MATLAB Implementation of LMS Algorithm with Complete Code Structure

This documentation provides a detailed explanation of an LMS (Least Mean Squares) algorithm implementation. The code includes complete modules for input signal processing, filtered output generation, and real-time error rate calculation. The algorithm can be freely downloaded from the specified repository for immediate use in your projects. The LMS algorithm represents one of the most widely used adaptive filtering techniques that automatically adjusts filter coefficients to match signal characteristics. The core implementation follows these key steps: First, the algorithm calculates the error signal by comparing the filter output with the desired reference signal. Then, it updates the filter coefficients using the gradient descent method with the mathematical formulation: W(n+1) = W(n) + μ * e(n) * X(n), where μ is the step-size parameter controlling convergence rate, e(n) denotes the instantaneous error, and X(n) represents the input vector. Key MATLAB functions included in this implementation: - lms_filter() - Main adaptive filtering function with configurable parameters - compute_error() - Real-time error calculation between desired and actual outputs - update_coefficients() - Coefficient adaptation using LMS update rule - performance_metrics() - Monitors convergence behavior and steady-state error The implementation allows users to adjust critical parameters like filter length, step size, and convergence criteria through structured input arguments. The code outputs both the filtered signal and comprehensive performance data including mean squared error plots and coefficient convergence trajectories. This information will help you gain deeper understanding of adaptive filtering principles and effectively integrate this algorithm into your signal processing applications.