Implementation of Active Noise Cancellation Using Adaptive Filter LMS Algorithm

This article presents the implementation of active noise cancellation using the adaptive filter Least Mean Squares (LMS) algorithm. We provide MATLAB code implementations along with details about the FLMS (Filtered-x LMS) algorithm. The adaptive LMS algorithm serves as an effective method for noise reduction and signal quality enhancement. This algorithm dynamically adjusts filter coefficients based on the error signal between the input and desired output, minimizing noise impact through iterative coefficient updates using the formula: W(n+1) = W(n) + μ·e(n)·X(n), where μ represents the step size, e(n) denotes the error signal, and X(n) is the input vector. The MATLAB implementation demonstrates practical application through key functions including: - System initialization for filter parameters and step size configuration - Real-time coefficient adaptation using vectorized operations - Performance evaluation through mean square error analysis Furthermore, we introduce the FLMS algorithm as an enhanced adaptive filtering approach that improves noise cancellation effectiveness by incorporating secondary path modeling. The FLMS algorithm modifies the standard LMS implementation by filtering the reference signal through an estimated model of the secondary path, thereby compensating for acoustic pathway distortions. Our MATLAB code includes comparative implementations of both standard LMS and FLMS variants, allowing users to observe performance differences in simulated acoustic environments. Through this article, you will gain comprehensive understanding of both LMS and FLMS algorithms' theoretical foundations and practical implementations for active noise control systems, complete with executable MATLAB examples that demonstrate real-time adaptive filtering techniques.