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日期：2024-03-08 11:06

Academic Year: 2023/24

Assessment Introduction:

Course:

BEng (Hons) Electronic Engineering Module Code: EL2106

Module Title: Signals and Systems

Title of the Brief:

Fourier Series for Synthesis and Analysis of Periodic Signals Type of assessment: Coursework

This Assessment Pack consists of a detailed assignment brief, guidance on what you need to prepare, and information on how class sessions support your ability to complete successfully. You’ll also find information on this page to guide you on how, where, and when to submit. If you need additional support, please make a note of the services detailed in this document.

How, when, and where to submit:

The deadline for this assessment is 22nd March 2024 at 23.59 via the submission zone found the EL2106 Blackboard area - Please note that this is the final time you can submit – not the time to submit!

Your work needs to be submitted via the Turnitin link on Blackboard, the link will be visible to you on: 12th December 2023

Feedback will be provided by: 26th April 2024

You should aim to submit your assessment in advance of the deadline.

Note: If you have any valid mitigating circumstances that mean you cannot meet an assessment submission deadline and you wish to request an extension, you will need to apply online, via MyUCLan with your evidence prior to the deadline. Further information on Mitigating Circumstances via this link.

We wish you all success in completing your assessment. Read this guidance carefully, and any questions, please discuss with your Module Leader or module team.

Additional Support available:

All links are available through the online Student Hub

1.Academic support for this assessment will be provided by contacting Wei Quan WQuan@uclan.ac.uk

2.Our Library resources link can be found in the library area of the Student Hub or via your subject librarian at SubjectLibrarians@uclan.ac.uk.

3.Support with your academic skills development (academic writing, critical thinking and referencing) is available through WISER on the Study Skills section of the Student Hub.

4.For help with Turnitin, see Blackboard and Turnitin Support on the Student Hub

5.If you have a disability, specific learning difficulty, long-term health or mental health condition, and not yet advised us, or would like to review your support, Inclusive Support can assist with reasonable adjustments and support. To find out more, you can visit the Inclusive Support page of the Student Hub.

6.For mental health and wellbeing support, please complete our online referral form, or email wellbeing@uclan.ac.uk. You can also call 01772 893020, attend a drop-in, or visit our UCLan Wellbeing Service  Student Hub pages for more information.

7.For any other support query, please contact Student Support via studentsupport@uclan.ac.uk.

8.For consideration of Academic Integrity, please refer to detailed guidelines in our policy document . All assessed work should be genuinely your own work, and all resources fully cited.  

9.For this assignment, you are not permitted to use any category of AI tools.

Preparing for your assignment.

Ensure that you fully understand the requirements for the assessment and what you are expected to complete. The assignment will be introduced in the lecture session where you can ask any questions, you can also ask for clarification by contacting the module team.

The following module learning outcomes will be assessed in this assignment:

·Use time domain and frequency-domain representations of signals and systems to analyse signal and system characteristics and system responses graphically and mathematically.

·Implement relevant processing techniques, such as Fourier analysis and s-plane analysis, using software tools such as spreadsheets or MATLAB, and demonstrate an understanding of the practical results acquired from the software-based implementations.

Please read over the guide to writing a technical document https://www.theiet.org/media/5182/technical-report-writing.pdf and ensure that you fully understand the requirements of the assessment. There will be a lecture session on the assignment and writing a technical document.

Ensure that you research and read into the subject area before writing the report so that you have a good background understanding to the subject area.

Assignment Brief

For all stages, select appropriate ranges (time, frequency etc.) for the plots to show the appropriate features of the signals and spectra.  Label both axes on all plots.  Throughout this assignment, the sampling frequency for all signals should be 200 kHz.

1)Periodic Discrete-Time Signal Generation (25 marks)

Generate a set of discrete-time sinusoids using MATLAB.  The signals should have a specified amplitude and phase (your choices, you may decide to experiment with these), and a frequency as specified below.  Plot the sample values against time and observe the resulting waveform.  Use a suitable time range so as to show the relevant features of the signal.  Comment on whether the observed waveform corresponds to the expected waveform and explain any significant differences. (HINT: a key word that you may wish to investigate and explain is ‘aliasing’).

Use the following values (individually) for the frequency of the sinusoid: 1 kHz, 10 kHz, 45 kHz, 55 kHz, 90 kHz, 99 kHz.

2)Fourier Synthesis for Periodic Signals (25 marks)

Synthesise periodic signals using MATLAB, each with a fundamental frequency of 100 Hz, using a d.c. component (a0), and a sum of ‘cos’ terms (with amplitudes given by the ak coefficients) and ‘sin’ terms (with amplitudes given by the bk coefficients).  Repeat the synthesis of these signals using MATLAB.

The synthesis equation is:

The ak and bk coefficients should be selectable by the user, and the signals should be synthesised with two different harmonic ranges:

(a) from d.c. up to and including the 10th harmonic (i.e. N = 10).

(b) from d.c. up to and including the 30th harmonic (i.e. N = 30).

Use the MATLAB program created above, with the two harmonic ranges, to synthesise the following signals:

(i)A signal f1(t) of fundamental frequency 200 Hz for which a0 = 5 V, and ak and bk are defined by the

equations below:

(ii)An approximation of square wave of amplitude 10 V and fundamental frequency 200 Hz, for which you should identify formulae for a0, ak and bk using Fourier series analysis as discussed in the EL2106 classes.

3)Fourier Analysis for Quasi-Periodic Signals (40 marks)

A different sampled signal will be provided (by another MAT file) to each student on or before 23rd January 2024.  The signal has frequency 250 Hz, sampled at 100 kHz.  Three practice signals (periodic and quasi-periodic) are available on Blackboard.  Each file will contain 2000 samples of the signal, covering five cycles of the quasi-periodic signal (400 points per cycle).  Note that slight differences are apparent between each ‘cycle’ of the quasi-periodic signals.

(a) Create a MATLAB program to perform Fourier analysis of the signal from d.c. up to and including the 20th harmonic.  The analysis should include all 2000 points provided, but the calculations should be based on the correct fundamental frequency (i.e. 1 cycle is specified by 400 points corresponding to a fundamental frequency of 250 Hz).  Include in your report a table listing the magnitude (Fk) and phase (φk) of each of the 25 frequency components.  Evaluate the d.c. component of the signal and identify the six dominant a.c. frequency components (i.e. those with the four largest magnitudes) present in your signal.

(b) Synthesise the signal using only the d.c. value and the six dominant frequency components, using the magnitude and phase values obtained from your analysis.

(c) Subtract the synthesised signal from part (b) from the original signal (provided) and observe and explain the resulting difference signal.  Calculate the RMS value of the difference signal and express this as a value in dB relative to the RMS value (over all five cycles) of the original signal provided.

Word limit: A maximum of 1000 words (see notes below for further information).

Technical Report Writing

To complete the report, you will have to thoroughly research the area using reliable sources and precisely reference where your information and statements are from. The aim of the report is to be clear, concise and convey technical information to the reader, note that the reader is familiar and experienced in the area. Ensure that you write your report for this audience.

A guide on writing a technical document can be found at the following (this will also be uploaded to blackboard):

https://www.theiet.org/media/5182/technical-report-writing.pdf

Please read over the above document to ensure that you are clear on what a technical report is and know what you are required to complete, note the above is a guide not an explicit standard you will be required to ensure that your technical report contains the relevant information presented correctly for the reader.

Ensure that you research and read into the subject area before writing the report so that you have a good background understanding to the subject area. You will need to provide a short report, which shows the calculation of each tasks in Marking Criteria and Weighting section below with an appropriate assumption, description and comments, no longer than 1,000 words. You should use the guideline below to structure your report. For the final reporting submission, make sure that each page is marked with the date of completion, the page number, and the total number of pages submitted.  Make sure that the front page of your submission has this information displayed prominently along with the module name and number and assignment title. Submit your reporting material with a single Word file through EL2106 Blackboard submission link with Matlab code attached in the back of the file. Your work must be referenced using Harvard Referencing system available here: https://v3.pebblepad.co.uk/v3portfolio/uclan/Asset/View/Gm3mmGk6sM3RgHZnjGfh7mm6pM.

Further information to support your development will be available to view on assignment briefing session and Blackboard.

Notes on Wordcount and Referencing

For good marks and given the limited wordcount you should produce work that is: accurate; thorough; well-argued; clear; accurately referenced; relevant and written in correct (UK) English grammar and spelling. You may include figures and tables with short captions (25 words each) and a list of references without affecting the overall word count. Remember that you have limited words so ensure that you “stick to the point” and do not get into detail on superficial elements.

Ensure that you include references when discussing technical facts and statements on the technology used. You must reference all your sources of information. These should be cited in the appropriate part of the report and fully identified to meet the Harvard referencing standard in a list at the end. Website articles must be properly referenced to be considered as legitimate references.

Presentation of assignment work

Except where specifically stated in the assignment brief, assignment work submissions should be word-processed, in Microsoft Word format, with a footer comprising: your module code; date; page number. Your work needs to be submitted via the Turnitin link on Blackboard.

The following module learning outcomes will be assessed in this assignment:

Use time domain and frequency-domain representations of signals and systems to analyse signal and system characteristics and system responses graphically and mathematically.

Implement relevant processing techniques, such as Fourier analysis and s-plane analysis, using software tools such as spreadsheets or MATLAB, and demonstrate an understanding of the practical results acquired from the software-based implementations.

Marking Criteria and Weighting

Your submission will be marked in accordance with the following marking scheme:

Item Weight (%) Model answer criteria

1.Periodic Discrete-Time Signal Generation 25 Neat diagram, clearly presenting the waveforms in MATLAB with appropriate descriptions and comments on the waveforms generated.

2.Fourier Synthesis for Periodic Signals 25 Concise and accurate demonstration on the process of calculation for the synthesised signals, appropriately referenced for the formula where required.

3.Fourier Analysis for Quasi-Periodic Signals 40 Concise and accurate demonstration on the process of calculation for the given signal/waveform. Accurate description of the results of calculation. Neat diagram for presenting the synthesised signals in MATLAB.

4.Presentation 10 Presentation requirements met in full. Concise, complete and well-structured documentation with correct use of English throughout.  Neat diagrams, clearly presented.  Contents page and page numbers.

Total 100

Feedback Guidance:

Reflecting on Feedback: how to improve.

From the feedback you receive, you should understand:

The grade you achieved.

The best features of your work.

Areas you may not have fully understood.

Areas you are doing well but could develop your understanding.

What you can do to improve in the future - feedforward.

Use the WISER: Academic Skills Development service. WISER can review feedback and help you understand your feedback. You can also use the WISER Feedback Glossary

Next Steps:

List the steps have you taken to respond to previous feedback.

Summarise your achievements

Evaluate where you need to improve here (keep handy for future work):