Data, Signals and Systems - 2023 entry
MODULE TITLE | Data, Signals and Systems | CREDIT VALUE | 15 |
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MODULE CODE | ECM2906 | MODULE CONVENER | Prof Stuart Townley |
DURATION: TERM | 1 | 2 | 3 |
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DURATION: WEEKS | 0 | 11 | 0 |
Number of Students Taking Module (anticipated) | 50 |
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Solar flares occur on eleven-year cycles, surfers wait for “every seventh wave”, porpoise calls have a distinctive signature that can be detected against the background noise of their marine environment, bats locate prey by elaborate use of sonar. In each case, complex time-series data is decomposed into frequency-determined characteristics. This decomposition is then used for explanative and predictive purposes. The analysis of these complex frequency characteristics is at the core of systems and transforms. You will study classical mathematical techniques of Fourier and Laplace transforms, applied in a modern context of a data-rich world. You will use real data from Cornwall-based applications in marine ecology, renewable wave energy and environment and human health.
Pre-requisite modules: “Calculus and Geometry” (ECM1901), “Vector and Matrices” (ECM1902), or equivalent, and familiarity with MATLAB.
The broad aims of the module are to develop the mathematics of modern signal processing, that is the interplay between signals and series, and the systems that operate on them, and then to apply these techniques to real data arising from scientific and engineering applications. Signal processing is ubiquitous across all aspects of science and technology – smart phones, on-line music and video streaming, digital TVs and cameras could not function without signal processing, whilst many areas of applied science would struggle to function. The mathematics of signal processing finds its roots in the 19th century work of Fourier, but leads up to modern tools of discrete Z-transforms and wavelets. This module will uncover the amazing and beautiful mathematics that underpins the digital revolution of the last few decades. The module also illustrates a fundamental issue: the lead-time for technology transfer from theoretical mathematics to commercial/technological products can be decades, if not centuries.
On successful completion of this module, you should be able to:
Module Specific Skills and Knowledge:
1 Demonstrate a sound understanding of essential mathematical aspects of signal processing, including an appreciation of the temporal and frequency content in data and the representation of time series data in terms of basis functions;
2 Reconstruct signals from their frequency content;
3 Appreciate the fundamental limitations of reconstructing a signal from its frequency- or time-sampled form;
Discipline Specific Skills and Knowledge:
4 Demonstrate sufficient knowledge of signal processing techniques for applications in engineering and science;
5 Show awareness and skills in applying a range of mathematical modelling techniques;
Personal and Key Transferable / Employment Skills and Knowledge:
6 Formulate and solve problems;
7 Communicate reasoning and solutions effectively in writing;
8 Make appropriate use of learning resources;
9 Demonstrate self-management and time management skills.
Theme 1. Modelling of systems: examples of systems arising in engineering and scientific applications including electrical circuits, wave energy systems and biological systems; state space models, nonlinear systems, linearization, numerical solutions [8 hours]:
Theme 2. Laplace and inverse Laplace transforms, partial fractions and use of Laplace transform tables; using Laplace Transforms to solve and manipulate linear ordinary differential equations [8 hours];
Theme 3. Generic interpretation of system data; odd and even functions; periodic funcions; signal processing using Fourier series and Fourier transforms; the celebrated Nyquist-Shannon sampling theorem [8 hours];
Theme 4. Transfer functions and input-output systems; poles and zeros; stability; gain and phase; frequency response and Bode; block diagram algebra; Simple feedback control, Z-transforms [8 hours];
Applied group project on one of the four themes in supported matlab classes [12 hours]
Scheduled Learning & Teaching Activities | 44 | Guided Independent Study | 106 | Placement / Study Abroad | 0 |
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Category | Hours of study time | Description |
Scheduled Learning and Teaching Activities | 16 | Formal lectures of new material |
Scheduled Learning and Teaching Activities | 16 | Example classes and computer demos |
Scheduled Learning and Teaching Activities | 12 | Tutorials for group project support |
Guided Independent Study | 106 | Lecture & assessment preparation; wider reading |
Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
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Fortnightly Exercise Sheets | 15 hours. Students expected (strongly encouraged) to attempt ALL formative questions | 1-9 | Written and Oral |
Coursework | 50 | Written Exams | 50 | Practical Exams | 0 |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
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Selection of questions similar to those from the formative sheets sat as tests. | 4 times 5 = 20 | At regular intervals in line with the 4-theme learning cycle, students will complete FOUR 30-minute tests. Students will be encouraged to complete ALL formative questions before hand. The tests aim to endorse understanding of formative work. But students will be able to attempt these questions from scratch. | 1-9 | Annotated scripts and oral feedback from module leader, discussion with peers |
In depth data, signals and systems group project | 30 | 8 hours | 1-9 | Written and oral |
Written exam | 50 | 1 hour 30 minutes | 1-7 | Annotated scripts |
Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-assessment |
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Selection of questions similar to those from the formative sheets sat as tests. | As original | 1-9 | August Ref/Def Period |
In depth data, signals and systems group project | As original | 1-9 | August Ref/Def Period |
Written exam | As original | 1-7 | August Ref/Def Period |
As original |
If mitigating circumstances prevent timely completion of one or more tests (normally within a specified week) or if candidates are referred or deferred, then candidates will complete a coursework assessment pro rata with the missed test(s).
If mitigating circumstances prevent candidates from completing the group project or if candidates are referred, then they will complete an alternative coursework.
If mitigating circumstances prevent attendance at the exam in May or if candidates are referred then they will sit an exam in the deferred assessment period.
information that you are expected to consult. Further guidance will be provided by the Module Convener
Basic reading:
ELE - http://vle.exeter.ac.uk
Reading list for this module:
Type | Author | Title | Edition | Publisher | Year | ISBN |
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Set | Kreyszig, E. | Advanced Engineering Mathematics | 9th | Wiley | 2006 | 978-0471728979 |
Set | McMahon, D. | Signals and Systems Demystified | McGraw Hill | 2006 | 978-0071475785 |
CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | ECM1901, ECM1902 |
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CO-REQUISITE MODULES |
NQF LEVEL (FHEQ) | 5 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Thursday 6th July 2017 | LAST REVISION DATE | Tuesday 26th September 2023 |
KEY WORDS SEARCH | Fourier series; Fourier Transforms; Laplace Transforms; Linear systems; ODEs; Signal processing |
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Please note that all modules are subject to change, please get in touch if you have any questions about this module.