ECE 130B Midterm Solutions
Exercise 1:
y n 1 6 y n 9 y n 1 0
y n 6 y n 1 9 y n 2 0
The characteristic equation is as follows:
z2 6z 9 0
z 3 z 3 0
z = 3, 3
Distinct Solutions: 3n and n3n
Therefore, the homogenous solution is:
n
n
yh n c1 3 c2 n 3
Exercise
ECE 130B HW 8 Solutions
Exercise 1:
X (! ) = DTFT cfw_x [n ] =
"
$ x [n]e
# j! n
n = #"
2!
$j
kn
2! &
%
X '" =
k ( = + x [n ]e 2 N
2 N * n=$#
)
#
2!
#j
kn
2! % N #1
$
2N
X &" =
k ' = * x [n ]e
(since x[n] = 0 for n < -N or n N)
2 N ) n=# N
(
x p [n ] =
2
ECE130C
April 15, 2015
Homework 3
Due date: April 22, 2015.
Reading assignment. Chapter 2 of the text book. It is essential that you look through the problems
at the end of each section. Both, the midterm and finals, will draw freely from these sets of pr
ECE130C
April 30, 2015
Homework 5
Due Date: May 6, 2015 at the homework box.
Reading assignment. Chapter 3 of the textbook.
Problem 1. Project b = (0, 3, 0) onto each of the orthonormal vectors a1 = (2 / 3, 2 / 3, 1 / 3) and a2 =
(1/3, 2/3, 2/3), and then
ECE130C
April 9, 2015
Homework 2
Due date: April 15, 2015
Reading assignment: Chapter 1. Remember to browse through all the problems in this chapter.
Start reading Chapter 2.
Inverse. The matrix B is said to be the inverse of the matrix A if B A = I and A
ECE130C
April 22, 2015
Homework 4
Due date: April 29, 2015.
Reading assignment. Chapter 2 of the text book. It is essential that you look through the problems
at the end of each section. Both, the midterm and finals, will draw freely from these sets of pr
ECE130C
March 29, 2015
Homework 1
Due Date: April 8, 2015, by 5p.m.
Reading assignment. The best way to learn this subject is to read the text book and attempt the
problems at the end of each section. Both the midterm and final will freely draw from the p
ECE130C
05/10/2015
HOME WORK 6
Due date: May 20, 2015
Reading assignment: Chapters 4 and 5 of the text book.
Problem 1. Find the value of b1 that minimizes
2
2
2
kb1 sin x cos xk =
(b1 sin x cos x) dx.
0
Problem 2. Find the fourth Legendre polynomial. It
ECE130C
March 27, 2015
Project 2
As part of this class students will form teams that will try and build a communications system using an
acoustic link. The goal of the overall project is to transmit data from one laptop to another using nothing
but the bu
ECE130C
March 27, 2015
Project 1
As part of this class students will form teams that will try and build a communications system using an
acoustic link. The goal of the overall project is to transmit data from one laptop to another using nothing
but the bu
ECE130C
May 25, 2011
Homework 8
Due date: None.
Reading assignment. Chapter 4 and 5 of the textbook.
Finals. Sections 1.11.6, 2.12.4, 3.13.4, 4.14.3, 5.15.3. Make sure that you look at the problems in
these sections and in the review sections of these cha
ECE130C
April 6, 2011
Homework 2
Due date: April 13, 2011
Reading assignment: Chapter 1. Remember to browse through all the problems in this chapter.
Start reading Chapter 2.
Inverse. The matrix B is said to be the inverse of the matrix A if B A = I and A
ECE130C
April 13, 2011
Homework 3
Due date: April 20, 2011 by 5:00p.m.
Reading assignment. Chapter 2 of the text book. It is essential that you look through the problems
at the end of each section. Both, the midterm and nals, will draw freely from these s
ECE130C
April 20, 2011
Homework 4
Due date: April 27, 2011 by 5p.m.
Reading assignment. Chapter 2 of the text book.
Problems are from chapter 2.
Problem 1. Find a basis for the plane x 2 y + 3z = 0 in R3. Then nd a basis for the intersection of
that plane
ECE130C
May 4, 2011
Homework 6
Due date: May 11, 2011.
Midterm. The midterm is on Monday, May 16. Problems from the following sections of the textbook
(fourth edition) will appear: 1.11.6, 2.12.4, 3.13.4. Also problems in the Review Exercises of chapters
ECE130C
May 18, 2011
Homework 7
Due date: May 25, 2011.
Reading assignment. Chapter 4 of the textbook.
Problem 1. If A is an n n matrix and det A = 2, nd det
det (A1).
Problem 2. Using L U factorizations, nd the determinants
1 2 2 0
2 3 4 1
and
1 2 0 2