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Group Assignment
Released: Thursday the 2nd of August, at 9am (Week 2) Group Plan Due: Thursday 9th of August, at 11:59pm (Week 3)
Final Assignment Due: Thursday 30th of August, at 11:59pm (Week 6)
Message from MARS-242 Mission Control
Welcome to the internship program of the Brisbane-based Australian Space Agency (BASA). You will be working with, and learning from, the engineering team in charge of this historic first mission to Mars. The agency is always looking for capable engineers, and has instructed the team to assess your competence in this multifaceted field. The team has provided opportunities for you to demonstrate your knowledge, skills and abilities, as individuals. You will also be demonstrating your ability to work as effective team members. This is the first of three tasks aimed at preparing you to contribute to the critical engineering work needed for the opera- tion, monitoring and safety of the MARS-242 astronauts and their spaceship. Figure 1 shows something you can aspire to!
Figure 1: ‘To Mars!’
BASA Headquarters: Preparation
The engineering team at BASA wishes to investigate the interference affecting the speech re- ceived by the spaceship. Communication disruptions often occur as periodic patterns and this formed the rationale for our engineers to consider periodic noise.
Follow these steps for preparation:
ii Open GenerateDataAssignment1A.m in your MATLAB working directory. This file gen- erates the data you will need for this assignment. Carefully read all of the comments and instructions in the file. Enter your student numbers into the appropriate variables and then run the script. This script only needs to be executed once. The generated data will be stored in the file Data1A at the current working directory. GenerateDataAssign- ment1A.m file can be closed once Data1A has been generated.
iii Write down your group’s test signal parameters for s1(t), s2(t) and s3(t) – displayed on the command window when you run the GenerateDataAssignment1A.m file.
iv Open preparation.m and mission.m, carefully reading the comments and instructions. You will be writing MATLAB code in these files to perform the required tasks. Always make sure that the data file Data1A.mat and your MATLAB code are in the same working directory. Data generated in Step (ii) will be loaded by the existing code upon execution of this script. Variables A, B and C are required in all sections of this assignment. The variable noiseSound will be used in Section A3.
v The parentheses at the end of each question refer to the particular criteria which are relevant for that part. These criteria, which will be used for marking can be found on the CRA sheet. Your Criteria 1 mark comes from the theoretical understanding that you demonstrate in the report, your Criteria 2 mark will come from your code implementation, and your Criteria 3 mark comes from the presentation of your report and your group reflection.
vi As a guide, a report with all sections complete should be between 20 and 30 pages, including figures and code.
Test Signal Definitions
A single period of the periodic functions s1(t), s2(t) and s3(t) are defined below,
s1(t) |
t , 0 ≤ t < 5 A |
s2(t) |
(t−B) e− 4 , 0 ≤ t < 5 |
s3(t) |
.C, 0 ≤ t < 2.5 6, 2.5 ≤ t < 5 |
A1.1 Substitute your group’s variables (A, B and C) into the corresponding signals, and graph two periods (0 to 10 seconds) of each signal by hand. These should be presented as separate figures with key elements of each signal labeled (such as amplitude and gradient changes, axes, units etc. where applicable). Ensure scanned material is easily readable. (Criteria: 1)
Parts A1.2 to A1.9 can be presented as either handwritten or using typeset equations.
A1.2 Determine the trigonometric and complex exponential Fourier series of s1(t) from first principles i.e. Using the integral definitions. Do not convert from one form to the other. Show all working. (Criteria: 1a)
A1.3 Explain how the trigonometric and exponential coefficients change for the signal s(t) =
s1(t) + 2. Describe in words, do not show mathematically. (Criteria: 1c)
A1.4 Expand the signal s2(t) into the Fourier series of your choosing (trigonometric or complex) from first principles, then convert to the other form. Show all working. (Criteria: 1a)
A1.5 Clearly explain your choice of Fourier series for first principle expansion of s2(t).
A1.6 Calculate the coefficients a0, an and bn for n ≤ 3, and the cn coefficients for −3 ≤ n ≤ 3 for s2(t). Show all working. (Criteria: 1b)
A1.7 Derive the Fourier series of s3(t) from first principles (trigonometric or complex), then convert to the other form. Show all working. (Criteria: 1a)
A1.8 Clearly explain your choice of Fourier series for first principle expansion of s3(t).
A1.9 Calculate the coefficients a0, an and bn for n ≤ 3, and the cn coefficients for −3 ≤ n ≤ 3 for s3(t). Show all working. (Criteria: 1b)
A1.10 Classify each of the the test signals as either even, odd or neither? Justify your answer using the mathematical definitions. (Criteria: 1c)
This section should be implemented in MATLAB – preparation.m. Be sure to include relevant figures and code snippets when presenting your results in your report. Discuss what you are doing, and most importantly why.
A2.1 Generate and plot a periodic signal based on s2(t) named s2 hinf 1.
The signal is to span 5 cycles (periods) and have a total of 500 sample points (i.e. 100 points per period).
A2.2 Compute the trigonometric coefficients of s2(t), numerically using MATLAB. Do not use the trapz or syms functions.
A2.3 Create a 4×500 matrix called s2 matrix. The first row represents the DC component of s2(t). Each remaining row contains a single harmonic component of the signal for n ∈ {0, 1, 2, 3}
A2.4 Now create a vector s2 approx which contains an approximation of the signal s2(t). You can use s2 matrix to do this.
A2.5 In the same figure as s2 hinf, and using different colours, also plot the following Fourier series approximations using the trigonometric coefficients:
Hint: this can be implemented in a for loop
• An approximation of s2(t) using the DC component and the fundamental frequency,
An approximation of s2(t) using the DC component, the fundamental frequency and the second harmonic,
An approximation of s2(t) using the DC component, the fundamental frequency and the second and third harmonics. Note that the fundamental, second harmonic and third harmonic correspond to n = 1, 2, 3 respectively.
Label the axes appropriately and include a legend. Ensure the signal and all approxima- tions can be easily seen in the report. Use different line styles if necessary. (Criteria: 1b, 2a)
A2.6 For s3(t), repeat the steps of A2.1 to A2.5 using exponential coefficients, and a 7×500 matrix. Maintain naming conventions i.e. s3 hinf, s3 matrix and s3 approx. (Criteria: 1b, 2a)
A2.7 What can be said about the approximations when the number of harmonics used in- creases? Are the previous approximations sufficient to represent these signals? Why or why not? What are the practical benefits and drawbacks of using 3 harmonics as opposed to more or fewer? Hint: Consider what it would be like to do by hand. (Criteria: 1c)
MATLAB variables that should be included in your workspace for section A2 (preparation.m),
t – Time vector T – Period n trig – Number of harmonics for Trigonometric Fourier Series a0, an, bn – Trigonometric Fourier series coefficient vectors s2 hinf – s2(t) ideal time series representation s2 matrix – s2(t) harmonic component matrix s2 approx – s2(t) signal approximation n comp – Number of harmonics for Complex Fourier Series c0, cn – Complex Fourier series coefficient vectors s3 hinf – s3(t) ideal time series representation s3 matrix – s3(t) harmonic component matrix s3 approx – s3(t) signal approximation |
This section should be implemented in MATLAB – mission.m. Be sure to include relevant figures and code snippets when presenting your results in your report. Senior analysts from the engineering team have determined that the received speech has been corrupted by an additive noise process. This model is illustrated in Figure 2.
Figure 2: Model of additive noise
Your primary objective in this task is to identify the noise signal and de-noise the speech (remove the noise). The speech is provided in the variable noiseSound. Original speech was recorded at a rate of 44100 samples per second for 20 seconds. Follow the instructions below to help you complete your task.
A3.1 One of the test signals that you have used above is the sample waveform of your periodic noise, which you will need to identify. Explain how you identified your noise waveform – consider things such as the period, offset and shape. (Criteria: 1c, 2a)
A3.2 Generate your noise waveform. Save this to the variable additive noise. It is to con- tain the same number of periods as the noise waveform in the corrupted speech signal. Make sure that an appropriate time domain vector, t, was generated for this waveform. (Criteria: 2a)
A3.3 Use MATLAB to evaluate the coefficients of your noise signal of either the Complex Fourier Series; c0 and cn for −10 ≤ n ≤ 10, or the Trigonometric Fourier Series; a0, an and bn for 0 ≤ n ≤ 10. (Criteria: 2b)
A3.4 Write code to generate the Fourier series approximation (FS1), using the time vector t
of your periodic noise. (Criteria: 2b)
A3.5 Using FS1, recover the corrupted speech by reversing the additive process illustrated in Figure 2. Store the de-noised result in the variable dnSnd. (Criteria: 2a)
A3.6 Plot and listen to the recovered speech signal. Comment on visual changes as compared with the noisy speech signal, along with an explanation of what has happened. Include a transcription of the message, you just listened to, in your report. (Criteria: 1c, 2b)
A two paragraph reflection is to be written and appended at the end of your report. In the first paragraph, discuss the effects that changes in noise amplitude and frequency have on the mes- sage signal transmitted to the spaceship i.e. summarize the conceptual understanding you have demonstrated in this assignment. The second paragraph should be a discussion/professional reflection that covers any lessons learned from doing this assignment, and things that you would have done differently. Each paragraph should not exceed 250 words. Marks for this are included as part of the criteria available on Blackboard.
The provided Academic Integrity Declaration and contribution online form must be completed and submitted along with the assignment. Each student from the group will need to complete their own form. Marks may be moderated depending on contributions. Assignments with incomplete or missing declarations will not be marked. Familiarise yourself with the university’s policy regarding plagiarism and collusion. See the file “Academic Honesty Slides.pdf ” posted with this assignment for some useful details.
If academic misconduct is discovered, the suspected student/s will be given an opportunity to explain the similarities to the teaching team. If no response if received within 1 business day of first contact, the matter will be escalated to the faculty, which may affect the release date of final marks for the subject. Please take this seriously. Do not share your code or report with other students, or use other students code or reports.
If you experience a significant personal event that interferes with your ability to complete this task, contact the teaching team as soon as possible. The team may be able to suggest optimal courses of action. The team can not approve extensions – Extension applications must be submitted through the faculty, with supporting documentation.