In this paper, the improved wavelet transform domain least mean squares (IWTDLMS) adaptive algorithm is established. The IWTDLMS algorithm has a faster convergence speed than the conventional WTDLMS for colored input signals. Since the performances of WTDLMS and IWTDLMS are degraded in impulsive noise interference, the IWTDLMS sign algorithm (IWTDLMS-SA) is proposed. In comparison with IWTDLMS, the IWTDLMS-SA has lower computational complexity. In order to improve the performance of IWTDLMS-SA, the variable step-size IWTDLMS-SA (VSS-IWTDLMS-SA) is introduced. The VSS-IWTDLMS-SA is derived by minimizing the \(\ell _1\)-norm of the a posteriori error vector. To increase the tracking ability of the VSS-IWTDLMS-SA, the modified VSS-IWTDLMS-SA (MVSS-IWTDLMS-SA)is presented. The simulation results demonstrate that the proposed algorithms have a faster convergence rate and lower misadjustment than the conventional WTDLMS. The robustness feature of the IWTDLMS-SA, VSS-IWTDLMS-SA, and MVSS-IWTDLMS-SA against impulsive noises is also verified through several experiments in a system identification setup.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
M.S.E. Abadi, H. Mesgarani, S.M. Khademiyan, The wavelet transform-domain LMS adaptive filter employing dynamic selection of subband-coefficients. Digit. Signal Process. A Rev. J. 69, 94–105 (2017)
M.S.E. Abadi, M.S. Shafiee, Diffusion normalized subband adaptive algorithm for distributed estimation employing signed regressor of input signal. Digit. Signal Process. 70, 73–83 (2017)
M.S.E. Abadi, M.S. Shafiee, M. Zalaghi, A low computational complexity normalized subband adaptive filter algorithm employing signed regressor of input signal. EURASIP J. Adv. Signal Process. 21(1), 1–23 (2018)
S. Attallah, The wavelet transform-domain lms algorithm: a more practical approach. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 47(3), 209–213 (2000)
S. Attallah, The Wavelet Transform-Domain LMS Adaptive Filter With Partial Subband-Coefficient Updating. IEEE Trans. Circuits Syst. II Express Br. 53(1), 8–12 (2006)
R.C. Bilcu, P. Kuosmanen, K. Egiazarian, A transform domain LMS adaptive filter with variable step-size. IEEE Signal Process. Lett. 9(2), 51–53 (2002)
J. Chambers, A. Avlonitis, A robust mixed-norm adaptive filter algorithm. IEEE Signal Process. Lett. 4(2), 46–48 (1997)
B. Farhang-Boroujeny, Adaptive Filters: Theory and Applications (Wiley, New York, 2013)
S.S. Haykin, Adaptive Filter Theory, 5th edn. (Pearson Education India, India, 2013)
J.H. Kim, J.H. Chang, S.W. Nam, Affine projection sign algorithm with \(\ell _1\) minimization-based variable step-size. Signal Process. 105, 376–380 (2014)
D.I. Kim, P.D. Wilde, Performance analysis of the DCT-LMS adaptive filtering algorithm. Signal Process. 80(8), 1629–1654 (2000)
K. Mayyas, A transform domain LMS algorithm with an adaptive step size equation, Proceedings of the Fourth IEEE International Symposium on Signal Processing and Information Technology, pp. 229–232, (2004)
K. Ozeki, T. Umeda, An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties. Electron. Commun. in Japan (Part I Commun.) 67(5), 19–27 (1984)
A.H. Sayed, Adaptive Filters (Wiley, New York, 2011)
T. Shao, Y.R. Zheng, A new variable step-size fractional lower-order moment algorithm for non-Gaussian interference environments, 2009 IEEE International Symposium on Circuits and Systems, pp. 2065–2068, (2009)
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)
H.C. Shin, A.H. Sayed, W.J. Song, Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11(2), 132–135 (2004)
J. Shin, J. Yoo, P. Park, Variable step-size affine projection sign algorithm. Electron. Lett. 48(9), 483–485 (2012)
D. Sundararajan, Discrete Wavelet Transform: A Signal Processing Approach (Wiley, New York, 2016)
L.R. Vega, H. Rey, J. Benesty, S. Tressens, A new robust variable step-size NLMS algorithm. IEEE Trans. Signal Process. 56(5), 1878–1893 (2008)
B. Widrow, D. Stearns, Adaptive Signal Processing (Prentice Hall Inc, NJ, 1985)
W.W. Wu, Y.S. Wang, J.C. Zhang, An adaptive filter based on wavelet transform and affine projection algorithm, 2010 International Conference on Wavelet Analysis and Pattern Recognition, pp. 392–397, (2010)
S.K. Yadav, R. Sinha, P.K. Bora, Electrocardiogram signal denoising using non-local wavelet transform domain filtering. IET Signal Process. 9(1), 88–96 (2015)
J. Yoo, J. Shin, P. Park, Variable step-size affine projection sign algorithm. IEEE Trans. Circuits Syst. II: Express Br. 61(4), 274–278 (2014)
J. Yoo, J. Shin, P. Park, Variable step-size sign algorithm against impulsive noises. IET Signal Process. 9(6), 506–510 (2015)
S. Zhao, D.L. Jones, S. Khoo, Z. Man, New variable step-sizes minimizing mean-square deviation for the LMS-type algorithms. Circuits Syst. Signal Process. 33(7), 2251–2265 (2014)
Y.R. Zheng, T. Shao, A variable step-size lmp algorithm for heavy-tailed interference suppression in phased array radar, 2009 IEEE Aerospace Conference, pp. 1–6, (2009)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Abadi, M.S.E., Mesgarani, H. & Khademiyan, S.M. Two Improved Wavelet Transform Domain LMS Sign Adaptive Filter Algorithms Against Impulsive Interferences. Circuits Syst Signal Process 40, 958–979 (2021). https://doi.org/10.1007/s00034-020-01508-5
- Adaptive filters
- Sign algorithm
- Variable step size
- Wavelet transform
- Impulsive noise interference