Least Mean Square (LMS) Adaptive Algorithm
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Resource Overview
The Least Mean Square (LMS) adaptive algorithm is an iterative optimization method that minimizes the mean square error between the desired response and the filtered output signal. It estimates the gradient vector during iteration based on input signals and updates weight coefficients to achieve optimal adaptive filtering. As a stochastic gradient descent approach, LMS is notable for its computational simplicity—requiring no correlation function calculations or matrix operations. Typical implementations involve weight updates using a step-size parameter and instantaneous error feedback.
Detailed Documentation
The Least Mean Square (LMS) adaptive algorithm operates by minimizing the mean square error between the desired response and the filtered output signal. Through iterative estimation of the gradient vector from input signals, it continuously updates filter coefficients to achieve optimal adaptive performance. As a stochastic gradient descent method, LMS is distinguished by its computational efficiency and straightforward implementation. A key advantage is its avoidance of complex operations such as correlation function computation or matrix inversion. In practice, the algorithm can be implemented with a simple weight update rule:
\[
w(n+1) = w(n) + \mu \cdot e(n) \cdot x(n)
\]
where \(w\) represents the weight vector, \(\mu\) the step size, \(e\) the error signal, and \(x\) the input vector. This efficiency has led to widespread successful applications in areas like noise cancellation and system identification.
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