School of Electrical Engineering & Telecommunications
Faculty of Engineering
ELEC 3104
Digital Signal Processing
Summer Session, 2014
ELEC3104: Digital Signal Processing
COURSE INTRODUCTION Summer Session, 2014
Course Staff
Mentor/ Tutor:
Dr. Karen Kua,
R
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing
Mock Lab Exam, Session 1, 2016
This is an open book exam - Duration: 90 minutes
Analytical Questions:
1. Let a causal linear time invariant discrete-time system be char
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing
Mock Lab Exam, Session 1, 2016
This is an open book exam - Duration: 90 minutes
Analytical Questions:
1. Determine the response [] of a system characterised by the impu
ELEC3104 Digital Signal Processing
Lecture Notes
Professor Eliathamby Ambikairajah
References
Course Outline
Lecture Notes
Chapter 1: Signals and Systems
Chapter 2: Digital Signal Processing Fundamentals
Chapter 3: Discrete-Time Systems
Chapter 4: Introdu
Solution
x [n] h [n]
=
x [k] y [n k]
y [n] =
Y ()
=
k=
n=
=
=
=
=
=
y [n] ejn
(
n=
)
x [k] y [n k] ejn
k=
x [k] y [n k] ejn
k= n=
k=
k=
n=
x [k] ejk
x [k] ejk
(
n=
y [n k] ej(nk)
y [n] ejn
n=
k=
=
y [n k] ejn
x [k]
) (
jk
x [k] e
)
y [n] e
jn
n=
k=
= X ()
Edmund Li
FOURIER TRANSFORM
The Fourier series enables us to represent a periodic function as the sum of sinusoids and to obtain the
frequency spectrum from the series. For signals which are not periodic, we can use the Fourier transform to
convert a func
Edmund Li
SIGNALS & SPECTRA
The use of Digital Signal Processing (DSP) is growing exponentially and we have seen its application in control
and power systems, biomedical engineering, instrumentation, automotive engineering, telecommunications,
mobile comm
Forms
Direct Form I
Feed forward before feed back.
Direct Form II
Feed back before feed forward, with uncombined delays.
Canonical
Feed back before feed forward, then combine the delays.
The denition of Canonical is the form which contains the minimum num
Edmund Li
FOURIER SERIES: CONTINUOUS TIME PERIODIC SIGNALS
According to the Fourier Theorem, any practical periodic function of fundamental frequency 0 = 20 rad/s
can be expressed as an infinite sum of sinusoidal functions that are integral multiples of 0
Fourier Transform Equations
Matthew Davis
m.davis@student.unsw.edu.au
More notes for ELEC3104 and other subjects can be found at
www.elsoc.net/notes.php.
Discrete Time Fourier Transform (DTFT)
From discrete time to continuous frequency
Equation 3.10 in
For an order n normalised low pass Butterworth lter, the poles what you
get if you spread 2n poles evenly around the unit circle in the s plane, and
then ignore the ones in the right half s plane. For odd n there is a pole at
s = 1. For even n there are
When solving problems with this, dont sub in
it as is and it will cancel out later.
2
T
into the calculator. Leave
No aliasing occurs, but this method requires prewarping.
To prewarp a desired cuto frequency c to get an analogue cut o
frequency:
c =
2
Linear Phase Filters
A lter has a linear phase response if () = b a.
The coecients must be symmetric
h [m + n] = h [m n]
(1)
z m H (z) = z m H z
(1)
H (z) = H z
The zeros of a linear phase system must occur in reciprocal pairs
Phase Delay
Tp =
()
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing
Mock Lab Exam, Session 1, 2016
This is an open book exam - Duration: 90 minutes
Before answering the exam, login to Moodle to download the file signal.wav, save it to M
ELEC3104 Digital Signal Processing
Lecture Notes
Professor Eliathamby Ambikairajah
Course Outline
References
Lecture Notes
Chapter 1: Signals and Systems
Chapter 2: Digital Signal Processing Fundamentals
Chapter 3: Discrete-Time Systems
Chapter 4: Introdu
Lab Exercises 2
ELEC 3104, Session 1 2015
What are P-files?
1. p-files are like m-files (scripts or functions) in MATLAB that are encrypted.
2. You cannot see the contents of a p-file but you can run them like you would run
an m-file
3. In this lab you wi
ELEC3104: Digital Signal Processing
MATLAB INTRODUCTION
INTRODUCTION
Developed by MathWorks
MATLAB stands for MATrix LABoratory
Numerical computing environment & programming
language
Allows matrix manipulations
Plotting data
Implementation of algori
Question 1:
A difference equation for a paticular filter is given by:
y[n]=0.12x[n] - 0.1x[n-2] + 0.82x[n-3] 0.1x[n-4] + 0.12x[n-6]
(i)
(ii)
Find the impulse response of the above filter
Using minimum number of multiplications, draw an implementation (i.e
ELEC3104
Digital Signal Processing
Course Outline Semester 1, 2015
Course Staff
Course Convener:
Prof. E. Ambikairajah, Room G8, e.ambikairajah@unsw.edu.au
Course & Lab Coordinator:
Tutorials:
Dr. Phu Le, Room 306, ngoc.le@unsw.edu.au
Prof. Andrew Dempste
Interactive Calculations
Introduction to
Matlab is interactive, no need to declare variables
> 2+3*4/2
> V = 50
> V + 2
> V
Ans =
52
> a=5e-3; b=1; a+b
Most elementary functions and constants are already
defined
> cos(pi)
> abs(1+i)
> sin(pi)
19-20 March
Nine billion devices and counting.
For almost 50 years, Dolby has led the way in developing innovative and amazing entertainment products and
technologies used by consumers and professionals worldwide. Innovations from Dolby can be heard in
consumer audio
Lab Exercises 1
ELEC 3104, Session 1 2015
PART 1
Write a function in MATLAB that accepts as inputs
(i)
A signal (array)
(ii)
The sampling frequency of the signal (value)
(iii) The number of points for a Discrete Fourier Transform (DFT)
(iv)
The frequency
Matlab Functions
1. Magnitude Spectrum
The following figure illustrates the relationship between number of FFT points (NFFT),
normalized frequency ( rad/sample) and sampling frequency (Hz).
Suppose that we have a sinusoid signal of 1 kHz sampled at 8 kHz
In the following system an analogue signal x(t) is sampled at a rate corresponding to a
sampling period of 1.25 millisecond to obtain a digital signal x[n] and then x[n] is
passed through the multi-rate system to produce the signal y[n].
(i)
(ii)
Determin
Lab Exercises 3 (Weeks 9-12)
ELEC 3104, Session 1 2015
Type load handel in MATLAB to load an Audio signal that you can use to test your
systems for this lab
According to Fourier theory, any time-domain signal can be represented as a sum of one or
more sin
Question 1 [15 marks]
(a) The impulse response, h[n], of a discrete time system is given in Figure 1. Sketch the
output signal, y[n], for the input signal, x[n], as given in Figure 1. [3 marks]
aqn
2 Figure 1
O 1 n
(b) (i) Show that the following system
Analogue Digital Equivalence
In past exams students have been asked to reproduce this proof. Doing so
requires rote learning the 2 magic substitutions.
Question
Prove that:
X () =
(
)
1
2
k= X + k
T
T
Solution
Using equation 8:
1
x (t) =
2
X () ejt d
=
S