EGB242 Assignment 1 – Part A (15%)

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:

 

i Read through the entire document before attempting the tasks.

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.

vii Ensure that all work (including process description, code used and plots) are included within the report. An example report showing how this should be presented is available on Blackboard.

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

 

 

Section A1 (BASA Headquarters: Problem Solving)

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, a_n and b_n for n ≤ 3, and the c_n 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, a_n and b_n for n ≤ 3, and the c_n 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)

Section A2 (BASA Headquarters: Training Exercise)

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

Section A3 (Mars Mission: De-noising Speech)

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)

 

 

Section A4 (Reflection) (Criteria: 3d)

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.

 

Academic Integrity Declaration and Group Contribution

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.

 

Hardship and Personal Matters

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.

Report and Code Presentation

This assignment includes elements of writing and coding. This is a group assessment item and you are expected to generate and submit:

• One assignment report, “The Report”,

One set of MATLAB code, “The Code” (including at least ‘preparation.m’ and ‘mis- sion.m’), and

• One Data1A.mat file.

The attached Criteria Reference Assessment (CRA) sheet has the outlines of the marking standards of this assignment.

The teaching team has put together some pointers for you to consider:

 

The Report (Criteria: 3)

An outstanding report demonstrates clear knowledge and understanding of the subject through a combination of visual, mathematical and coding elements. Correct information that is not articulated clearly will attract deductions. Remember that you are writing to inform.

• Present the report so it can be understood without reference to the assignment brief.

• Figures or code referenced should be no more than 1 page turn away.

• You should only include code that is relevant to the question.

• Avoid the use of “see appendix” and “refer to .m file”.

• Full working is required in mathematics-based sections.

• Ensure legibility in any handwritten working.

Include a title page that states the unit name, unit code, group number, and your names and student ID numbers.

• Do not include a table of contents, list of figures, nor a list of tables.

As a guide, a report with all sections complete should be between 20 and 30 pages, including figures and code.

 

The MATLAB Code (Criteria: 2)

Working MATLAB code is expected to be submitted, alongside your report to Blackboard. The code needs to be executable (in *.m) and without run-time errors. No error correction will be made to make your code “run.”

Code should be fully commented to describe intent. Quality comments encapsulate your un- derstanding of the topic.

You may use the code provided in the weekly tutorials to check your solutions. However, you are expected to generate your own code for your assignment. Submitting supplied .p code as your own work constitutes academic misconduct and will not be awarded any marks.

Code for this assignment will be marked with the assistance of an automated marking system. Ensure that you follow given instructions carefully, including naming conventions. Your code submitted will also be checked for academic misconduct.

Interview

Group interviews will take place (at the discretion of the teaching team) to ensure demonstrated understanding and skills required for this assignment, by the group, and the individual mem- bers. You may be selected and contacted to attend an interview if the teaching team requires clarification about how you arrived at your solutions. Interviews will be a casual discussion. These interviews are compulsory and grades are withheld until they are completed. Marks may be deducted for poor demonstration of understanding of content or assignment knowledge. Consult the CRA sheet for the guidelines of what is expected.

 

Submission Protocol

Assignments are to be submitted in soft-copy through QUT Blackboard in three parts

 

A completed academic integrity and group contribution online form. This form is to be completed individually by every student.

The report. Only ONE group member is required to submit the report to the Turnitin link. Coordinate within your group who this will be.

Your data and code files. Include everything here that your code needs to run. You may submit as either a single zip file, or attach your required files individually.

 

 

Some further points:

 

• Submission deadline is on Thursday the 30th of August, at 11:59pm.

This will be a hard deadline, and late submission will not be accepted. As per QUT policy, late assignments receive 0 marks, unless you have applied for and received approval for extension, as per the university policy.

• You do not need to assign your submission with a special name.

• You will need to be registered to a group before you can submit your assignment.

You may submit as many times as you like before the deadline. New submissions overwrite old submissions. Therefore, only the latest submission will be marked.

All documents can be reviewed after submission, and thus it is your responsibility to verify the uploaded documents.

Be aware that the electronic time stamp is placed only after all files have been uploaded successfully.

 

Don’t risk the late penalty and submit early.

 

 

 

Criteria and Standards for Grading

 

Criteria	Standards
CR1a – Theory: Derive the Trigonometric (TSF) and Complex Fourier series (CFS) representations of periodic signals,	CR1. Conceptual understanding    45% Weighting
	7+	7	6	5	4	3	2/1
	· Demonstrates exceptional conceptual understanding of the theoretical concepts behind TFS and CFS, through the use of graphical and mathematical methods that are clear, accurate and logical. · Expresses correct mathematical relationships between function symmetry, TFS and CFS with no errors.	· Demonstrates accurate conceptual understanding of the theoretical concepts behind TFS and CFS, through the use of graphical and mathematical methods that are clear and logical. · Expresses correct mathematical relationships between function symmetry, TFS and CFS with one minor error.	· Demonstrates mostly correct conceptual understanding of the theoretical concepts behind TFS and CFS, through the use of graphical and mathematical methods that are clear and logical. · Expresses correct mathematical relationships between function symmetry, TFS and CFS with a couple of minor errors or one theoretical error.	· Demonstrates conceptual understanding of the theoretical concepts behind TFS and CFS, through the use of graphical and mathematical methods. · Expresses mathematical relationships between function symmetry, TFS and CFS with several minor errors, a couple theoretical errors or one critical theoretical error.	· Demonstrates conceptual understanding of most theoretical concepts behind TFS and CFS, through the use of graphical and mathematical methods. · Expresses mathematical relationships between function symmetry, TFS and CFS with many minor errors, a few theoretical errors or two critical theoretical errors.	· Demonstrates some understanding of some theoretical concepts behind TFS and CFS. · Expresses mathematical relationships between function symmetry, TFS and CFS with several theoretical errors or more than two critical theoretical errors.	· Fails to demonstrate understanding of most theoretical concepts behind TFS and CFS. · Mostly fails to correctly express mathematical relationships between function symmetry, TFS and CFS.
CR1b – Maths Application: Apply the theory to given signals.	· Applies mathematical relationships to given signals with no errors. · Accurately identifies effects of altering the number of coefficients. · Performs all mathematical simplifications necessary.	· Applies mathematical relationships to given signals with a couple minor errors. · Correctly identifies effects of altering the number of coefficients. · Performs almost all mathematical simplifications necessary.	· Applies mathematical relationships to given signals with a few minor errors or one misapplication of the relationships. Performs most mathematical simplifications necessary.	· Applies mathematical relationships to given signals with a several minor errors or a couple misapplications of mathematical relationships. Performs some mathematical simplifications necessary.	· Applies mathematical relationships to given signals with a many minor errors or a few misapplications of mathematical relationships. Fails to perform necessary mathematical simplifications.	· Applies mathematical relationships to given signals with several misapplications of mathematical relationships. Fails to perform any mathematical simplifications.	· Does not correctly apply mathematical relationships to given signals.
CR1c – Justification: Justify the selection of either the TFS or CFS for signal analysis.	· Thoroughly justifies both quantitatively and qualitatively, the selection of parameters, methods, and techniques. · Shows evidence of further research with appropriate references.	· Thoroughly justifies the selection of parameters, methods, and techniques.	· Justifies the selection of parameters, methods, and techniques.	· Justifies the selection of parameters, methods, and techniques with one error or has omitted one necessary justification.	· Justifies the selection of parameters, methods, and techniques with a few errors or has omitted a couple necessary justifications.	· Mostly fails to correctly justify the selection of parameters, methods, and techniques.	· Fails to correctly justify any selection of parameters, methods, and techniques.

 

 

 

 

CR2a – Develop and write code for signal analysis, using Fourier Series analysis.	CR2. Application using MATLAB Coding   30% Weighting
	7+	7	6	5	4	3	2/1
	· Well-commented code has all appropriate simplifications and optimisations performed. · MATLAB functions have been developed to optimise code for repeated processes.	· Well-commented code has most of the appropriate simplifications. · MATLAB functions are optimisations are performed.	· Code is commented throughout and · simplifications and optimisations are performed.	· Code is commented and · some simplifications and/or optimisations are performed.	· Code has some structured approach · Code is difficult to follow.	· Code is unstructured, · Code is difficult to follow and exhibits major flaws in understanding of the concepts.	· Little attempt made to write code.
CR2b – Analyse and perform computations on real signals in the presence of noise.	· Correctly calculates all required variables with no errors.	· Correctly calculates all required variables with only a couple minor errors.	· Correctly calculates all required variables with a few minor errors.	· Calculates all required variables with several minor errors or one major error.	· Calculates required variables with many minor errors or a couple of major errors. There must be no run time errors in the code.	· Attempts to calculate required variables with more than a couple major errors or a run time error.	· No attempts to calculate required variables.
	CR3. Effective written communication   15% Weighting
	7+	7	6	5	4	3	2/1
Assignment solution	· Professional report format, that is easy to read and core technical ideas are clearly and accurately conveyed. All processes and solution steps are clearly outlined. · Code is seamlessly integrated into the report and are used effectively to convey ideas in the report. Code snippets are selectively chosen to succinctly demonstrate all necessary key technical ideas. · Figures are effectively used throughout the report to demonstrate results and facilitate explanations. Figures are labelled and plots are appropriately scaled and visible. · Solution is contextualised to the MARS242 mission, and includes reflections conveying accurate technical knowledge and insights.	· Professional report format, that is easy to read and core technical ideas are clearly and accurately conveyed. Almost all appropriate processes and solution steps are clearly outlined. · Code is integrated into the report and are used to convey the ideas in the report. Selected code snippets demonstrate all key technical ideas. · Figures are effectively used throughout the report to demonstrate results and facilitate explanations. Figures are labelled and plots are appropriately scaled and visible. · Solution is contextualised to the MARS242 mission, and includes reflections conveying accurate technical knowledge.	· Professional report format, that is easy to read and core technical ideas are conveyed. Most of the appropriate processes and solution steps are clearly outlined. · Code is integrated into the report and are used to convey ideas in the report. Selected code snippets demonstrate most key technical ideas. · Figures are used throughout the report to demonstrate results and facilitate explanations. Figures are labelled and plots are appropriately scaled and visible. · Solution is contextualised, and includes reflections. conveying accurate technical knowledge.	· Report is mostly easy to read and most core technical ideas are conveyed. Some key explanations of processes and solution steps are missing. · Code is integrated into the report and are used to convey ideas in the report. Code snippets are used. · Figures are used to demonstrate results and facilitate explanations. Most figures are labelled and plots are appropriately scaled and visible. · Solution is contextualised, and includes reflections.	· Report is missing some key components of a report. Report is difficult to read in some parts and some core technical ideas are conveyed. Many key explanations of processes and solution steps are missing. · Code is not integrated into the report or is not used to connect with the ideas discussed in the report. · Figures are included but do not demonstrate results or facilitate explanations. Some important figures are missing. · Solution contains some contextualisation and reflections.	· Report is missing multiple key components of a report. Report is difficult to read. A significant number of key explanations of processes and solution steps are missing. · Code is not integrated and is mostly a code and figure dump. · Multiple key figures are missing and little effort has been made to link the figures with the report. · Attempts to contextualise the solution but with no reflections.	· Report has little to no structure. Large portions of the report are missing/not attempted. · Code is incorrect or missing from the report. · Figures are almost entirely missing from the report. · No contextualisati on or reflections.
is presented in a
Report format
considering:
CR3a – Structure,
CR3b –Integration,
CR3c – Figures,
graphs and tables
CR3d – Reflections
and
Contextualisation.

 

 

 

 

	Group Plan 10% Weighting
	Full 10% is given if: All Group members have signed up and Group plan completed before the deadline.			Group plan not completed before the deadline.
For moderation of overall marks: At the discretion of the teaching team, your group may be selected to attend an interview if the teaching team require clarification about how the group arrived at their solutions, or how individuals contributed to the overall solution. If selected, you will be notified and given details of the location and time of the interview.
Oral interview – Group Post-submission theoretical and applied skills.	Demonstrate excellent theoretical and applied knowledge retention after assignment submission. All members of the group must be able to correctly explain theory and justify methods used in their submission including MATLAB code.	Demonstrate adequate knowledge retention. If a student fails to show adequate understanding of their assignment and its components, including MATLAB code, his/her overall mark for this assignment may be moderated down by a maximum of 20%.	Demonstrate inadequate knowledge retention. If a student does not attend the interview, or fails to demonstrate fundamental knowledge of their submission and its components, including MATLAB code, his/her overall mark may be moderated down by up to 100%.

 

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