ECE 310, Spring 2015 Semester
Homework 6
Chapter 5: Fourier Transforms using tables of pairs and properties
Instructions:
Solve the following problems using Table 5.1 (pp. 5-10 and 5-11) and Table 5.2 (pp. 5-21 and 5-22)
in our textbook. Specify what en
Is sin(4t) even, odd, neither even nor odd, or both even and odd?
odd
Is rect(t) even, odd, neither even nor odd, or both even and odd?
even
Is u(t) even, odd, neither even nor odd, or both even and odd?
neither
Is sgn(t) even, odd, neither even nor odd,
ECE 310: Discrete and Continuous Signals and Systems, Fall 2015 Semester
Homework #1 Solution
Complex number refresher (Chapter 1)
Solve the following by hand, showing all work.
1. Find the real part of /2 :
/2 = (/2) = cfw_cos(/2) + sin(/2) = cos(/2) =
sgn(t-2)
sgn(t 2)
a.)
5
I I I I I I I I I I I I I I I II4
I I I l l I I J J I J I | I J |3
III Illlm2
_
_
_
I | | | I I IIIIII |I|1
_
_
_
_
_
I I I I I I [1.1: 11.10
_
Illlrlrl -j_1
_ _ .
_ _
n _
p _
_ _
|.II|_.IIII_IIII IIIIQ
_ _
_
1. The convolution product of u(t) and u(t) is equal to:
a) tu(t)
b) tu(t)
tu(t)
d) - t u(t)
2. The convolution product of tu(t) and t2 u(t) is equal to:
amt)
b) M u(t)
c) #12 u(t)
d) %tu(t)
3. The convolution product of ezua) and ez'ua) is equal. to:
He
Find the Fourier Transform of 3" e"-:
a) 271: (5 (a) - 1) mo (a) + 1)
b) 27:(5(co+1)6(co1)
_é) zjsin<w>
5' - .-
5 v d) 272:(ej'e"j')6(a) ' -
3. Find the Fourier Transform of the impulse train function 62,r (t):
a) 5(a)
b) 27 6271
C) 61()
d) 27:
4. Fi
ECE 310, Spring 2014 Semester
Review of topics for Exam #3
This exam will cover material from Lectures 11-1 through 15-2.
Lecture 11-1 (sampling theory):
( ) may be obtained by sampling ( )
( ) is sampled by multiplying it with impulse train
( ) is then t
ECE 310 Discrete and Continuous Signals and Systems
Fall 2013 Semester
Quiz 1: Wednesday, September 25, 2013
Answers and grading guide for version 1
1. Simplify the following expressions:
a)
(
b)
(
, because the impulse is located at
)
(
sec.
, because
ECE 310 Discrete and Continuous Signals and Systems
Educational Outcomes Survey
These problems are intended to evaluate the effectiveness of our teaching in the department. Your responses will not factor
into determining your grade for the course.
Student
Dr. Vladimir Goncharoff, Instructor
Action Form
Last name:
First name:
Email:
Date:
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(e.g. ECE 310, etc.)
Your request for Dr. Goncharoff:
Anastasios Kokkinias
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ECE 310
HW #3
1. a) sgn(t-2)
function y = sgn(x)
y = zeros(size(x);
y(find(x>0) = 1;
y(find(x<0) = -1;
end
I did this in order to define the sgn function into matlab.
t = linspace(-5,5,1000);
plot(t,sgn(t-2)
axis([-5 5
W
University of Illinois at Chicago
Department of Electrical and Computer Engineering
ECE 310 - Discrete and Continuous Signals and Systems
Questions
1. What is the area of 6(1) ?
2. What is the area of 260 - l) ?
3. What is the area of 6(1 + 2)?
4. What
La'wf Table 4.1
A. Short Table of Fourier Transforms
f (t) F (w)
1
1 e11(t) _ a > 0
a + you
2 cu(t) ' 1 _ a > 0
- y a. # 3w
_ . _20 .
3 e m 2 + w? a'> 0
4 te"'°tu(t') 1 a. > 0
. (a + 3w)2
5 te_t(t) L- a > o
#3 9 H (a + jw)n+1 . .
6 6(t) - ,1
7 1 2mm
Midterm Exam 2 (Wednesday 4/4): 21 problems, equally weighted.
1. What is the value of A when x(t) = (1 +j)ej2t + (1 -j)ej2t is expressed in the form
x(t) = A cos(2t + 0)?
. ,s . '21- 26
W: WW {W
s: stZzi') ~' 4/692 w )
J
z .2 m (216) asm (if) - ,4 :]/47
ECE 310 Discrete and Continuous Signals and Systems
Spring 2015 Semester
Exam 3 Solutions, ver. 1/2
(16 problems, equally weighted)
1. What differential equation relates voltage to current in an inductor?
() =
()
2. Derive the impedance of a capacitor
Is sin(4t) even, odd, neither even nor odd, or both even and odd?
odd
Is rect(t) even, odd, neither even nor odd, or both even and odd?
even
Is u(t) even, odd, neither even nor odd, or both even and odd?
neither
Is sgn(t) even, odd, neither even nor odd,
ECE 310 Discrete and Continuous Signals and Systems
Spring 2015 Semester
Exam 1 questions (version 3)
1.
Find the real part of :
2.
Find the imaginary part of :
4.
Find the phase of 1 in degrees:
3.
Find the magnitude of 1 + 2 :
5.
Express 4 cos() + 4 sin