University of Washington
Department of Electrical Engineering
EE 235 Lab 5:
Time Domain to Frequency Domain
In this lab, we will learn how to transform signals in Matlab from the time domain to the
frequency domain. In addition, we use will Matlab to iden
3/28/2016
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #1 (Introduction)
ANNOUNCEMENTS
This week plan:
Lectures: 1.0-1.2
Labs: No
Assignments: No
Office Hours: Monday, Tuesday, Wednesday, & Friday 01:302:30 pm at C
EE235
Name:
Student ID:
Midterm Exam #2
University of Washington EE235, Winter 2016
February 26th, 2016
Exam Information:
The test is closed book, and no calculators/devices are allowed. You are allowed ONE 8.5x11 (twosided) page of notes.
Please show a
EE235
Name:
Student ID:
Midterm Exam #1
University of Washington EE235, Winter 2016
January 29th, 2016
Exam Information:
The test is closed book, and no calculators/devices are allowed. You are allowed ONE 8.5x11 (twosided) page of notes.
Please show al
University of Washington
Department of Electrical Engineering
EE 235 Lab 1 Part Two:
Introduction to Matlab
In this lab, you will work through another series of exercises to finish off your introduction to
Matlab (Matrix Laboratory). Note: All lab exercis
Homework 3
EE235, Spring 2012
Solution
Each problem or problem-part worth one point.
1
1. An LTI system has impulse response h(t) = (t 2) 2 (t 4). Describe in words what
the output signal y (t) would be given an input x(t).
The system y (t) would be a lin
University of Washington
Department of Electrical Engineering
EE 235 Lab 1 Part One:
Introduction to Matlab
In this lab, you will work through a series of exercises to get you started with Matlab (Matrix
Laboratory). You will learn how to use Matlab varia
University of Washington
Department of Electrical Engineering
EE 235 Lab 3:
Unit Impulse and Continuous-Time LTI Systems
In this lab, we will investigate unit impulses and its significance and usage in LTI systems. In
particular, we will revisit the time
EE-235 Summer 2011
Signals & Systems
Leo Lam
Final Exam
Name
Student Number
Notes:
This exam is closed book, closed notes, closed homework and homework solutions. You are
permitted two 8.5 x 11 double-sided sheet of summary notes. No calculator is permitt
University of Washington
Department of Electrical Engineering
EE 235 Lab 2
Continuous-Time Signals and Transformations in Time
In this lab, we will use Matlab to perform transformations in time on continuous-time signals.
We will also introduce students t
University of Washington
Department of Electrical Engineering
EE 235 Lab 2
Continuous-Time Signals and Transformations in Time
In this lab, we will use Matlab to perform transformations in time on continuous-time signals.
We will also introduce students t
12/8/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #36
UWEE TC Chen
POLES AND ZEROS
Poles are where the Laplace-transform function blows up
Zeros are where the Laplace-transform function goes to 0
There will be no
12/7/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #35
UWEE TC Chen
COMPLEX EXPONENTIALS ARE THE UNIQUE
EIGENFUNCTIONS OF LTI SYSTEMS!
Impulse Response:
()
Exponential Response:
()
()
e st h( t ) h e s( t )d
e
12/4/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #34
UWEE TC Chen
HOW TO AVOID ALIASING?
We ANTI-alias.
time signal
()
Anti-aliasing
filter
Sample
Reconstruct
UWEE TC Chen
1
12/4/2015
ANTI-ALIASING FILTERS
Low-Pa
11/30/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #31
UWEE TC Chen
EXAMPLE (CIRCUIT DESIGN WITH FT!)
Goal: Build a circuit to give () with an input current ()
= ()
?
= 2 ()
Find ()
Convert to differential eq
11/23/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #29
UWEE TC Chen
FOURIER TRANSFORM AND LTI
(EXAMPLE)
Assume an LTI system as following (Delay):
()
( 3)
Exponential response
3 =
3
Responding to Fourier Se
11/25/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #30
UWEE TC Chen
BANDWIDTH PART 3/3
Notes:
1) High-Pass and Band-Stop filters have infinite bandwidth.
2) By multiplying two signals in time, the result has the s
12/2/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #33
UWEE TC Chen
SAMPLING / ALIASING REMIX!
Consider sin 3) sampled at 2Hz. = 2 = 4
(
2
-4
0
2
4
Since the original frequency was between /2 and . What
you se
12/11/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #38
UWEE TC Chen
WHAT CAN YOU LEARN FROM A POLEZERO PLOT?
Assume we have a rational (), then:
1) from shape of ROC, can learn the direction of the time signal
()
12/9/2015
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #37
UWEE TC Chen
INTERPRETING THE ROC 1/2
1) All ROCs have boundaries parallel to the -axis.
2) Right-sided signals have right-sided ROCs, left-sided signals
have
/*
* bufbomb.c - Bomb program that is solved using a buffer overflow attack
*
* Copyright (c) 2002, R. Bryant and D. O'Hallaron, All rights reserved.
* May not be used, modified, or copied without permission.
*/
#include
#include
#include
#include
#includ
EE 235, Winter 2016, SOLUTIONS Homework 2: Continuous-Time Signals
Due Friday January 15, 2016 via Canvas Submission
Write down ALL steps for full credit
HW2 Topics:
Continuous Time Signal Properties: Periodic, Even/Odd, Energy/Power
Operations on Signa
EE 235, Winter 2016
Homework 1: Math Review SOLUTIONS
Due Friday January 8, 2016 by 1:30pm via ONLINE SUBMISSION
HW1 Topics: Complex Numbers, Functions, and Integration
HW1 References: OWN Sections 1.2, 1.2.1, HW1 Supplementary Notes
HW1 Problems:
1. Comp
EE 235, Winter 2016, Homework 1 Supplementary Notes
1. Complex Number Representation. Any complex number z can be represented in rectangular (Cartesian)
form or in polar form.
(a) In rectangular form, z = x + jy, where x = Recfw_z and y = Imcfw_z .
i. Com
EE 235, Winter 2016
Homework 1: Math Review
Due Friday January 8, 2016 by 1:30pm via ONLINE SUBMISSION
HW1 Topics: Complex Numbers, Functions, and Integration
HW1 References: OWN Sections 1.2, 1.2.1, HW1 Supplementary Notes
HW1 Problems:
1. Complex Number
EE 235, Winter 2016, Homework 2: Continuous-Time Signals
Due Friday January 15, 2016 via Canvas Submission
Write down ALL steps for full credit
HW2 Topics:
Continuous Time Signal Properties: Periodic, Even/Odd, Energy/Power
Operations on Signals
Expone
EE 235, Winter 2016, Homework 2 Supplementary Notes
1. Sums of Periodic Signals. Suppose x1 (t) is periodic with period T1 , x2 (t) is periodic with period T2 ,
and so on. We want to know if x(t) = x1 (t) + x2 (t) + . is also gonna be periodic.
(a) The ge
EE 235, Winter 2016, Homework 4: LTI Systems and Convolution SOLUTIONS
Due Wednesday January 27, 2016 via Canvas Submission
Write down ALL steps for full credit
HW4 Topics:
LTI Systems and Impulse Response
Echo Property of Convolution
Convolution Integ
EE 235, Winter 2016
SOLUTIONS Homework 3: Continuous-Time Systems
(Due Friday January 22, 2016 via Canvas Submission)
Write down ALL steps for full credit
HW3 Topics:
System Properties: C, S, I, L, TI
HW3 Course Learning Goals Satised:
Goal 1: Describe
EE 235, Winter 2016, Homework 4: LTI Systems and Convolution
Due Wednesday January 27, 2016 via Canvas Submission
Write down ALL steps for full credit
HW4 Topics:
LTI Systems and Impulse Response
Echo Property of Convolution
Convolution Integral
HW4 Co
EE235
Name:
Student ID:
Final Exam
University of Washington EE235, Winter 2017
March 13th, 2016
Exam Information:
The test is closed book, and no calculators/devices are allowed. You are allowed TWO 8.5x11 (twosided) pages of notes.
Please show all work
1/17/17
Quiz 3
t
T cfw_ x(t) =
x( )d
0
1) Is the system T 3me-invariant?
2) Is the system T linear?
1
Solu3on
1) Is the system T 3me-invariant? NO
t
System:
T cfw_ x(t) =
x( )d
0
t
Step 1:
y(t) =
x( )d
Step 1: nd y(t)
Step 2: nd y(t-t0)
Step
1/25/17
Quiz 4
1
1
x(t)
-1
1
1
2
t
1
1) What will the width of y(t)=x(t)*h(t) be?
2) Sketch y(t); show any zero, increasing, constant and
decreasing regions
1
Solution
1) What will the width of y(t)=x(t)*h(t) be?
Answer: 3
0.5
2
1
2/14/17
Quiz 7
Given: x(t) = (t a) + (t + a)
Find X(j )? Show your work
1
Solution
x(t) = (t a) + (t + a)Find X( j )
X( j ) = FT cfw_ x(t) = FT cfw_ (t a) + FT cfw_ (t + a)
= e j a + e j a = ( e j a + e j a ) = [ 2 cos( a)]
= 2 cos(a )
2
1