MATLAB Implementation of LMS Algorithm for Single-Frequency Signal Extraction

The LMS (Least Mean Squares) algorithm is an effective method for extracting single-frequency signals from broadband signals, known for its simplicity and practical implementation. This algorithm processes input signals through adaptive filtering to isolate specific frequency components. The core principle involves adaptively adjusting filter weights based on error signals, continuously optimizing filter performance through iterative updates. In practical applications, the LMS algorithm proves highly valuable for audio signal processing, communication systems, and spectral analysis. The implementation typically involves initializing filter coefficients, calculating the output signal, computing the error between desired and actual output, and updating weights using the formula: w(n+1) = w(n) + μ * e(n) * x(n), where μ represents the step size parameter controlling convergence rate. Through MATLAB implementation, we can effectively process broadband signals, extract target single-frequency components, and achieve more accurate analytical results in signal processing applications.