Digital Signal Processing
Exam 2
Last name
First name
SID
You have 1 hour and 45 minutes to complete this exam.
The exam is closed-book and closed-notes; calculators, computing and communication
devices are not permitted.
No form of collaboration betwe
Digital Signal Processing
Exam 2
Last name
First name
SID
You have 1 hour and 45 minutes to complete this exam.
The exam is closed-book and closed-notes; calculators, computing and communication
devices are not permitted.
No form of collaboration betwe
COMP171
Fall 2005
Depth-first search
Graph / Slide 2
Depth-First Search (DFS)
DFS is another popular graph search strategy
Idea is similar to pre-order traversal (visit children
first)
DFS can provide certain information about
the graph that BFS cannot
It
Tree Searching
Tree searches
A
B
D
C
E
F
H
L
M
I
N
O
G
J
P
K
Q
A tree search starts at the root
and explores nodes from there,
looking for a goal node (a
node that satisfies certain
conditions, depending on the
problem)
For some problems, any goal
node
DepthFirstSearch
A
B
D
E
C
DepthFirstSearch
1
OutlineandReading
Definitions(6.1)
Subgraph
Connectivity
Spanningtreesandforests
Depthfirstsearch(6.3.1)
Algorithm
Example
Properties
Analysis
ApplicationsofDFS(6.5)
Pathfinding
Cyclefinding
Depth-First Search
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
front
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
enqueuesourcenode
front
A
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
dequeuenextvertex
front
A
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
visitneighborsofA
f
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
front
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
enqueuesourcenode
front
A
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
dequeuenextvertex
front
A
FIFOQueue
BreadthFirstSearch
B
E
C
D
F
A
G
H
I
visitneighborsofA
f
BreadthFirstSearch
L0
L1
B
L2
2004Goodrich,Tamassia
A
C
E
BreadthFirstSearch
D
F
1
BreadthFirstSearch
Breadthfirstsearch
(BFS)isageneral
techniquefortraversing
agraph
ABFStraversalofa
graphG
Visitsalltheverticesand
edgesofG
DetermineswhetherGis
connected
Heapsort
Why study Heapsort?
It is a well-known, traditional sorting algorithm
you will be expected to know
Heapsort is always O(nlogn)
Quicksort is usually O(nlogn) but in the worst case
slows to O(n2)
Quicksort is generally faster, but Heapsort is bette
EE562: Digital Signal Processing
Time domain
1. Discrete-time systems
2. Convolution
3. Linear Constant-Coefficient Difference
Equations (LCCDEs)
2006
1
1. Discrete-time systems
A system converts input to output:
x[n]
DT System
y[n]
cfw_y[n] = f (cfw_x[n]
Introduction to the z transform
Page 1 of 1
History of the z transform
The z transform is unusual, in being named after a letter of the alphabet rather than a famous
mathematician. The Fourier transform is named after Baron Jean Baptiste Joseph Fourier (1
Discrete-Time Systems
A discrete-time system processes a given
input sequence x[n] to generates an output
sequence y[n] with more desirable
properties
In most applications, the discrete-time
system is a single-input, single-output
system:
x[n]
1
Input s
The z-Transform
EE406-041 Discrete-Time Signal Processing
The z-Transform
q The discrete-time Fourier transform provides a frequency domain representation of
discrete-time signals and LTI systems. However, because of the convergence condition, in
many cas
EE406 Discrete-Time Signal Processing
Introduction
Introduction
Signal
q A signal is a function of independent variables such as time, distance, position,
temperature, pressure.
q A signal carries information.
q Examples of signals are speech, music, imag
Discrete-Time Signals:
Time-Domain Representation
Signals represented as sequences of
numbers, called samples
Sample value of a typical signal or sequence
denoted as x[n] with n being an integer in
the range n
x[n] defined only for integer values of n
The z-transform
See Oppenheim and Schafer, Second Edition pages 94139, or First Edition
pages 149201.
1 Introduction
The z-transform of a sequence xn is
X.z/ D
1
X
n
xnz
:
nD 1
The z-transform can also be thought of as an operator Zfg that transforms a
se
Signals and Signal Processing
Signals play an important role in our daily
life
A signal is a function of independent
variables such as time, distance, position,
temperature, and pressure
Some examples of typical signals are shown
next
EE 562
1
Examples
The Frequency Response Function
Recall for an LTI system: y (n) = h(n) x(n).
Suppose we inject a complex exponential into the LTI
system:
h(k)x(n k)
y (n) =
k=
jn
x(n) = Ae
Note: we consider x(n) to be comprised of a pure
frequency of rad/s
The Frequency
LTI Discrete-Time Systems in
the Transform Domain
An LTI discrete-time system is completely
characterized in the time-domain by its
impulse response sequence cfw_h[n]
Thus, the transform-domain representation
of a discrete-time signal can also be equall
EEE4001F: Digital Signal Processing
Class Test 1
27 March 2006
SOLUTIONS
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Determine
EEE4001F: Digital Signal Processing
Class Test 2
15 May 2006
SOLUTIONS
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Consider th
EEE4001F: Digital Signal Processing
Class Test 1
27 March 2006
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Determine the impul
EEE4001F: Digital Signal Processing
Class Test 2
15 May 2006
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Consider the z-transf
EEE401F: Digital Signal Processing
Class Test 2
25 May 2005
SOLUTIONS
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) A signal has
EEE401F: Digital Signal Processing
Class Test 1
7 April 2005
SOLUTIONS
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) A system ha