Aims: 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.

Content: 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 offers a comprehensive introduction to the fundamental aspects of DSP, reinforcing understanding through practical applications using programming languages like Python.

Main Topics:

1. Data Acquisition and Sampling: Understanding discrete sequences and systems, diving into the essence of sampling, addressing aliasing, quantization, and signal reconstruction

2. Time Domain Methods: Delving into techniques like correlation and various forms of convolution

3. Frequency Domain Methods: Introducing forward and inverse z-transforms, as well as discrete Fourier transforms

4. Digital Filter Design: Exploring finite and infinite impulse response filters and the realization of digital filters

5. Foundations of Multirate Signal Processing: While advanced topics in multirate signal processing might be touched upon, the primary focus will be on its foundational principles

Objectives: By the end of the module, students should be able to:

• Describe the terminology and concepts of core methods and techniques of digital signal processing
• Design and develop digital signal processing systems and applications
• Formulate and code DSP algorithms to simulate and implement digital signal processing algorithms
• Analyse and explain the behaviour of digital systems
• Design and implement various digital filters including FIR and IIR filters

Books: Indicative reading list:

• Ifeachor, Emmanuel C, Jervis, Barrie W. Digital Signal Processing: A Practical Approach. Prentice Hall, ISBN: 0201596199
• Proakis, John G, Manolakis, Dimitris G. Digital Signal Processing. Pearson Prentice Hall, ISBN: 0131873741
• Porat, Boaz. A Course in Digital Signal Processing. John Wiley, ISBN: 0471149616
• Paulo S. R. Diniz, Eduardo A. B da Silva, and Sergio L. Netto. Digital Signal Processing: System Analysis and Design. ISBN: 0521781752
• Steven B. Damelin, Willard Miller. The Mathematics of Signal Processing (2012)
• Jonathan M. Blackledge. Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications (2006)
• Charles L. Byrne. Signal Processing: A Mathematical Approach, Second Edition (2014)