LMS Adaptive Filter Implementation for Signal Denoising

In this documentation, I will demonstrate how to implement an adaptive filter using MATLAB source code to achieve signal denoising functionality. Adaptive filters are digital filters that automatically adjust their parameters based on the characteristics of input signals. This implementation specifically utilizes the Least Mean Squares (LMS) algorithm, which employs gradient descent optimization to minimize the mean square error between the desired signal and filter output. The source code provides a complete MATLAB implementation featuring: - A configurable step-size parameter (mu) controlling convergence rate and stability - Real-time coefficient updating using the Widrow-Hoff LMS update rule: w(n+1) = w(n) + μ·e(n)·x(n) - Input signal processing with noise component identification - Performance visualization through error signal monitoring and convergence plots Through this practical example, you'll learn how to: 1. Initialize filter coefficients and set algorithm parameters 2. Implement the core LMS adaptation loop for coefficient adjustments 3. Process noisy signals and extract clean components 4. Analyze filter performance using MATLAB's plotting capabilities This comprehensive source code serves as an educational example to help you understand both the theoretical principles and practical applications of adaptive filtering in signal processing. The implementation includes detailed comments explaining key MATLAB functions such as filter(), mean(), and plot() for signal processing and result visualization.