MATLAB Implementation of Adaptive Filter with Code Analysis

Adaptive filters are implemented using an 11-tap FIR filter structure in MATLAB. Several key aspects are investigated in adaptive filter research. (1) First, the impact of varying noise variance σ² on filter performance can be analyzed through Monte Carlo simulations, where changing the input signal variance helps evaluate the filter's robustness to different noise conditions. (2) The LMS (Least Mean Squares) algorithm implementation involves computing the error convergence curve for a single experiment with 500 training iterations, extracting the final filter coefficients using the weight update equation w(n+1) = w(n) + μ·e(n)·x(n). For comprehensive analysis, 20 independent experiments are conducted with different step sizes (μ values), and the average convergence curve is calculated to study the trade-off between convergence speed and steady-state error. (3) Finally, a comparative study between LMS and RLS (Recursive Least Squares) algorithms is performed, where RLS implementation uses the recursive covariance matrix inversion with forgetting factor λ, providing insights into their convergence properties, computational complexity, and tracking capabilities for real-time signal processing applications.