An Improved Filtered-x Least Mean Square Algorithm for Acoustic Noise Suppression

  • Asutosh KarEmail author
  • Ambika Prasad Chanda
  • Sarthak Mohapatra
  • Mahesh Chandra
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 27)


In the modern age scenario noise reduction is a major issue, as noise is responsible for creating disturbances in day-to-day communication. In order to cancel the noise present in the original signal numerous methods have been proposed over the period of time. To name a few of these methods we have noise barriers and noise absorbers. Noise can also be suppressed by continuous adaptation of the weights of the adaptive filter. The change of weight vector in adaptive filters is done with the help of various adaptive algorithms. Few of the basic noise reduction algorithms include Least Mean Square algorithm, Recursive Least Square algorithm etc. Further we work to modify these basic algorithms so as to obtain Normalized Least Mean Square algorithm, Fractional Least Mean Square algorithm, Differential Normalized Least Mean Square algorithm, Filtered-x Least Mean Square algorithm etc. In this paper we work to provide an improved approach for acoustic noise cancellation in Active Noise Control environment using Filtered-x LMS (FXLMS) algorithm. A detailed analysis of the algorithm has been carried out. Further the FXLMS algorithm has been also implemented for noise cancellation purpose and the results of the entire process are produced to make a comparison.


adaptive filter active noise control Least Mean Square Mean Square Error FXLMS 


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  1. 1.
    Elliot, S.J.: Signal Processing for Active Control. Academic Press, London (2001)Google Scholar
  2. 2.
    Elliot, S.J., Nelson, P.A.: Active noise control. IEEE Signal Processing Magazine 10, 12–35 (1993)CrossRefGoogle Scholar
  3. 3.
    Lueg, P.: Process of silencing sound oscillations. U.S. Patent, 2043416 (1936)Google Scholar
  4. 4.
    Kuo, S.M.: Morgan, D.R.: Active Noise Control Systems-Algorithms and DSP Implementations. Wiley (1996)Google Scholar
  5. 5.
    Kuo, S.M., Morgan, D.R.: Active Noise Control: A tutorial review. Proceedings of IEEE 87, 943–973 (1999)CrossRefGoogle Scholar
  6. 6.
    Widrow, B., Stearns, S.D.: Adaptive Signal Processing. Prentice Hall, New Jersey (1985)zbMATHGoogle Scholar
  7. 7.
    Morgan, D.R.: An analysis of multiple correlation cancellation loops with a filter in the auxiliary path. IEEE Transactions in Acoustics, Speech, and Signal Processing 28, 454–467 (1980)CrossRefGoogle Scholar
  8. 8.
    Boucher, C.C., Elliot, S.J., Nelson, P.A.: Effects of errors in the plant model on the performance of algorithms for adaptive feedforward control. IEE Proceedings F138(4), 313–319 (1991)Google Scholar
  9. 9.
    Widrow, B., McCool, J.M., Larimore, M., Johnson, C.R.: Stationary and non-stationary learning characteristics of the LMS adaptive filter. IEEE Proceedings 64(8), 1151–1162 (1976)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Butterweck, H.: A wave theory of long adaptive filters. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications 48(6), 739–747 (2001)CrossRefzbMATHGoogle Scholar
  11. 11.
    Warnaka, G.E., Poole, L.A., Tichy, J.: Active acoustic attenuators. U.S. Patent 4473906 (1984)Google Scholar
  12. 12.
    Elliott, S.J., Stothers, I.M., Nelson, P.A.: A multiple error LMS algorithm and its applications to active control of sound and vibration. IEEE Transactions on Acoustic, Speech and Signal Processing Processing 35, 1423–1434 (1987)CrossRefGoogle Scholar
  13. 13.
    Rupp, M., Sayed, A.H.: Two variants of the FxLMS algorithm. In: IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics, pp. 123–126 (1995)Google Scholar
  14. 14.
    Rupp, M., Sayed, A.H.: Robust FxLMS algorithms with improved convergence performance. IEEE Transactions on Speech and Audio Processing 6(1), 78–85 (1998)CrossRefGoogle Scholar
  15. 15.
    Davari, P., Hassanpour, H.: A variable step-size FxLMS algorithm for feedforward active noise control systems based on a new online secondary path modelling technique. In: IEEE/ACS International Conference on Computer Systems and Applications, pp. 74–81 (2008)Google Scholar
  16. 16.
    Kunchakoori, N., Routray, A., Das, D.: An energy function based fuzzy variable step size fxlms algorithm for active noise control. In: IEEE Region 10 and the Third International Conference on Industrial and Information Systems, pp. 1–7 (2008)Google Scholar
  17. 17.
    Eriksson, L., Allie, M., Melton, D., Popovich, S., Laak, T.: Fully adaptive generalized recursive control system for active acoustic attenuation. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. II/253–II/256 (1994)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Asutosh Kar
    • 1
    Email author
  • Ambika Prasad Chanda
    • 1
  • Sarthak Mohapatra
    • 1
  • Mahesh Chandra
    • 2
  1. 1.Department. of Electronics and Telecommunication EngineeringIndian Institute of Information TechnologyBhubaneswarIndia
  2. 2.Department of Electronics and Communication EngineeringBirla Institute of TechnologyMesraIndia

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