[n] = {-1, 2, 1, 0, -2}. Sketch x[n] and produce
the new sequence for
a) x[n/3]
b) x[-n]
c) x[-n/3]
d) x[n-2]
e) x[-n/3 + 2/3]
DT Signal Manipulations
• The basic concept of discrete-time signal manipulations is
similar to the continuous-time signal manipulations
Example:
Given x[n] = e-n/2.u[n]. Produce the new sequence if
a) 2x[5n/3]
b) x[2n]
Questions and Answers …
TO BE CONTINUED …