LMS Algorithm Implementation for Filtering

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Implementation of LMS algorithm for filtering with weight vector reconstruction, enabling noise signal reconstruction and time delay calculation through adaptive filtering techniques

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The LMS (Least Mean Squares) algorithm is a widely used adaptive filtering algorithm that effectively filters noise signals by reconstructing its weight vector, thereby enabling accurate time delay calculation. The algorithm continuously adjusts the filter weights through an iterative process: w(n+1) = w(n) + μ * e(n) * x(n), where w represents the weight vector, μ is the step size parameter, e(n) denotes the error signal, and x(n) is the input signal vector. This weight adaptation mechanism allows the filter to dynamically track signal variations while minimizing noise interference. By implementing this approach, the LMS algorithm achieves precise signal reconstruction and time delay estimation, significantly enhancing signal processing performance in practical applications such as system identification and echo cancellation.

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