MA3K9-15 Mathematics of Digital Signal Processing
Introductory description
Digital signal processing is based on many, core disciplines covering many theoretical and application fields. In the field of Mathematics, calculus, probability statistics, deterministic and stochastic processes, and numerical analysis are all core disciplines for digital signal processing. It also lies at the core of many new and emerging areas of science and technology, including network theory and interconnected systems, signals and systems, cybernetics, communication theory, control theory, and fault diagnosis. In addition, digital signal processing forms the basic foundation for the exciting fields of artificial intelligence, pattern processing and analysis, and neural networks. This module comprehensively introduces the main topics in digital signal processing design and analysis including interpolation, convolution, correlation, discrete Fourier transform, z transform, and filter designs. It will also be supported by examples and other modelling techniques using programming languages such as Matlab and Python.
Module aims
The module aims at developing an in-depth knowledge of discrete-time signal processing algorithms and approaches to measure, analyse and understand and improve the performance of digital systems and their applications. It will then be structured around the following topics:
1- Data acquisition and sampling
- Discrete sequences and systems
- Sampling and sampling theorem
- Aliasing,
- Quantisation
- Signal reconstruction
2- Time domain Methods
- Correlation
- Linear convolution
- Circular convolution
2- Frequency domain methods
- Forward and inverse z-transform
- Forward and inverse discrete Fourier transform
3- Digital filter design
- Finite and infinite impulse response filters
- Realisation of digital filters
4- Introduction to multirate signal processing
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Digital signal processing lies at the core of many new and emerging areas of science and technology including telecommunication, biomedical applications, image processing and recognition, and digital media. This module is an introduction to the basic mathematical tools that are required to present, analyse, understand and design digital signal processing systems. This includes the basics of sampling of continuous time signals, digital filters, digital spectral analysis and digital multirate signal processing.
Learning outcomes
By the end of the module, students should be able to:
- 1. Describe the terminology and concepts of core methods and techniques of digital signal processing.
- 2. Design and develop digital signal processing systems and applications.
- 3. Formulate and code DSP algorithms to simulate and implement digital signal processing algorithms.
- 4. Analyse and explain the behaviour of digital systems.
- 5. Design and implement various digital filters including FIR and IIR filters.
Indicative reading list
1- Ifeachor, Emmanuel C, Jervis, Barrie W. Digital signal processing: a practical approach. Prentice Hall, ISBN: 0201596199.
2- Proakis, John G, Manolakis, Dimitris G. Digital signal processing. Pearson Prentice Hall, ISBN: 0131873741.
3- Porat, Boaz. A course in digital signal processing. John Wiley, ISBN: 0471149616.
4- Paulo S. R. Diniz, Eduardo A. B da Silva, and Sergio L. Netto. Digital signal processing: System Analysis and Design. ISBN: 0521781752.
Interdisciplinary
DSP is a highly interdisciplinary field. It is dependent on technical studies in many adjacent fields including Communication Theory, Numerical Analysis, Probability and Statistics, and Digital Electronics, etc.
Subject specific skills
Students taking the module will be able to analyse discrete signals and systems, apply introduced methods in the design of basic signal processing applications, work independently on Matlab/Python signal and analysis tools, design and apply digital filters to separate required/desired signal form signals with noise, and critically assess digital signal processing systems in terms of performance.
Transferable skills
Specialist knowledge and application. Critical thinking and problem solving. Critical analysis. Numeracy. Effective Information retrieval and research skills. Computer literacy. Creativity, innovation & independent thinking.
Study time
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (20%) |
| Tutorials | 9 sessions of 1 hour (6%) |
| Online learning (independent) | (0%) |
| Private study | 56 hours (37%) |
| Assessment | 55 hours (37%) |
| Total | 150 hours |
Private study description
Review lectured material and work on set exercises.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Assignments | 15% | 25 hours | No |
|
4 homeworks assignments. This will ensure that the students keep up with the module during the term. The students’ understanding of the basic concepts and theory and their application to real world problems will be assessed through continuous coursework assignments that are lined up with the lecture topics and learning outcomes. |
|||
| Final Exam | 85% | 30 hours | No |
|
A standard 3 hour exam |
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Assessment group R1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Resit exam | 100% | No | |
|
The same as above. |
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Feedback on assessment
Marked assignments
Courses
This module is Optional for:
-
UMAA-G100 Undergraduate Mathematics (BSc)
- Year 3 of G100 Mathematics
- Year 3 of G100 Mathematics
- Year 3 of G100 Mathematics
-
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G100 Mathematics
- Year 3 of G103 Mathematics (MMath)
- Year 3 of G103 Mathematics (MMath)