Mathematical Modelling and Implementation of an Online Time‑Varying Adaptive Noise Reduction System

Noise remains a fundamental challenge in modern communication and signal processing systems, significantly affecting signal quality, reliability, and information accuracy. In dynamic and non-stationary environments, traditional fixed-coefficient filters often fail to provide satisfactory performance, creating a growing demand for adaptive real-time noise reduction techniques. This thesis investigates online noise reduction using time-varying filters, which dynamically adjust their parameters to track changing noise characteristics during signal acquisition or transmission. The study explores the theoretical foundations of time-varying filtering, with particular emphasis on adaptive filtering algorithms such as Least Mean Squares (LMS) and Recursive Least Squares (RLS). It analyzes key implementation challenges, including system stability, convergence speed, computational efficiency, and latency constraints, especially in embedded and real-time systems. Mathematical modeling of discrete-time signals is presented to describe the dynamic behavior of time-varying filters and their role in minimizing noise influence while preserving signal integrity.