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
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing,
Course Convener: Prof. E. Ambikairajah
Tutorial-Lab Coordinator: Dr. Phu Le
Tut_Lab 3 (Chapters: 6, 7 & 8), Session 1, 2016
Q1 (a) Prove the following properties of li
ELEC3104: Digital Signal Processing Lab
Professor Eliathamby Ambikairajah,
Head of School
Electrical Engineering and Telecommunications
UNSW Australia
Programming in MATLAB
MATLAB provides an on-line help
using the help command
For example, to find inform
ELEC3104: Digital Signal Processing
Session 1, 2016
The University of New South Wales
School of Electrical Engineering and Telecommunications
IMPULSE RESPONSE, FREQUENCY RESPONSE AND POLES/ZEROS OF
SYSTEMS
INTRODUCTION
Impulse Response and Frequency Respo
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing,
Course Convener: Prof. E. Ambikairajah
Tutorial-Lab Coordinator: Dr. Phu Le
Tut_Lab 1 (Chapters: 1, 2 & 3), Session 1, 2016
Q1
(a)
The discrete-time signal x[n] is def
The University of New South Wales
School of Electrical Engineering and Telecommunications
Sample Final Exam Paper
Candidates should attempt ALL questions
1.
Time allowed: 3 hours.
2.
The paper contains 5 questions.
3.
The questions are NOT of equal value.
PROBLEM SHEET - 3
Q1)
Draw the block diagrams of the following system in both Direct form I and Direct Form II.
w[n ] = 0.5w[n 1] + 7 x[n ]
y[n ] = 2 w[n ] 4 w[n 1]
(Note: x[n] is the input and y[n] is the output)
Q2)
Consider the cascade of the following
ELEC3104: Digital Signal Processing
PROJECT S1, 2017
This project is an important part of the laboratory component of this course and is designed to
focus on the application of the theory you learn in the lectures and tutorials to practically
implement DS
PROBLEM SHEET - 2
Q1) An analogue signal x(t) = sin(480t)+3sin(720t) is sampled 600 times per
second.
(a) Determine the Nyguist sampling rate for x(t).
(b) Determine the folding frequency (or half the sampling frequency).
(c) What are the frequencies, in
The University of New South Wales
School of Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing
Assignment, Session 1, 2017
ATTACH THIS PAGE TO THE FRONT OF YOUR ASSIGNMENT
1.
2.
3.
4.
5.
6.
7.
Assignment is due on the 9th Ma
Matlab Exercises
Matlab Exercises for Chapter 1
Matlab Exercises for Chapter 2
Matlab Exercises for Chapter 3
Matlab Exercises for Chapter 4
Matlab Exercises for Chapter 5
Matlab Exercises for Chapter 6
Matlab Exercises for Chapter 7
Matlab Exercises for
UNSW Electrical Engineering and Telecommunications
ELEC3104: Digital Signal Processing,
Course Convener: Prof. E. Ambikairajah
Tutorial-Lab Coordinator: Dr. Phu Le
Tut_Lab 2 (Chapters: 4 & 5), Session 1, 2016
Q1
(a) By determining the transfer functions o
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 =
()
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
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
Fourier Transform Equations
Matthew Davis
[email protected]
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
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
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
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
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
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 ()
PROBLEM SHEET - 6
Q1)
A speech signal is sampled with a sampling period of 125ms. A frame of 256 samples is
selected and a 256 point DFT is computed. What is the spacing between the DFT values in
Hz.
Ans: 0.03125Hz
Q2)
Compute the N-point DFT, [ ] of the
PROBLEM SHEET - 4
Q1)
Find the inverse of each of the following z-transforms:
a)
X ( z) =
1
3 ,z >1
+
2
1
1
1
1 z 1 1 z
3
2
n
n0
Ans: x[n] = 2(2) n u[n] (1) n u[n]
n0
2
b)
X (z) =
1
1 + 3 z 1 + 2 z 2
n
Ans: x[n ] = 1 u [n ] + 3 1 u [n ]
3
z >2
Q2)
Show th
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
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
PROBLEM SHEET - 8
Q1)
a)
A second-order analogue band pass filter with an s-domain transfer function is given
by
H (s) =
(1)
bps
s2 + b p s + p2
Where p and bp are the centre frequency and bandwidth of the filter; respectively,
both expressed in rad/s. By
PROBLEM SHEET - 5
Q1)
a)
Show that both digital filters given below have the same magnitude response:
y [n ] =
i)
m
c x[n i ]
ii)
i
y [n ] =
i= m
m
c x[n m i ]
i
i=m
y[n] = output; x[n] = input; ci = coefficients
b)
Compute the 3dB bandwidth of the foll
ELEC3104: Digital Signal Processing
Chapter 3: Discrete Time Systems
3.1 Introduction
A discrete - time system is a device or algorithm that operates on a discrete-time signal
called the input or excitation according to some well-defined rule, to produce
ELEC3104: Digital Signal Processing
Chapter 1: Signals and Spectra
1.1 Introduction
The interpretation and modification of signals plays a key role in almost all systems and in
most cases this takes the form of digital signal processing. i.e., the signals
ELEC3104: Digital Signal Processing
Chapter 2: Discrete Time Signals
2.1 Discrete Signals
Digital Signal Processing (DSP) is a rapidly developing technology for scientists and
engineers. In the 1990s the digital signal processing revolution started, both