Statistical Adaptive Signal Processing with MATLAB

This article presents comprehensive MATLAB implementations for statistical adaptive signal processing, designed to facilitate deeper understanding of core concepts and methodologies. The codebase includes practical implementations of key algorithms such as LMS (Least Mean Squares) filters, RLS (Recursive Least Squares) adaptive filters, and statistical parameter estimation techniques. Each program contains commented sections explaining the mathematical foundations, including covariance matrix updates, gradient descent optimization for filter coefficients, and real-time adaptation mechanisms. Researchers can modify parameters like step sizes, filter orders, and convergence criteria to observe algorithm behavior under different conditions. The implementations feature data visualization components that plot learning curves, error convergence patterns, and frequency response characteristics. Whether you're beginning your journey in adaptive systems or developing advanced applications like noise cancellation or channel equalization, these modular programs provide hands-on experience with Wiener filter derivations, stability analysis, and performance evaluation metrics. The code structure emphasizes computational efficiency through vectorized operations and includes practical examples using both synthetic and real-world signal data.