Least Mean Squares Filter - Normalised Least Mean Squares Filter (NLMS)

Normalised Least Mean Squares Filter (NLMS)

The main drawback of the "pure" LMS algorithm is that it is sensitive to the scaling of its input . This makes it very hard (if not impossible) to choose a learning rate that guarantees stability of the algorithm (Haykin 2002). The Normalised least mean squares filter (NLMS) is a variant of the LMS algorithm that solves this problem by normalising with the power of the input. The NLMS algorithm can be summarised as:

Parameters: filter order
step size
Initialization:
Computation: For

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