Filtered-x generalized mixed norm (FXGMN) algorithm for active noise control

• Published in: Mechanical systems and signal processing 2018-07, Vol.107, p.93-104
• Main Authors: Song, Pucha, Zhao, Haiquan
• Format: Article
• Language: English
• Subjects: Active noise control; Adaptive algorithms; Adaptive control; Adaptive filtering; Adaptive filters; Adaptive technology; Computer simulation; Convergence; Convex analysis; Convex combination; Filtering systems; Filtration; Generalized linear models; Generalized mixed norm; Impulsive noise; Noise control; Noise reduction; Normal distribution; Norms; Random noise; Stability analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2018.01.035

•The filtered-x generalized mixed norm (FXGMN) algorithm for active noise control.•A convex combination of the FXGMN algorithm (C-FXGMN) for active noise control.•The stability condition of the proposed algorithm is analyzed, and computational complexity is provided.•Computer simulations demonstrate robust performance for impulsive noise control. The standard adaptive filtering algorithm with a single error norm exhibits slow convergence rate and poor noise reduction performance under specific environments. To overcome this drawback, a filtered-x generalized mixed norm (FXGMN) algorithm for active noise control (ANC) system is proposed. The FXGMN algorithm is developed by using a convex mixture of lp and lq norms as the cost function that it can be viewed as a generalized version of the most existing adaptive filtering algorithms, and it will reduce to a specific algorithm by choosing certain parameters. Especially, it can be used to solve the ANC under Gaussian and non-Gaussian noise environments (including impulsive noise with symmetric α-stable (SαS) distribution). To further enhance the algorithm performance, namely convergence speed and noise reduction performance, a convex combination of the FXGMN algorithm (C-FXGMN) is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXGMN and C-FXGMN algorithms can achieve better convergence speed and higher noise reduction as compared to other existing algorithms under various noise input conditions, and the C-FXGMN algorithm outperforms the FXGMN.