FxLMS(Filtered-X Least Mean Square) 演算法是最經典常用的方法於主動噪音控制(Active Noise Control,ANC) 中，它運用在高斯環境的情況下通常會有良好的收斂成效，並且已經有大量的學者在進行研究並探討如何進一步改善它的效能，但是應用在現實世界中，ANC 系統可能會接收到來自環境中突然生成的詭異訊號，我們稱作脈衝噪音(Impulse Noise,IN)，這可能導致廣為人知的FxLMS 演算法效能出現劇烈下降或收斂失敗，翻閱過往一些文獻已經有在探討這方面的問題，但是許多提出的解決方法是取決於預先確定的參數，在本文中，對於脈衝噪音的問題是採用穩健函數來抑制，並且新提出的演算法與過去文獻所提的不同，不需要透過事前條件來定義參數，並結合嵌入式架構，達成播放音訊時，同時可以消除噪音，經由模擬所得的結果，我們將與過往的方法做比較與討論，而提出的演算法會擁有更良好的(Noise Reduction Ratio,NRR) 效能。

The Filtered-X Least Mean Square(FxLMS) is the most classic and commonly used method for Active Noise Control(ANC), which usually has a good convergence effect in a Gaussian environment.Therefore, there have been already a lot of scholars conducting research and discussing how to improve its performance. However,in real world the ANC system may receive a special signal suddenly generated from the environment and we called the impulsive noise(IN),which can result in degraded of performance or convergence failure to the well-known FxLMS algorithm. Some previous literatures have been taking into account this problem, but many of the proposed solutions depend on the setup of pre-determined parameters. In this article,the IN problem is dealt with robust function and the newly proposed algorithm is different from those proposed in the previous literature. It does not need to define parameters through prior conditions, and it can eliminate noise while playing audio.The results
obtained through simulations are compared and discussed with the previous methods and show that the proposed has better noise reduction ratio(NRR) performance.

[1] L. Liu, S. Gujjula, P. Thanigai, and S. M. Kuo, “Still in Womb: Intrauterine Acoustic Embedded Active Noise Control for Infant Incubators,” Advances in Acoustics and Vibration, vol. 2008, p. 495317,2008.
[2] P. Lueg, “Process Of Silencing Sound Oscillations,” Granted Patent US 2 043 416 A.
[3] M. A. Swinbanks, “The active control of sound propagation in long ducts,” Journal of Sound and Vibration, vol. 27, no. 3, pp. 411–436,1973.
[4] B. Widrow, J. R. Glover, J. M. McCool, J. Kaunitz, C. S. Williams, R. H. Hearn, J. R. Zeidler, J. Eugene Dong, and R. C. Goodlin, “Adaptive noise cancelling: Principles and applications,” Proceedings
of the IEEE, vol. 63, no. 12, pp. 1692–1716, 1975.
[5] J. H. B. Poole and H. G. Leventhall, “An experimental study of
swinbanks’ method of active attenuation of sound in ducts,” Journal
of Sound and Vibration, vol. 49, no. 2, pp. 257–266, 1976.
[6] C. F. Ross, “An adaptive digital filter for broadband active sound control,” Journal of Sound and Vibration, vol. 80, no. 3, pp. 381–388, 1982.
[7] J. C. Burgess, “Active adaptive sound control in a duct: A computer simulation,” The Journal of the Acoustical Society of America, vol. 70, no. 3, pp. 715–726, 1981.
[8] S. M. Kuo and D. R. Morgan, “Active noise control: a tutorial review,” Proceedings of the IEEE, vol. 87, no. 6, pp. 943–973, 1999.
[9] “Front Matter,” in Signal Processing for Active Control, ser. Signal Processing and its Applications, S. J. ELLIOTT, Ed. London:Academic Press, 2001, p. iii.
[10] S. J. Elliott and P. A. Nelson, “Active noise control,” IEEE Signal Processing Magazine, vol. 10, no. 4, pp. 12–35, 1993.
[11] S. M. Kuo and D. Morgan, Active Noise Control Systems: Algorithms and DSP Implementations, 1st ed. USA: John Wiley & Sons, Inc., 1995.
[12] L. A. Berry, “Understanding Middleton’s Canonical Formula for Class a Noise,” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-23, no. 4, pp. 337–344, 1981.
[13] K. Vastola, “Threshold Detection in Narrow-Band Non-Gaussian Noise,” IEEE Transactions on Communications, vol. 32, no. 2, pp.134–139, 1984.
[14] M. Ghosh, “Analysis of the effect of impulse noise on multicarrier and single carrier QAM systems,” IEEE Transactions on Communications, vol. 44, no. 2, pp. 145–147, 1996.
[15] R. Pighi, M. Franceschini, G. Ferrari, and R. Raheli, “Fundamental performance limits of communications systems impaired by impulse noise,” IEEE Transactions on Communications, vol. 57, no. 1, pp. 171–182, 2009.
[16] M. Shao and C. L. Nikias, “Signal processing with fractional lower order moments: stable processes and their applications,” Proceedings of the IEEE, vol. 81, no. 7, pp. 986–1010, 1993.
[17] C. L. Brown and A. M. Zoubir, “A nonparametric approach to signal detection in impulsive interference,” IEEE Transactions on Signal Processing, vol. 48, no. 9, pp. 2665–2669, 2000.
[18] G. A. Tsihrintzis and C. L. Nikias, “Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process,” IEEE Transactions on Communications, vol. 43, no. 2/3/4, pp. 904–914, 1995.
[19] E. E. Kuruoglu, W. J. Fitzgerald, and P. J. W. Rayner, “Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution,” IEEE Communications Letters, vol. 2, no. 10, pp. 282–284, 1998.
[20] R. Leahy, Z. Zhou, and Y.-C. Hsu, “Adaptive filtering of stable processes for active attenuation of impulsive noise,” in 1995 International Conference on Acoustics, Speech, and Signal Processing, vol. 5, 1995, pp. 2983–2986 vol.5.
[21] X. Sun, S. M. Kuo, and G. Meng, “Adaptive algorithm for active control of impulsive noise,” Journal of Sound and Vibration, vol.291, no. 1, pp. 516–522, 2006.
[22] M. T. Akhtar and W. Mitsuhashi, “Improved adaptive algorithm for active noise control of impulsive noise,” in 2008 51st Midwest Symposium on Circuits and Systems, 2008, pp. 330–333.
[23] M. T. Akhtar and W. Mitsuhashi, “Robust adaptive algorithm for active noise control of impulsive noise,” in 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009, pp.261–264.
[24] P. Petrus, “Robust Huber adaptive filter,” IEEE Transactions on Signal Processing, vol. 47, no. 4, pp. 1129–1133, 1999.
[25] P. Thanigai, S. M. Kuo, and R. Yenduri, “Nonlinear Active Noise Control for Infant Incubators in Neo-Natal Intensive Care Units,” in 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP ’07, vol. 1, 2007, pp. I–109–I–112.
[26] L. J. Eriksson and M. C. Allie, “Use of random noise for on‐line transducer modeling in an adaptive active attenuation system,” The Journal of the Acoustical Society of America, vol. 85, no. 2, pp.797–802, 1989.
[27] C. Bao, P. Sas, and H. Van Brussel, “Comparison of two-on-line identification algorithms for active noise control,” in Proceedings of the 2nd Conference on Recent Advances in Active Control of Sound and Vibration, 1993, pp. 38–54.
[28] S. M. Kuo and D. Vijayan, “Optimized secondary path modeling technique for active noise control systems,” in Proceedings of APCCAS’94 - 1994 Asia Pacific Conference on Circuits and Systems, 1994, pp. 370–375.
[29] M. Zhang, H. Lan, and W. Ser, “Cross-updated active noise control system with online secondary path modeling,” IEEE Transactions on Speech and Audio Processing, vol. 9, no. 5, pp. 598–602, 2001.