Technical Paper: "The Maths Behind the FxLMS Algorithm"

As part of my PhD research on active noise control for ventilation systems, I authored a technical paper aimed at making my work more accessible to colleagues and fellow researchers. The paper provides a clear and structured explanation of the Filtered-x Least Mean Square (FxLMS) algorithm, which is the mathematical backbone of my thesis work. Starting from the foundational Least Mean Square (LMS) algorithm, I walk the reader through the core principles, key equations, and the critical adaptations that make FxLMS suitable for real-world acoustic environments. The goal was to bridge the gap between theoretical block-diagram understanding and practical implementation, connecting the mathematics to their physical meaning in Active Noise Control systems. This paper reflects both my deep technical expertise in acoustics and signal processing, and my ability to communicate complex engineering concepts clearly and pedagogically.