LMS Algorithm Implementation of Notch Filter

This implementation demonstrates a notch filter developed in MATLAB using the Least Mean Squares (LMS) algorithm. The LMS algorithm adaptively minimizes the mean square error between the desired signal and the filter output, enabling effective cancellation of specific sinusoidal interference. Through real-time analysis and processing of input signals, the notch filter identifies target frequencies and suppresses their interference. Key implementation steps include initializing filter coefficients, calculating the error signal, and updating weights using the LMS update rule: W(n+1) = W(n) + μ * e(n) * X(n), where μ represents the step size parameter controlling convergence rate. The algorithm allows parameter adjustment (e.g., step size, filter order) to optimize filtering performance based on application requirements. The notch filter demonstrates high real-time performance and stability, making it suitable for various applications including communication systems (e.g., power line interference removal), audio processing (e.g., harmonic elimination), and biomedical engineering (e.g., ECG signal purification). Code implementation typically involves iterative weight updates and frequency response monitoring to ensure accurate notch positioning.