### Abstract

The paper concerns active control of impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance (second order moment) of error signal, and hence, becomes unstable for the impulsive noise. In order to improve the robustness of adaptive algorithms for processes having distributions with heavy tails (i.e. signals with outliers), either (1) a robust optimization criterion may be used to derive the adaptive algorithm or (2) the large amplitude samples may be ignored or replaced by an appropriate threshold value. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm (approach 1). The other is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm (approach 2). In this paper we propose two solutions to improve the robustness of the FxLMP algorithm. In first proposed algorithm, the reference and the error signals are thresholded before being used in the update equation of FxLMP algorithm. As another solution to improve the performance of FxLMP algorithm, a modified normalized step size is proposed. The computer simulations are carried out, which demonstrate the effectiveness of the proposed algorithms.

Original language | English |
---|---|

Pages (from-to) | 688-694 |

Number of pages | 7 |

Journal | Applied Acoustics |

Volume | 72 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 1 2011 |

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### Keywords

- Active noise control
- FxLMP algorithm
- FxLMS algorithm
- Impulse noise
- Stable processes

### ASJC Scopus subject areas

- Acoustics and Ultrasonics

### Cite this

**Improving robustness of filtered-x least mean p-power algorithm for active attenuation of standard symmetric-α-stable impulsive noise.** / Akhtar, Muhammad Tahir; Mitsuhashi, Wataru.

Research output: Contribution to journal › Article

*Applied Acoustics*, vol. 72, no. 9, pp. 688-694. https://doi.org/10.1016/j.apacoust.2011.02.009

}

TY - JOUR

T1 - Improving robustness of filtered-x least mean p-power algorithm for active attenuation of standard symmetric-α-stable impulsive noise

AU - Akhtar, Muhammad Tahir

AU - Mitsuhashi, Wataru

PY - 2011/9/1

Y1 - 2011/9/1

N2 - The paper concerns active control of impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance (second order moment) of error signal, and hence, becomes unstable for the impulsive noise. In order to improve the robustness of adaptive algorithms for processes having distributions with heavy tails (i.e. signals with outliers), either (1) a robust optimization criterion may be used to derive the adaptive algorithm or (2) the large amplitude samples may be ignored or replaced by an appropriate threshold value. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm (approach 1). The other is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm (approach 2). In this paper we propose two solutions to improve the robustness of the FxLMP algorithm. In first proposed algorithm, the reference and the error signals are thresholded before being used in the update equation of FxLMP algorithm. As another solution to improve the performance of FxLMP algorithm, a modified normalized step size is proposed. The computer simulations are carried out, which demonstrate the effectiveness of the proposed algorithms.

AB - The paper concerns active control of impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance (second order moment) of error signal, and hence, becomes unstable for the impulsive noise. In order to improve the robustness of adaptive algorithms for processes having distributions with heavy tails (i.e. signals with outliers), either (1) a robust optimization criterion may be used to derive the adaptive algorithm or (2) the large amplitude samples may be ignored or replaced by an appropriate threshold value. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm (approach 1). The other is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm (approach 2). In this paper we propose two solutions to improve the robustness of the FxLMP algorithm. In first proposed algorithm, the reference and the error signals are thresholded before being used in the update equation of FxLMP algorithm. As another solution to improve the performance of FxLMP algorithm, a modified normalized step size is proposed. The computer simulations are carried out, which demonstrate the effectiveness of the proposed algorithms.

KW - Active noise control

KW - FxLMP algorithm

KW - FxLMS algorithm

KW - Impulse noise

KW - Stable processes

UR - http://www.scopus.com/inward/record.url?scp=79956160418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956160418&partnerID=8YFLogxK

U2 - 10.1016/j.apacoust.2011.02.009

DO - 10.1016/j.apacoust.2011.02.009

M3 - Article

AN - SCOPUS:79956160418

VL - 72

SP - 688

EP - 694

JO - Applied Acoustics

JF - Applied Acoustics

SN - 0003-682X

IS - 9

ER -