Structure and Interpretation of signals and systems
EECS 20

Fall 2009
EECS 20. Final Exam Solution. December 21, 2004. 1. 15 points, 3 points each part Give precise denitions of the following: (a) The space Images of all 600 900 images with pixel values in cfw_0, 1, , 2
Structure and Interpretation of signals and systems
EECS 20

Fall 2009
EECS 20. Midterm No. 2, Solution November 19, 2004.
1. 20 points A system is described by the difference equation
y (n) = x(n) + x(n 1) + 0.5y (n 1).
(1)
(a) 7 points Obtain the [A, b, cT , d] represe
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Graphs and
Graph Terminology
UM EECS 203 Fall 2016
Lecture 20
Partial Orders
A relation R on a set S is called partial order
when R is:
Reflexive
Edges (1,1), (2,2), etc.
the divides partial
Antisymme
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Graphs: Isomorphisms and
Connectivity
UM EECS 203 Fall 2016
Lecture 21
Announcements
Reminder: No discussion sections on
Thanksgiving and day after. You can attend a
Monday or Tuesday section of your
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Equivalence Relations
& Partial Orders
UM EECS 203 Fall 2016 L19
First: Review of L18
Closures
The closure of a relation
where A=n,
with respect to a property (reflexive, transitive, symmetric, etc.
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Euler and Hamilton Paths
+ Shortest Paths
UM EECS 203 Fall 2016
Lecture 22
Graphs
A graph G = (V,E) consists of
a nonempty set V of vertices (or nodes),
and a set E of edges.
Each edge is associated
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Asymptotic Notation
and the Complexity of Algorithms
UM EECS 203 Fall 2016
Lecture 24
Fall 2016
UM EECS 203 L24
1
Continuing From Last Lecture
Key questions to ask about an algorithm:
Is it correct?
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Divide and Conquer
and the Master Theorem
UM EECS 203
Fall 2016
Lecture 26
Dynamic Programming
Recursion in algorithms: Dynamic
Programming
D.P. is a very powerful algorithmic technique.
(1) Define wh
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
L25: Recursion and
Recurrence Relations
UM EECS 203 Fall 2016
Lecture 25
Announcements
This week: lectures on advanced algorithms,
HW13 due tomorrow, ungraded HW14 (on next
weeks lectures) out today a
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Algorithms
UM EECS 203 Fall 2016
Lecture 23
Announcements
This week: lectures on algorithms, HW12 due
tomorrow, discussion sections emphasize HW13
Next week: lectures on advanced algorithms,
HW13 du
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Relations
UM EECS 203 L17 Fall 2016
Announcements
The second midterm is next Monday night!
A sample exam is posted, as is the cheat sheet.
You will also get cheat sheet from Exam1
It is important that
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
Homework1
AbhijitGhumanasghuman
September14th,2016
Section1.1:Problem12
a. Ifyouhavetheflu,thenyoumissthefinalexamination.
b. Ifandonlyifyoudonotmissthefinalexamination,thenyoupassthecourse.
c. Ifyou
Structure and Interpretation of signals and systems
EECS 20

Spring 2005
L18: More Relations
UM EECS 203 Fall 2016
Review: Functions & Relations
the enrolledindiscussionsection function
A function maps each element
of the domain D to some element
in the codomain C.
Ali