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EE313 Linear Systems and Signals - Homework
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EE313 Linear Systems and Signals - Homework - Fall 2024
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EE313 Linear Systems and Signals - Homework
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EE313 Linear Systems and Signals - Homework - Fall 2024
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MATLAB will be needed on the homework assignments.
Here are
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installation instructions
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installation instructions
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and
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a handout for MATLAB.
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a handout for MATLAB.
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- Homework #9:
assignment,
hints, and
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solution.
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solution.
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- Homework #8:
assignment,
hints, and
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solution.
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solution.
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- Homework #7:
assignment,
hints, and
solution.
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- Mini-Project #2:
assignment,
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hints, and
solution.
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hints,
solution, and
code.
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- Homework #6:
assignment,
hints, and
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solution.
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solution.
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- Homework #5:
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assignment
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assignment,
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hints, and
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solution.
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solution.
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- Homework #4:
assignment and
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solution
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solution.
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- Homework #3:
assignment and
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solution
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solution.
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- Mini-Project #1:
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assignment and
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assignment,
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hints, and
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hints,
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solution.
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solution, and
code.
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- Homework #2:
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assignment and
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assignment,
hints, and
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solution.
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solution.
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- Homework #1:
assignment and
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solution.
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solution.
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Marker board notes for problem 1.4:
part (a) and
parts (b) and (c).
Previous homework and mini-project assignments and solutions are available for
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Fall 2017,
Fall 2018,
Fall 2021 and
Fall 2023 and
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Fall 2017,
Fall 2018,
Fall 2021 and
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Fall 2023 and
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Fall 2023.
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Homework and Mini-Project Guidelines
Here are some things you should follow for all assignments.
Amount of work to show:
- An explanation should be given for every single answer.
Answers written without explanation will lose two-thirds of the
points allotted for that part.
- Only "standard" formulas (like Euler's formula, trigonometric formulas, etc.)
can be used without a reference.
If you're using something non-standard, then please put a reference
to the formula number in the book, or whatever source you got it from.
Just using the final result of a similar problem done in the class,
and omitting the intermediate steps, is not okay.
You have to show show your work.
- There shouldn't be big jumps in logic from one step to the next.
- For everything, expect to show at least one intermediate step between
the first line and the answer.
Even if it seems unnecessary to you, please err on the side of caution.
Things that seem obvious to you when you're writing the solution are not
quite so obvious for someone reading it.
- If you're in any doubt about how much work to show, please ask the
instructor or the teaching assistant.
MATLAB source code guidelines:
- Put a comment before the solution of each part, telling the question number
of the solution.
- If you're using complicated logic, leave a comment telling what that block
of code is supposed to do.
- Use variable names that related to their meaning/use.
- Avoid using two different variables for the same thing.
- Try to avoid using "magic numbers" in the code.
If you're using a number, write a comment telling me how you derived it.
- Make sure that your code will compile & run in a clean workspace; i.e.,
one without any variables present.
Use a clear all; at least once before submitting it.
- No marks will be deducted based on the efficiency of the code unless the
problem asks you to write efficient code.
Technical points:
- Merge all the files together into one PDF file.
- Please adjust the contrast, exposure etc., to get a good scan quality so that the TA
can easily read what you write.
Take extra care to get a good scan for parts written in pencil.
- For the MATLAB code you write for an assignment, please copy the code into Word or
include a screenshot showing the code.
Do not submit handwritten code.
Other things:
- All plots must have axis labels, with units.
- Final answers must be boxed, or underlined or otherwise differentiated from the rest of the solution.
- All final answers must have units, if they exist.
- Read the questions carefully.
- Try to answer all parts of a question together.
If the solution to some parts of a question is written elsewhere, then leave a note telling
the reader where to find it.
Organization of a mini-project report:
Please write a self-contained narrative report.
The audience is someone who has taken the equivalent of this class.
The report should provide references to the textbook and other sources as needed.
Please refer to the hints above, which apply to homework assignments and mini-project
reports, as well as the following additional guidelines for the mini-project:
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For mini-project #2:
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- The assignment is to design, analyze, and simulate averaging and nulling FIR filters.
- The project covers three key ideas concerning linear time-invariant (LTI) filters:
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- Theme: The assignment is to design, analyze, and simulate averaging and nulling FIR filters.
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- Takeways: The project covers three key ideas concerning linear time-invariant (LTI) filters:
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- Takeways: The project covers three key ideas concerning linear time-invariant (LTI) systems:
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Theme: The assignment is to design, analyze, and simulate averaging and nulling FIR filters.
Takeways: The project covers three key ideas concerning linear time-invariant (LTI) systems:
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- Time domain: Output signal is the convolution of the input signal and the filter’s impulse response.
- Frequency domain: Output signal is the product of the input signal and
the filter’s frequency response. The filter’s frequency response is the Fourier transform of the impulse response
- Filtering: The magnitude of the frequency response can be designed to pass,
attenuate, and amplify bands of frequencies as well as eliminate individual frequencies.
The phase of the frequency response can be designed to delay all frequencies by the
same amount in the time domain (linear phase) or assign a different delay to each frequency component.
Practical filters have different frequency responses than ideal filters.
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- Introduction.
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Report:
- Introduction. 4 points
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Explain in your own words without equations the time-domain and
frequency-domain response for LTI FIR filters.
Build on your experiences so far in the class.
You can also use ideas from Sections 1.1 Objective and 1.2 Overview in the mini-project assignment.
Use appropriate references.
Probably half of a page for this section.
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- Frequency Response
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- Frequency Response. 16 points.
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Explain in your own words the content in the sections
Section 1.3 Frequency Response of FIR Filters and
Section 1.4 Periodicity of the Frequency Response.
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Explain in your own words the content in the
Sections 1.3 Frequency Response of FIR Filters and
1.4 Periodicity of the Frequency Response.
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Complete all parts.
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- Averaging and Nulling FIR Filters
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- Averaging and Nulling FIR Filters. 20 points.
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Explain in your own words the content in the sections
Section 1.5 Frequency Response of the Four-Point Averager and
Section 1.6 FIR Nulling Filters.
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Explain in your own words the content in the
Sections 1.5 Frequency Response of the Four-Point Averager and
1.6 FIR Nulling Filters.
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Complete all parts.
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- Ideal and Practical Filters
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- Ideal and Practical Filters. 30 points.
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Explain in your own words the content in the sections
Section 1.7 Ideal Filters and Practical Filters,
Section 2.1 LTI Frequency Response Demo, and
Section 2.2 Ideal Filters and Practical Filters.
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Explain in your own words the content in
Sections 1.7 Ideal Filters and Practical Filters,
2.1 LTI Frequency Response Demo, and
2.2 Ideal Filters and Practical Filters.
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Complete all parts.
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- Removing Interference from a Speech Signal
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- Removing Interference from a Speech Signal. 20 points.
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Explain in your own words the content in the section
Section 2.3 Removing Interference from a Speech Signal.
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Explain in your own words the content in
Section 2.3 Removing Interference from a Speech Signal.
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Complete all parts.
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- Conculsion
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- Conculsion. 10 points.
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Draw conclusions from your work and explanations in the earlier sections.
Probably half of a page for this section.
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For mini-project #2:
- Introduction -- explain in your own words why FIR and IIR filtering are useful.
Build on your experiences so far in the class.
You can also use ideas from the lab assignment.
Use appropriate references.
Probably half of a page for this section.
- Overview -- explain in your own words and with appropriate references the
mathematical descriptions of discrete-time FIR and IIR filtering in the
in the time, frequency, and z domains.
Also explain how an image is acquired and how is its information represented
(matrix of pixels).
About 2 pages for this section.
- Section 2.5.
Explain applying a 1-D FIR filter to an image.
Include all images.
- Section 3.2.
Explain image distortion and image restoration.
Explain how an IIR filter could completely compensate for the distortion caused
by the FIR filter with coefficients [1 -0.9].
Include all images.
Give a numerical comparison using MSE, PSNR, and SSIM measures of
- original echart image with the distorted image
- original echart image with the restored image
- Conclusion -- draw conclusions from your work and explanations in the earlier sections.
Probably half of a page for this section.
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For mini-project #1:
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For mini-project #1:
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- Introduction -- explain in your own words when a sum of sinusoids can be
used to analyze and synthesize a signal.
Build on your experiences so far in the class.
You can also use ideas from the Introduction section in the mini-project assignment.
Use appropriate references.
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- Introduction -- 3 points.
Explain in your own words when a sum of sinusoids can be
used to analyze and synthesize a signal.
Build on your experiences so far in the class.
You can also use ideas from the Introduction section in the mini-project assignment.
Use appropriate references.
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Probably half of a page for this section.
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- Overview -- explain in your own words and with appropriate references the general
approach for representing a signal as a sum of sinsuoids in the mini-project,
including mathematical formulas.
You can also use ideas from other sections in the mini-project #1 assignment.
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- Pre-lab -- explain in your own words the content in the sections
"Piano Keyboard" and "Gaussian Forms".
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- Pre-lab -- 6 points.
Explain in your own words the content in the sections
"Piano Keyboard" and "Gaussian Forms".
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About a page for this section.
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- Analyzing an audio signal -- answer the questions in Section 2 of the assignment
and use information from Section 2 in your writeup.
- Synthesizing an audio signal -- answer the questions in Section 3 of the assignment.
and use information from Section 3 in your writeup.
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- Warm-up -- describe Gaussian weighting in your own words using information from
from Section 2 in your writeup.
About a page for this section.
- A Musical Illusion -- describe the Shepard Scale and answer the questions in
Section 4 of the assignment.
Include all plots asked for.
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- Warm-up -- 36 points.
In Section 3.1, parts (a), (c), and (d) are six points each.
In Section 3.2, parts (a) and (b) are nine points each.
Describe Gaussian weighting in your own words using information from
from Section 2 in your writeup.
Complete all parts.
This section will be several pages -- hard to predict how many pages.
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- A Musical Illusion -- 48 points.
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- A Musical Illusion -- 48 points.
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All parts are six points except for part (f) which is 12 points.
Describe the Shepard Scale and answer the questions in Section 4 of the assignment.
Complete all parts.
Include all plots asked for.
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Describe how you computed amplitude, frequency, and phase values for the frequency
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components.
Complete all parts.
Refer to information in earlier sections.
Please include the Matlab code you've written in an Appendix.
This section will be several pages.
Hard to predict how many pages you'll need.
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- Conclusion -- draw conclusions from your work and explanations in the earlier sections.
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components.
Refer to information in earlier sections.
Please include the Matlab code you've written in an Appendix.
This section will be several pages -- hard to predict how many pages.
- Conclusion -- 7 points.
Draw conclusions from your work and explanations in the earlier sections.
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Probably half of a page for this section.
This mini-project report is something that you could bring with you on interviews
to show as an example of your work.
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Here are example mini-project #1 reports written by the instructors on
"FM Synthesis for Musical Instruments" (2018) and
"Sinusoidal Speech Synthesis" (2021).
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Here are example mini-project #1 reports written by the instructors:
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Last updated %G%.
Send comments to
bevans@ece.utexas.edu.
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