Simulation of AR(2) Model Using LMS Adaptive Filter

In this project, we develop a simulation-based adaptive filter for an AR(2) model using the Least Mean Squares (LMS) algorithm. The implementation involves creating a real-time adaptive filtering system that processes input signals to enhance signal quality and accuracy through iterative coefficient updates. Key components include: - Initialization of filter coefficients using zero vectors or small random values - Implementation of the LMS update rule: w(n+1) = w(n) + μ·e(n)·x(n), where μ represents the step size, e(n) the error signal, and x(n) the input vector - Real-time error calculation between desired and filtered outputs - Convergence analysis through mean-squared error tracking The project aims to research and develop an efficient filtering model suitable for various applications, with emphasis on performance metrics including convergence speed, stability analysis, and steady-state error. Experimental validation involves testing with synthetic AR(2) processes (characterized by second-order difference equations) and comparing results with theoretical predictions. Through this work, we contribute to AR modeling research and provide foundational support for advanced signal processing applications in fields like system identification and predictive filtering.