Circuits, Systems, and Signal Processing

, Volume 38, Issue 2, pp 891–903 | Cite as

Sign-Normalized IIR Spline Adaptive Filtering Algorithms for Impulsive Noise Environments

  • Chang LiuEmail author
  • Zhi Zhang
  • Xiao Tang
Short Paper


In this paper, a new sign-normalized least-mean-square adaptive filtering algorithm based on IIR spline adaptive filter (IIR-SAF-SNLMS) is proposed. By using the absolute value of the a posteriori error as the cost function and solving the optimization problem, the proposed algorithm achieves robustness against impulsive noise. Furthermore, to further improve the performance of the IIR-SAF-SNLMS, its variable step-size variant is proposed. Simulation results in the identification of the IIR-SAF nonlinear model show that the proposed algorithms provide better tracking and steady-state performance as compared to the existing spline algorithms.


IIR spline adaptive filter Sign-adaptive algorithm Variable step-size 



This research was supported by the National Natural Science Foundation of China under Grant 61501119.


  1. 1.
    S. Guan, Z. Li, Normalised spline adaptive filtering algorithm for nonlinear system identification. Neural Process. Lett. 46(2), 1–13 (2017)CrossRefGoogle Scholar
  2. 2.
    S. Guarnieri, F. Piazza, A. Uncini, Multilayer feedforward networks with adaptive spline activation function. IEEE Trans. Neural Netw. 10(3), 1–13 (1999)CrossRefGoogle Scholar
  3. 3.
    J.H. Kim, J.H. Chang, S.W. Nam, Sign subband adaptive filter with \(L_1\)-norm minimiza-tion based variable step-size. Electron. Lett. 49(21), 1325–1326 (2013)CrossRefGoogle Scholar
  4. 4.
    R.H. Kwong, E.W. Johnston, A variable step size LMS algorithm. IEEE Trans. Signal Process. 40(7), 1633–1642 (1992)CrossRefzbMATHGoogle Scholar
  5. 5.
    H.S. Lee, S.E. Kim, W. Lee, W.J. Song, A variable step-size diffusion LMS algorithm for distributed estimation. IEEE Trans. Signal Process. 63(7), 1808–1820 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    J. Ni, X. Chen, J. Yang, Two variants of the sign subband adaptive filter with improved convergence rate. Signal Process. 96(5), 325–331 (2014)CrossRefGoogle Scholar
  7. 7.
    M.O.B. Saeed, A. Zerguine, S.A. Zummo, A noise-constrained algorithm for estimation over distributed networks. Int. J. Adapt. Control Signal Process. 27(10), 827–845 (2013)MathSciNetzbMATHGoogle Scholar
  8. 8.
    M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Nonlinear spline adaptive filtering. Signal Proces. 93(4), 772–783 (2013)CrossRefzbMATHGoogle Scholar
  9. 9.
    M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Hammerstein uniform cubic spline adaptive filtering: learning and convergence properties. Signal Proces. 100(7), 112–123 (2014)CrossRefGoogle Scholar
  10. 10.
    M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Novel cascade spline architectures for the identification of nonlinear systems. IEEE Trans Circuits Syst.I: Reg Pap. 62(7), 1825–1835 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Nonlinear system identification using spline adaptive filters. Signal Proces. 108(C), 30–35 (2015)CrossRefzbMATHGoogle Scholar
  12. 12.
    T. Shao, Y.R. Zheng, J. Benesty, An affine projection sign algorithm robust against impulsive interferences. IEEE Signal Process. Lett. 17(4), 327–330 (2010)CrossRefGoogle Scholar
  13. 13.
    S. Wang, J. Feng, C.T. Tse, Kernel affine projection sign algorithms for combating impulse interference. IEEE Trans. Circuits Ssyst.II: express Briefs 60(11), 811–815 (2012)CrossRefGoogle Scholar
  14. 14.
    P. Wen, J. Zhang, Robust variable step-size sign subband adaptive filter algorithm against impulsive noise. Signal Process. 139, 110–115 (2017)CrossRefGoogle Scholar
  15. 15.
    Y. Zhou, S.C. Chan, T.S. Ng, Least mean M-estimate algorithms for robust adaptive filtering in impulse noise. IEEE Trans. Circuits Syst.II: Analog Digit. Signal Process 47(12), 1564–1569 (2000)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electronic EngineeringDongguan University of TechonologyDong’guanChina

Personalised recommendations