This course explores the theoretical underpinnings and practical applications of signal processing techniques for analysing, manipulating, and extracting meaningful information from signals. Students will gain a comprehensive understanding of the mathematical principles governing diverse signal processing methodologies and acquire the skills necessary to address real-world challenges across a broad spectrum of electronic engineering and cognate domains, including digital communications, medical imaging, audio and video systems, human-machine interaction, robotics, remote sensing, finance, and autonomous vehicles.

This course commences with an introduction to signal synthesis and analysis, employing foundational tools such as orthogonal bases, Hilbert spaces, and matrix decompositions. It then explores Fourier methods for comprehensive time-frequency analysis, statistical signal processing techniques designed to leverage inherent statistical properties, and adaptive methods for effectively addressing the complexities of time-varying or non-linear signals and systems. The course concludes with a discussion on foundational contributions of non-linear signal processing to the core concepts of neural networks and deep learning. Emphasis will be placed on both theoretical rigour and practical implementation using computational tools.