Adaptive Noise Cancellation Source Code with LMS Algorithm Implementation

This document presents an adaptive noise cancellation source program and simulation of LMS algorithm-based adaptive filters. Adaptive noise cancellation is a technique designed to mitigate noise interference by automatically adjusting filter parameters to adapt to changing noise environments. The LMS (Least Mean Squares) algorithm serves as a widely-used adaptive filtering approach that updates filter weights based on the minimum mean-square error criterion. The simulation implementation typically involves key components: a primary input containing both desired signal and noise, a reference input correlated with the noise, and an adaptive filter that processes the reference input to generate a noise estimate. The core algorithm continuously adjusts filter coefficients using the weight update equation: 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. Through systematic simulations, we validate the performance of the adaptive noise cancellation system and LMS algorithm under various noise conditions. These experiments demonstrate the filter's convergence behavior, steady-state error characteristics, and tracking capabilities in dynamic environments. The simulation framework includes parameter tuning for step size selection, filter length optimization, and performance metrics calculation such as mean-square error and signal-to-noise ratio improvement. The implementation details cover critical aspects including: initialization of filter coefficients, real-time adaptation logic, convergence monitoring mechanisms, and performance visualization tools. This comprehensive analysis facilitates deeper understanding of adaptive filter operational principles and enables quantitative evaluation of system effectiveness across different noise scenarios.