Nonlinear Dynamics

, Volume 85, Issue 3, pp 1363–1376 | Cite as

Fractional-order adaptive signal processing strategies for active noise control systems

  • Syed M. Shah
  • R. Samar
  • N. M. Khan
  • M. A. Z. Raja
Original Paper


Robust and computationally efficient adaptive algorithms are required in active noise control systems (ANCS) to cancel out the effects of noise in the presence of secondary path (SP) as the latter makes the identification problem more challenging. To ensure stability in such applications, the step size parameter is kept small, but it results in slow convergence which limits the usefulness of such algorithms in ANCS. In this paper, we propose a novel fractional-order adaptive filter structures such that the output from the conventional filtered-x least mean square algorithm is passed through a new update equation derived from a cost function based on a posteriori error and optimized using fractional derivatives. The proposed algorithms are designed for the feed-forward configuration of ANCS; the schemes are validated using the performance metrics of mean squared error, mean squared deviation and mean relative modeling error. We consider a number of scenarios where different step sizes and fractional orders have been used for evaluation with input signals modeled as binary or Gaussian. Simulation results show that the proposed algorithms outperform the conventional counterparts with convergence improvements in the range of 75–80 %, while they offer the same steady- state behavior even for large step sizes, thereby providing better modeling in the presence of SP.


Active noise control Filtered-x least mean square  Fractional derivatives Mean square error/deviation Secondary path modeling 



Syed Muslim Shah acknowledges the Higher Education Commission (HEC), Islamabad, Pakistan, for supporting his research work.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Syed M. Shah
    • 1
  • R. Samar
    • 1
  • N. M. Khan
    • 1
  • M. A. Z. Raja
    • 2
  1. 1.Department of Electrical EngineeringCapital University of Science and TechnologyIslamabadPakistan
  2. 2.Department of Electrical EngineeringComsats Institute of Information TechnologyAttockPakistan

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