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EE313 Linear Systems and Signals - Midterm #2
EE313 Linear Systems and Signals - Midterm #2
Each midterm exam will be an open book, open notes, open laptop exam
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that is scheduled to last the entire period.
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that is scheduled to last the entire lecture period (11:00am-12:15pm).
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The laptop must have all external networking connections disabled.
Because each midterm is an open book, notes and laptop exam, you'll
likely need to move quickly through the exam but also need to think
deeply about possible ways to solve the problems.
To this end, having a week of regular sleep, eating, and exercise will
be very helpful.
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Midterm #2 for the Fall 2017 semester will be on Thursday, Nov. 16th,
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during lecture time (12:30pm to 2:00pm) but in
a room TBA.
With 60 students in the class, you should have several empty
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during lecture time (12:30pm to 2:00pm) but in the following rooms:
- EER 1.516 if your last name starts with A-L
- WRW 102 if your last name starts with M-Z
WRW 102 seats 123, and EER 1.516 seats 122.
(WRW is the Aerospace Engineering Bldg.)
With 64 students in the class, you should have several empty
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seats or an aisle on either side of you.
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Midterm #2 for the Fall 2018 semester will be on Tuesday, Nov. 20th,
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during lecture time (12:30pm to 1:45pm) but in a larger room TBA.
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during lecture time (12:30pm to 1:45pm) in EER 1.516 and additional
rooms.
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during lecture time (12:30pm to 1:45pm) in EER 1.516 (seats 122) and
additional rooms.
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Room assignments will be announced shortly.
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The extra space will help you be more comfortable to arrange your
books, notes, and laptop for the midterm exam.
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during lecture time (12:30pm to 1:45pm) in
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Midterm #2 for the Fall 2021 semester will be on Tuesday, Nov. 16th,
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Please download in advance of the midterm exam a
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zip archive of the course Canvas site (TBA)
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zip archive of the course Canvas site (930 MB)
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zip archive of the course Canvas site (930 MB)
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which includes the lecture slides, marker board pictures, handouts,
homework assignments and solutions, and previous tests and their solutions.
By placing the files on your laptop in advance, you can search the files
for keywords when taking practice tests and the actual midterm exam.
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Midterm #2 for the Fall 2021 semester will be in person on Tuesday, Nov. 16th,
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during lecture time (11:00am to 12:30pm) in the lecture room (EER 1.516).
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during lecture time (11:00am-12:15pm) in the lecture room (EER 1.516).
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EER 1.516 seats 122 and enrollment is 36 students.
The extra space will help you be more comfortable to arrange your
books, notes, and laptop for the midterm exam.
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Midterm #2 for the Fall 2023 semester will be on Tuesday, Nov. 7th,
during lecture time (11:00am to 12:15pm) in
GLT 5.104.
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Midterm #2 for the Fall 2024 semester will be on Thursday, Nov. 14th,
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during lecture time (11:00am to 12:15pm) room TBA.
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This classroom seats 150 and 45 students are in the class.
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during lecture time (11:00am to 12:15pm) in UTC 1.102 and UTC 1.130.
Each room seats 74 students, and there are 70 students in the class.
Please leave one empty seat or an aisle on either side of you.
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The extra space will help you be more comfortable to arrange your books,
notes, and laptop for the midterm exam.
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Please leave at least two empty seats or an aisle on your left and right.
GLT is the new Gary L. Thomas Energy building immediately to the South of the EER Building.
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- EER 0.810 (seats 32) for the 16 last names that begin with S or T
- EER 1.516 (seats 122) for everyone else
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Current enrollment is 72 students.
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In both rooms, there will be an aisle or at least one empty seat on
either side of you.
There won't be as much space as you had for midterm #1, but there should
still be adequate space for your laptop, books and notes.
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You might consider bringing pens or pencils of different colors
to help you in drawing different cases in graphical "flip-and-slide"
convolution.
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Coverage
For midterm #2 in EE 313, you will be responsible for the
following sections of Signal Processing First book
by McClellan, Schafer and Yoder:
- Chapter 5: FIR Filters
- Chapter 6: Frequency Response of FIR Filters
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- Chapter 7: z-Transforms
- Chapter 8: IIR Filters
- Chapter 9: Continuous-Time Signals and LTI Systems
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- Chapter 7: z-Transforms (except Section 7-8)
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- Chapter 8: IIR Filters (except Sections 8-9, 8-10, and 8-11)
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- Chapter 8: IIR Filters
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- Chapter 9: Continuous-Time Signals and LTI Systems (except Sections 9-8 and 9-9)
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You will also be responsible for the material in
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There will likely be five questions on midterm #2.
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There will likely be four questions on midterm #2.
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There will be no questions about Matlab.
A review of midterm #2
material is available from a previous offering of the course.
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We haven't covered the material on the Laplace transform yet.
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We haven't yet covered continuous-time convolution or
the Laplace transform yet.
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Worked Problems from Signal Processing First
The companion Web site
for the Signal Processing First book has dozens of worked
problems on FIR filters, z-transforms and IIR filters.
Here is the correspondence between chapters in the two books:
- Signal Processsing First chapter 5 on FIR Filters is DSP First chapter 5.
- Signal Processsing First chapter 6 on FIR Filters is DSP First chapter 6.
- Signal Processsing First chapter 7 on z-transforms is DSP First chapter 9.
- Signal Processsing First chapter 8 on IIR filters is DSP First chapter 10.
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Previous Tests
Here are several example midterm #2 exams:
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Here are the questions from the previous exams that are related to the
material to be covered on midterm #2 this semester.
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- Midterm #1 Questions:
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- Midterm #1 Questions
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- Midterm #1, Summer 2016, Problem 4. Continuous-Time Convolution.
"Zero state" means that the system state is zero; i.e., the initial
conditions are zero.
So, the systems in this problem are linear and time-invariant.
In problem 4(b), please note that δ(t) is the Dirac delta even
though the plot of h(t) seems to imply otherwise.
- Midterm #1, Summer 2016, Problem 5. Discrete-Time Convolution.
"Zero state" means that the system state is zero; i.e., the initial
conditions are zero.
So, the systems in this problem are linear and time-invariant.
- Midterm #1, Fall 2010, Problem 1.2. Convolution.
- Midterm #1, Fall 2010, Problem 1.3. Continuous-Time System Properties.
- Midterm #1, Fall 2010, Problem 1.4. Discrete-Time Convolution.
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This problem asks us to design an equalizer.
In part (b), one obtains
g[n] = b0 delta[n] + a1 g[n-1].
This is in the form of a first-order difference equation with input
signal delta[n] and output signal g[n].
That is, g[n] is the impulse response of the LTI system.
A characteristic root is the same as a pole in the transfer function
in the z-domain for an LTI system.
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- Midterm #1, Fall 2010, Problem 1.5. Discrete-time systems part only.
We haven’t covered most of the continuous-time systems mentioned in the answer.
- Midterm #1, Spring 2009, Problem 1.2. Continuous-Time Convolution.
- Midterm #1, Spring 2009, Problem 1.3. Continuous-Time Tapped Delay Line.
- Midterm #1, Spring 2009, Problem 1.4. Potpourri. Signal Properties, System Properties.
- Midterm #1, Fall 2005, Problem 1.3. Continuous-Time Tapped Delay Line.
- Midterm #1, Fall 2005, Problem 1.4. Continuous-Time System Properties.
- Midterm #1, Fall 2005, Problem 1.5. Potpourri. We haven’t covered 1.5(b) part ii yet.
- Midterm #1, Fall 2003, Problem 1.2. Discrete-Time System Response (Convolution).
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This problems asks us to convolve an exponential signal in discrete time
with itself
Please see Case #2 in
Handout E Convolution of Exponential Sequences.
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- Midterm #1, Fall 2003, Problem 1.3. Continuous-Time Tapped Delay Line.
- Midterm #1, Fall 2003, Problem 1.4. Differentiator.
- Midterm #1, Fall 2003, Problem 1.5. Potpourri. Convolution, resonators, and oscillators.
- Midterm #1, Fall 2001, Problem 1.2. Continuous-Time Convolution.
- Midterm #1, Fall 2001, Problem 1.3. Continuous-Time System Properties.
- Midterm #1, Spring 2001, Problem 1.2. Continuous-Time Convolution.
- Midterm #1, Spring 2001, Problem 1.3. Discrete-Time Tapped Delay Line.
- Midterm #1, Spring 2001, Problem 1.4. Step Response.
- Midterm #1, Fall 1999, Problem 1.2. Continuous-Time Convolution.
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- Midterm #2 Questions
- Midterm #2, Summer 2016, Problem 2.3, Z-Transforms
- Midterm #2, Summer 2016, Problem 2.4, Discrete-Time LTI Oscillator with Infinite Impulse Response
- Midterm #2, Spring 2009, Problem 2.1, Difference Equation
- Midterm #2, Spring 2009, Problem 2.2, Discrete-Time Convolution
- Midterm #2, Spring 2009, Problem 2.3, Discrete-Time Tapped Delay Line
- Midterm #2, Spring 2009, Problem 2.5a, Discrete-Time Convolution
- Midterm #2, Fall 2003, Problem 2.2, Z-Transforms
- Midterm #2, Fall 2003, Problem 2.4, Transfer Functions and Frequency Responses for a Discrete-Time LTI System
- Midterm #2, Spring 2001, Problem 2.1, Solving a Difference Equation
- Midterm #2, Spring 2001, Problem 2.2, Discrete-Time Impulse and Step Responses
- Midterm #2, Spring 2001, Problem 2.5(a) and (b), Discrete-Time Filter Design
- Midterm #2, Fall 1999, Problem 2.3, Discrete-Time Tapped Delay Line
- Midterm #2, Fall 1999, Problem 2.4, Discrete-Time Transfer Functions
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- Final Exam Questions
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- Final Exam Questions
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- Final Exam, Summer 2016, Problem 3, Discrete-Time Fourier Transform
- Final Exam, Summer 2016, Problem 4, Discrete-Time Frequency Response
- Final Exam, Summer 2016, Problem 5, Discrete-Time Filter Design
- Final Exam, Summer 2016, Problem 7, Continuous-Time Convolution
- Final Exam, Summer 2016, Problem 8, Discrete-Time Averaging Filters
- Final Exam, Fall 2010, Problem 4, Discrete-Time Stability
- Final Exam, Fall 2010, Problem 6, Discrete-Time Filter Analysis
- Final Exam, Fall 2010, Problem 7, Discrete-Time Filter Design
- Final Exam, Spring 2009, Problem 3, Discrete-Time Convolution and Continuous-Time Convolution
- Final Exam, Spring 2009, Problem 6, Discrete-Time Filter Analysis
- Final Exam, Spring 2009, Problem 7, Discrete-Time Filter Design
- Final Exam, Fall 2005, Problem 4a, Discrete-Time Convolution
- Final Exam, Fall 2005, Problem 6, Discrete-Time Filter Analysis
- Final Exam, Fall 2005, Problem 7, Discrete-Time Filter Design
- Final Exam, Fall 2003, Problem 4, Z-Transforms
- Final Exam, Fall 1999, Problem 1, Difference Equations
- Final Exam, Fall 1999, Problem 2, Discrete-Time Convolution
- Final Exam, Fall 1999, Problem 8e, Discrete-Time Filter Design
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Coverage
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A review of midterm #2
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material is availale.
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material is available.
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material is available from a previous offering of the course.
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We haven't covered the material on the Laplace transform yet.
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For midterm #2 in EE 313, you will be responsible for the
following sections of Signal Processing First book
by McClellan, Schafer and Yoder:
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- Chapter 5: Sections 6-8
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9: Sections 1-7
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- Chapter 5: FIR Filters
- Chapter 6: Frequency Response of FIR Filters
- Chapter 7: z-Transforms
- Chapter 8: IIR Filters
- Chapter 9: Continuous-Time Signals and LTI Systems
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You will also be responsible for the material covered in homework
assignments 6-10 and the solution sets for those homework assignments.
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You will also be responsible for the material in
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In the reader, you will be responsible for
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- Slides for lectures 8-13 and 16-20
- All appendices
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- Slides for lectures 7-14
- Presentations and discussions for lecture 7-14 slides
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- Slides for lectures 7-13
- Presentations and discussions for lecture 7-13 slides
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- Homework 4-7 assignments and their solutions
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- Homework 4-8 assignments and their solutions
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- Mini-project #2 assigment and its solution
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- Handouts C-J
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- Handouts C-J, O, and U
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- Canvas announcements
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You are responsible for what we said during lecture and
what is on the course Blackboard site (e.g. homework hints).
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There will likely be 5-6 questions on midterm #2.
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There will likely be five questions on midterm #2.
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There will be no questions about Matlab.
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Other Questions
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Is the region of convergence affected when
there is a time shift?
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A review of midterm #2
material is available from a previous offering of the course.
We haven't covered the material on the Laplace transform yet.
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The region of convergence is not affected by a time shift.
A time shift simply causes the Laplace transform to have
a multiplication term in the form on exp(-s t0) where t0
is the time shift.
Also, if it is a unilateral Laplace transform, do we
need to worry about how to find the region of convergence
(in lecture slide 11-10 it states that there is no need
to specify a region of convergence)?
The region of convergence is not necessary if one is computing
the inverse Laplace transform and the time-domain signal
that will result is causal. However, for other reasons,
such as BIBO stability checking for transfer functions and
converting transfer functions to frequency responses, knowing
the region of convergence is critical.
Problem 2 on Fall 1999 Midterm #2
This problem gives the step response of an LTI system, which
we'll call ystep(t).
It then asks you to find the response to a new signal
x(t).
Here are two different approaches for solving this problem:
- Special case: We can write x(t) as
5 u(t) - 5 u(t-2).
Using linear and time-invariant properties, the output is
y(t) =
5 ystep(t) -
5 ystep(t - 2).
- General case: From the given information, we can
find the transfer function of the LTI system:
H(s) =
Ystep(s) / U(s)
where U(s) is the Laplace transform of the
unit step function, i.e. U(s) = 1 / s.
Once we know the transfer function H(s),
Y(s) = H(s) X(s)
Finally, we can take the inverse Laplace transform of
Y(s) to obtain y(t).
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Last updated %G%.
Send comments to
bevans@ece.utexas.edu.
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