Fundamental Structure of Adaptive Filters and Least Mean Square Error Algorithm (LMS Algorithm)

In this paper, we systematically study the fundamental structure of adaptive filters and the Least Mean Square (LMS) algorithm. The LMS algorithm implementation involves iterative weight updates using the formula w(n+1) = w(n) + μ·e(n)·x(n), where μ represents the step size parameter, e(n) denotes the error signal, and x(n) is the input vector. We conducted detailed simulation experiments using MATLAB, implementing key functions including signal generation, filter initialization, and real-time coefficient adaptation loops to validate the algorithm's performance and effectiveness. Subsequently, we deployed the algorithm on the SY-5402EVM evaluation board for DSP implementation, optimizing the code structure for real-time processing through fixed-point arithmetic and pipeline operations. Through analysis of the implementation results, we thoroughly investigated the algorithm's applications and optimization potential in various scenarios. Our research demonstrates that this adaptive filter with LMS algorithm possesses broad application prospects in signal processing domains such as noise cancellation, system identification, and channel equalization.