EE313 Linear Systems and Signals - Homework - Fall 2024

Homeworks Assigned

• Homework #8: assignment, hints, and solution.
• Homework #7: assignment, hints, and solution.
• Mini-Project #2: assignment, hints, and solution.
• Homework #6: assignment, hints, and solution.
• Homework #5: assignment, hints, and solution.
• Homework #4: assignment and solution.
• Homework #3: assignment and solution.
• Mini-Project #1: assignment, hints, and solution.
• Homework #2: assignment, hints, and solution.
• Homework #1: assignment and solution. 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 Fall 2017, Fall 2018, Fall 2021 and Fall 2023.

Homework and Mini-Project Guidelines

Amount of work to show:

1. An explanation should be given for every single answer. Answers written without explanation will lose two-thirds of the points allotted for that part.
2. 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.
3. There shouldn't be big jumps in logic from one step to the next.
4. 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.
5. If you're in any doubt about how much work to show, please ask the instructor or the teaching assistant.

MATLAB source code guidelines:

1. Put a comment before the solution of each part, telling the question number of the solution.
2. If you're using complicated logic, leave a comment telling what that block of code is supposed to do.
3. Use variable names that related to their meaning/use.
4. Avoid using two different variables for the same thing.
5. Try to avoid using "magic numbers" in the code. If you're using a number, write a comment telling me how you derived it.
6. 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.
7. No marks will be deducted based on the efficiency of the code unless the problem asks you to write efficient code.

Technical points:

1. Merge all the files together into one PDF file.
2. 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.
3. 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.

1. All plots must have axis labels, with units.
2. Final answers must be boxed, or underlined or otherwise differentiated from the rest of the solution.
3. All final answers must have units, if they exist.
4. Read the questions carefully.
5. 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.

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:

For mini-project #2:

1. Theme: The assignment is to design, analyze, and simulate averaging and nulling FIR filters.
2. Takeways: The project covers three key ideas concerning linear time-invariant (LTI) systems:
   • 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.
3. Introduction.
   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.
4. Frequency Response
   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.
   Complete all parts.
5. Averaging and Nulling FIR Filters
   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.
   Complete all parts.
6. Ideal and Practical Filters
   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. Complete all parts.
7. Removing Interference from a Speech Signal
   Explain in your own words the content in Section 2.3 Removing Interference from a Speech Signal.
   Complete all parts.
8. Conculsion
   Draw conclusions from your work and explanations in the earlier sections.
   Probably half of a page for this section.

For mini-project #1:

1. 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.
   Probably half of a page for this section.
2. Pre-lab -- 6 points.
   Explain in your own words the content in the sections "Piano Keyboard" and "Gaussian Forms".
   About a page for this section.
3. 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.
4. A Musical Illusion -- 48 points.
   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.
   Describe how you computed amplitude, frequency, and phase values for the frequency 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.
5. Conclusion -- 7 points.
   Draw conclusions from your work and explanations in the earlier sections.
   Probably half of a page for this section.

• "FM Synthesis for Musical Instruments" (2018)
• "Sinusoidal Speech Synthesis" (2021)
• "Music Synthesis" (2023)

Last updated 11/17/24. Send comments to bevans@ece.utexas.edu.