Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control

Ramos Lorente, Pedro; Martín Ferrer, Raúl; Arranz Martínez, Fernando; Palacios-Navarro, Guillermo

doi:10.3390/app11010344

Open AccessArticle

Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control

by

Pedro Ramos Lorente

^1,*

,

Raúl Martín Ferrer

²,

Fernando Arranz Martínez

¹

and

Guillermo Palacios-Navarro

¹

Department of Electronic Engineering and Communications, University of Zaragoza, 44003 Teruel, Spain

²

Department of Computer Science and Systems Engineering, University of Zaragoza, 44003 Teruel, Spain

^*

Author to whom correspondence should be addressed.

Appl. Sci. 2021, 11(1), 344; https://doi.org/10.3390/app11010344

Submission received: 26 November 2020 / Revised: 25 December 2020 / Accepted: 28 December 2020 / Published: 31 December 2020

(This article belongs to the Collection Recent Applications of Active and Passive Noise Control)

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Abstract

In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-dependent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS.

Keywords: adaptive signal processing; active control of periodic noise; modified filtered-x LMS; hierarchical filter; sequential partial updates

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Ramos Lorente, P.; Martín Ferrer, R.; Arranz Martínez, F.; Palacios-Navarro, G. Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control. Appl. Sci. 2021, 11, 344. https://doi.org/10.3390/app11010344

AMA Style

Ramos Lorente P, Martín Ferrer R, Arranz Martínez F, Palacios-Navarro G. Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control. Applied Sciences. 2021; 11(1):344. https://doi.org/10.3390/app11010344

Chicago/Turabian Style

Ramos Lorente, Pedro, Raúl Martín Ferrer, Fernando Arranz Martínez, and Guillermo Palacios-Navarro. 2021. "Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control" Applied Sciences 11, no. 1: 344. https://doi.org/10.3390/app11010344

APA Style

Ramos Lorente, P., Martín Ferrer, R., Arranz Martínez, F., & Palacios-Navarro, G. (2021). Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control. Applied Sciences, 11(1), 344. https://doi.org/10.3390/app11010344

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Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control

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