IEICE Electronics Express, Vol.6, No.5, 230–236
A self-tuning feedforward active noise control system Pooya Davaria) and Hamid Hassanpour School of Information Technology and Computer Engineering, Shahrood University of Technology, Shahrood, Iran. a)
[email protected]
Abstract: This paper proposes a self-tuning feedforward active noise control (ANC) system with online secondary path modeling. The stepsize parameters of the controller and modeling filters have crucial rule on the system performance. In literature, these parameters are adjusted by trial-and-error. In other words, they are manually initialized before system starting, which require performing extensive experiments to ensure the convergence of the system. Hence there is no guarantee that the system could perform well under different situations. In the proposed method, the appropriate values for the step-sizes are obtained automatically. Computer simulation results indicate the effectiveness of the proposed method. Keywords: ANC, Self-tuning, Online modeling, FxLMS, Feedforward Classification: Science and engineering for electronics References
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IEICE 2009
DOI: 10.1587/elex.6.230 Received December 18, 2008 Accepted January 28, 2009 Published March 10, 2009
[1] S. M. Kuo and D. R. Morgan, “Active noise control: a tutorial review,” Proc. IEEE, vol. 8, no. 6, pp. 943–973, June 1999. [2] L. J. Eriksson and M. C. Allie, “Use of random noise for on-line transducer modeling in an adaptive active attenuation system,” J. Acoust. Soc. Am., vol. 85, no. 2, pp. 797–802, 1989. [3] M. Zhang, H. Lan, and W. Ser, “Cross-updated active noise control system with online secondary path modeling,” IEEE Trans. Speech, Audio Proc., vol. 9, no. 5, pp. 598–602, 2001. [4] M. T. Akhtar, M. Abe, and M. Kawamata, “A Method for Online Secondary Path Modeling in Active Noise Control Systems,” Proc. IEEE 2005 Intern. Symp. Circuits Systems (ISCAS2005), pp. I-264–I-267, 2005. [5] P. Davari and H. Hassanpour, “A Variable Step-Size FxLMS Algorithm for Feedforward Active Noise Control Systems Based On a New Online Secondary Path Modeling Technique,” 6th ACS/IEEE International Conference Computer Systems and Applications, pp. 74–81, 2008. [6] P. Davari and H. Hassanpour, “A New Feedback ANC System Approach,” Springer-Verlag, International CSI Computer Science, pp. 324– 331, 2008. [7] H. Hassanpour and P. Davari, “An Efficient Online Secondary Path Estimation for Feedback Active Noise Control Systems,” Digital Signal Processing, vol. 19, no. 2, pp. 241–249, 2009.
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[8] B. Widrow and S. D. Stearns, Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, NJ. 1985. [9] A. Feuer and E. Weinstein, “Convergence Analysis of LMS Filters with Uncorrelated Gaussian Data,” IEEE trans. Acoust., Speech, Signal Process., vol. ASSP-33, no. 1, pp. 222–230, 1985. [10] S. M. Kuo and D. R. Morgan, Active Noise Control Systems-Algorithms and DSP Implementation. New York: Wiley, 1996.
1
Introduction
In recent years, with the advances in technology and industry, ANC systems have received an important and interesting application area. ANC is based on the simple principle of destructive interference of an anti-noise with equal amplitude and opposite phase replica unwanted noise. The effect shown by the secondary path transfer function, the path leading from the noise controller output to the error sensor measuring the residual noise, generally causes instability to the standard LMS algorithm. The filtered-x-least-mean-square (FxLMS) algorithm uses estimation of the secondary path to compensate the problem raised by the transfer function [1]. In many applications the secondary path is usually time varying, which leads to a poor performance or system instability. Hence, online modeling of secondary path is required to ensure convergence of the ANC algorithm [1, 2, 3, 4, 5, 6, 7]. In literature, the step size parameters of the controller filter and the secondary path estimator need to be manually initialized before the system starts the process [2, 3, 4, 5, 6, 7]. These parameters are adjusted, by trial-and-error, for fast and stable convergence. Hence, comprehensive experiments are needed to find the appropriate values. Although the optimal values of these parameters are obtained through extensive experiments, but it doesn’t guarantee that the system has a suitable performance under different situation. This fact becomes more evident in practical applications, where a system may encounter unknown noise or situations. Considering the above situation raises the need for a self-tuning ANC system, which automatically tunes its step-size parameters. As the first novelty, this paper proposes a self-tuning feedforward ANC system. The proposed system is design in a way that it automatically determines the suitable step-size parameters and correspondingly changes their values to adapt the system with noise and environment variations. The second novelty of the proposed system is that it also considers online estimation of the secondary path.
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IEICE 2009
DOI: 10.1587/elex.6.230 Received December 18, 2008 Accepted January 28, 2009 Published March 10, 2009
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2
Proposed self-tuning ANC system
2.1 Controller Filter Let consider Fig. 1 showing block diagram of the proposed method. The output signal y(n) is computed as: y(n) = wT (n)xL (n),
(1)
where w(n) = [w0 (n), w1 (n), . . . , wL−1 (n)]T is the tap-weight vector, and xL (n) = [x(n)x(n − 1) . . . x(n − L + 1)]T represents L samples of the reference signal vector. The residual error signal e(n) is expressed as: e(n) = d(n) − y (n) + v (n), y (n) = s(n) ∗ y(n), v (n) = s(n) ∗ v(n),
(2)
where v(n) is an internally generated white Gaussian noise injected at the ˆ output of the control filter W (z). In this Figure S(z) is the modelling FIR filter with length M . As the figure shows, vˆ (n)generates the error signal for the controller filter W (z) as: f (n) = [d(n) − y (n) + v (n)] − vˆ (n),
(3)
vˆ (n) = ˆsT (n)vM (n).
(4)
where
The noise control filter W (z) is updated using FxLMS algorithm: x (n)f (n), w(n + 1) = w(n) + μw (n)ˆ
(5)
ˆ (n) = [ˆ where x x (n), x ˆ (n − 1), . . . , x ˆ (n − L + 1)]T and μw is the step size, and the filtered reference signal is: x ˆ (n) = ˆsT (n)xM (n),
(6)
where xM (n) = [x(n), x(n−1), . . . , x(n−M +1)]T , and ˆs(n) = [ˆ s0 (n)ˆ s1 (n) . . . T ˆ sˆM −1 (n)] is the impulse response of the modelling filter S(z).
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IEICE 2009
DOI: 10.1587/elex.6.230 Received December 18, 2008 Accepted January 28, 2009 Published March 10, 2009
Fig. 1. Block diagram of the proposed method.
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The self-tuning controller filter automatically obtains a proper value for μw at each time (n). To calculate a suitable value for μw it is required to consider the convergence analysis of LMS algorithm. It has been shown in [8, 9] that the convergence is guaranteed only if: 0 < μw
