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Frequency domain analysis of the mirror‐modified filtered‐x least mean squares algorithm with low ambient noise
Author(s) -
Lopes Paulo A. C.,
Gerald José A. B.
Publication year - 2021
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3246
Subject(s) - noise (video) , least mean squares filter , algorithm , frequency domain , convergence (economics) , active noise control , noise power , residual , least squares function approximation , context (archaeology) , path (computing) , mathematics , noise reduction , computer science , power (physics) , adaptive filter , statistics , artificial intelligence , physics , mathematical analysis , paleontology , estimator , economics , image (mathematics) , biology , programming language , economic growth , quantum mechanics
Summary The mirror‐modified filtered‐x least mean squares (MMFxLMS ) algorithm is a variation of the FxLMS algorithm with online secondary path modeling that cannot diverge due to secondary path modeling errors. However, problems may occur when the ambient noise is not limited due to insufficient modeling power. This work shows that under a frequency domain analysis without ambient noise, the MMFxLMS algorithm is always stable, and expressions for the maximum residual noise level at any given time are obtained. It is also shown that, under the same context, convergence to the minimum residual noise is guaranteed. Still, convergence can be much slower for high secondary path modeling errors than that of the LMS or MFxLMS algorithms. Simulations confirm these results.