Analysis of Frequency Mismatch in Narrowband Active Noise Control

This paper analyzes the effects of frequency mismatch between the actual frequency of the primary noise and the frequency of the synthesized reference signal in narrowband active noise control (ANC) systems using the filtered-X least-mean-square (FXLMS) algorithm. Two stability conditions are derived in terms of the frequency mismatch and the phase error of the estimated secondary-path model. Conditions to guarantee that ANC systems can achieve noise reduction are also developed by considering the overall effect of frequency mismatch and phase error. The optimum step-size to reach the minimum excess mean-square error is obtained and analyzed. Theoretical analysis shows that the noise reduction and convergence rate are functions of frequency mismatch, step size, and phase error in the secondary-path model for the FXLMS algorithm. Computer simulations are conducted to verify the analysis results presented in the paper.

[1]  Hideaki Sakai,et al.  An exact analysis of the LMS algorithm with tonal reference signals in the presence of frequency mismatch , 2004, 2004 12th European Signal Processing Conference.

[2]  Sen M. Kuo,et al.  Active Noise Control Systems: Algorithms and DSP Implementations , 1996 .

[3]  Hideaki Sakai,et al.  Exact Convergence Analysis of Adaptive Filter Algorithms Without the Persistently Exciting Condition , 2005, IEEE Transactions on Signal Processing.

[4]  Akira Ikuta,et al.  A New Robust Narrowband Active Noise Control System in the Presence of Frequency Mismatch , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[5]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[6]  Hideaki Sakai,et al.  A Filtered-X LMS Algorithm for Sinusoidal Reference Signals—Effects of Frequency Mismatch , 2007, IEEE Signal Processing Letters.

[7]  Akira Ikuta,et al.  A filtered-X RLS based narrowband active noise control system in the presence of frequency mismatch , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[8]  Sen M. Kuo,et al.  Active noise control: a tutorial review , 1999, Proc. IEEE.

[9]  Rabab Kreidieh Ward,et al.  Statistical properties of the LMS fourier analyzer in the presence of frequency mismatch , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Sen M. Kuo,et al.  Analysis and Correction of Frequency Error in Electronic Mufflers using Narrowband Active Noise Control , 2007, 2007 IEEE International Conference on Control Applications.

[11]  Dennis R. Morgan,et al.  An analysis of multiple correlation cancellation loops with a filter in the auxiliary path , 1980, ICASSP.

[12]  Yegui Xiao,et al.  A robust narrowband active noise control system for accommodating frequency mismatch , 2004, 2004 12th European Signal Processing Conference.

[13]  Hideaki Sakai,et al.  Convergence analysis of a complex LMS algorithm with tonal reference signals , 2005, IEEE Transactions on Speech and Audio Processing.

[14]  J. Burgess.  Active adaptive sound control in a duct: A computer simulation , 1981 .

[15]  Ingvar Claesson,et al.  Convergence analysis of a twin-reference complex least-mean-squares algorithm , 2002, IEEE Trans. Speech Audio Process..

[16]  Philip A. Nelson,et al.  Active Control of Sound , 1992 .

[17]  B. Widrow,et al.  Adaptive noise cancelling: Principles and applications , 1975 .

[18]  Stephen J. Elliott,et al.  A multiple error LMS algorithm and its application to the active control of sound and vibration , 1987, IEEE Trans. Acoust. Speech Signal Process..

[19]  Hideaki Sakai,et al.  Analysis of the filtered-X LMS algorithm and a related new algorithm for active control of multitonal noise , 2006, IEEE Transactions on Audio, Speech, and Language Processing.