EE313 Linear Systems and Signals - Mini Project 1 - Fall 2026

Here are Matlab and sound files that will help you complete the project, which you can download the above files in a single zip file miniproj1code.zip:

• audio_effects_echo.m starter code for implementing echo
• audio_effects_tremolo.m starter code for implementing tremolo
• audio_effects_vibrato.m starter code for implementing vibrato
• mysterySignal_echo.wav audio recording with echo
• mysterySignal_tremolo.wav audio recording with tremolo
• plot_freqDomainAnalysis.m Matlab function to plot a time-domain signal in the frequency domain and the time-frequency domain (see below)
• plot_timeDomainAnalysis.m Matlab function to plot a time-domain signal in the time domain (see below)

addpath("LOCATION");

C:\Users\Brian\Documents\MATLAB\miniproj1

MATLAB function plot_freqDomainAnalysis

% FUNCTION plot_freqDomainAnalysis(s,fs,sType)
% PURPOSE:
%   This function plots the frequency represntation and spectrogram of a
%   given signal.
%
% INPUTS:
%   1)  s, a vector of size (N x 1), where N is the number of elements
%          s represents the signal to analyze%
%   2) fs, a scalar
%          fs is the sampling frequency that signal s was generated with
%   3) sType, a string that describes the signal s
%             OPTIONAL INPUT TO FUNCTION
% OUTPUTS:
%   none (generates 2 plots)
%
% EXAMPLE CALLS TO FUNCTION...
%   1) plot_freqDomainAnalysis(s,fs)
%   2) plot_freqDomainAnalysis(s,fs,"Vibrato")

MATLAB function plot_timeDomainAnalysis

% FUNCTION plot_timeDomainAnalysis(s,fs,sType)
% PURPOSE:
%   This function plots the time-domain representation of a given signal.
%
% INPUTS:
%   1)     s, a vector of size (N x 1), where N is the number of elements
%             s represents the signal to analyze
%             REQUIRED INPUT TO FUNCTION
%   2)    fs, a scalar
%             fs is the sampling frequency that signal s was generated with
%             REQUIRED INPUT TO FUNCTION
%   3) sType, a string that describes the signal s
%             OPTIONAL INPUT TO FUNCTION
% OUTPUTS:
%   none (generates 1 plot)
%
% EXAMPLE CALLS TO FUNCTION...
%   1) plot_timeDomainAnalysis(s,fs)
%   2) plot_timeDomainAnalysis(s,fs,"Vibrato")

Tips and Tricks

figure(4);
ylim( [0 1] );

Mystery Signals. Each mystery signal is a recording of an instrument playing a note (principal frequency). The mystery signal will also contain harmonics of the note being played, which you'll see in the frequency domain plots.

The mystery signals are not necessarily at full scale in amplitude between -1 and 1. You can check this by playing the audio signal from Matlab and compare it against the synthesized signal. Another way is to compute the minimum and maximum values for each mystery signal:

max(mysterySignal)
min(mysterySignal)

Delay. For the echo mystery signal, you can visually evaluate the spectrogram to estimate how many delays are present. It's possible that a delayed signal appears with lower amplitude that the initial signal. Also, please plot the echo mystery signal in the time domain.

References. Please add the mini-project assignment and link as a reference.

Homework and Mini-Project Guidelines

Here are some things you should follow for all assignments.

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:

1. Introduction - introduce the purpose of this mini-project and provide an overview of what their report will discuss. 5 points.
2. Modulation - 40 points
   • Vibrato Discussion and Analysis
   • Tremolo Discussion and Analysis
3. Time Shifts - 40 points
   • Echo Discussion and Analysis
4. Conclusion - discuss any insights or knowledge gained as a result of completing the mini-project. 10 points.
5. References - 5 points
6. Usage of additional MATLAB Toolboxes (if any)

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

Last updated 09/22/26. Send comments to bevans@ece.utexas.edu.