FIR System Identification Using Feedback

ABSTRACT

This paper describes a new approach to finite-impulse (FIR) system identification. The method differs from the traditional stochastic approximation method as used in the traditional least-mean squares (LMS) family of algorithms, in which we use deconvolution as a means of separating the impulse-response from the system input data. The technique can be used as a substitute for ordinary LMS but it has the added advantages that can be used for constant input data (*i.e.* data which are not persistently exciting) and the stability limit is far simpler to calculate. Furthermore, the convergence properties are much faster than LMS under certain types of noise input.

This paper describes a new approach to finite-impulse (FIR) system identification. The method differs from the traditional stochastic approximation method as used in the traditional least-mean squares (LMS) family of algorithms, in which we use deconvolution as a means of separating the impulse-response from the system input data. The technique can be used as a substitute for ordinary LMS but it has the added advantages that can be used for constant input data (

Cite this paper

T. Moir, "FIR System Identification Using Feedback,"*Journal of Signal and Information Processing*, Vol. 4 No. 4, 2013, pp. 385-393. doi: 10.4236/jsip.2013.44049.

T. Moir, "FIR System Identification Using Feedback,"

References

[1] B. Widrow and M. E. Hoff, “Adaptive Switching Circuits,” IRE Wescon Convention Record, Vol. 4, 1960, pp. 96-104.

[2] S. Haykin, “Adaptive Filter Theory,” Englewood Cliffs, Prentice Hall, New Jersey, 1986.

[3] J. J. Shynk, “Adaptive IIR Filtering,” IEEE of ASSP Magazine, Vol. 6, No. 2, 1989, pp. 4-21.

[4] P. Hagander and B. Wittenmark, “A Self-Tuning Filter for Fixed-Lag Smoothing,” IEEE Transactions on Information Theory, Vol. 23, 1977, pp. 377-384.

[5] L. Ljung and T. Sodestrom, “Theory and Practice of Recursive Estimation,” MIT Press, Cambridge, 1987.

[6] L. R. Vega and H. Rey, “A Rapid Introduction to Adaptive Filtering,” Springer, New York, 2013.

[7] J. V. Berghe and J. Wouters, “An Adaptive Noise Canceller for Hearing Aids Using Two nearby Microphones,” Journal of the Acoustical Society of America, Vol. 103, No. 6, 1998, pp. 3621-3626.

[8] B. Widrow, “A Microphone Array for Hearing Aids,” IEEE of Circuits and Systems Magazine, Vol. 1, 2001, pp. 26-32.

[9] L. Horowitz and K. Senne, “Performance Advantage of Complex LMS for Controlling Narrow-Band Adaptive Arrays,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, 1981, pp. 722-736.

[10] F. Reed, P. L. Feintuch and N. J. Bershad, “Time Delay Estimation Using the LMS Adaptive Filter—Static Behavior,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, 1981, pp. 561-571.

[11] B. Farhang-Boroujeny, “Fast LMS/Newton Algorithms Based on Autoregressive Modeling and Their Application to Acoustic Echo Cancellation,” IEEE Transactions on Signal Processing, Vol. 45, 1997, pp. 1987-2000.

[12] S. U. H. Qureshi, “Adaptive Equalization,” Proceedings of the IEEE, Vol. 73, 1985, pp. 1349-1387.

[13] P. C. Young, “Recursive Estimation and Time-Series Analysis,” 2nd Edition, Springer-Verlag, Berlin, 2011.

[14] S. Haykin and B. Widrow, “Least-Mean-Square Adaptive Filters (Adaptive and Learning Systems for Signal Processing, Communications and Control),” Wiley Interscience, 2003.

[15] E. Eweda, “Comparison of RLS, LMS, and Sign Algorithms for Tracking Randomly Time-Varying Channels,” IEEE Transactions on Signal Processing, Vol. 42, 1994, pp. 2937-2944.

[16] T. Aboulnasr and K. Mayyas, “A Robust Variable Step-Size LMS-Type Algorithm: Analysis and Simulations,” IEEE Transactions on Signal Processing, Vol. 45, 1997, pp. 631-639.

[17] R. C. Bilcu, P. Kuosmanen and K. Egiazarian, “A Transform Domain LMS Adaptive Filter with Variable Step-Size,” IEEE of Signal Processing Letters, Vol. 9, 2002, pp. 51-53.

[18] T. J. Moir, “Loop-Shaping Techniques Applied to the Least-Mean-Squares Algorithm,” Signal, Image and Video Processing, Vol. 5, 2011, pp. 231-243.

[19] A. G. J. MacFarlane, “Return-Difference and Return-Ratio Matrices and Their Use in Analysis and Design of Multivariable Feedback Control Systems,” Proceedings of the Institution of Electrical Engineers, Vol. 117, 1970, pp. 2037-2049.

[1] B. Widrow and M. E. Hoff, “Adaptive Switching Circuits,” IRE Wescon Convention Record, Vol. 4, 1960, pp. 96-104.

[2] S. Haykin, “Adaptive Filter Theory,” Englewood Cliffs, Prentice Hall, New Jersey, 1986.

[3] J. J. Shynk, “Adaptive IIR Filtering,” IEEE of ASSP Magazine, Vol. 6, No. 2, 1989, pp. 4-21.

[4] P. Hagander and B. Wittenmark, “A Self-Tuning Filter for Fixed-Lag Smoothing,” IEEE Transactions on Information Theory, Vol. 23, 1977, pp. 377-384.

[5] L. Ljung and T. Sodestrom, “Theory and Practice of Recursive Estimation,” MIT Press, Cambridge, 1987.

[6] L. R. Vega and H. Rey, “A Rapid Introduction to Adaptive Filtering,” Springer, New York, 2013.

[7] J. V. Berghe and J. Wouters, “An Adaptive Noise Canceller for Hearing Aids Using Two nearby Microphones,” Journal of the Acoustical Society of America, Vol. 103, No. 6, 1998, pp. 3621-3626.

[8] B. Widrow, “A Microphone Array for Hearing Aids,” IEEE of Circuits and Systems Magazine, Vol. 1, 2001, pp. 26-32.

[9] L. Horowitz and K. Senne, “Performance Advantage of Complex LMS for Controlling Narrow-Band Adaptive Arrays,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, 1981, pp. 722-736.

[10] F. Reed, P. L. Feintuch and N. J. Bershad, “Time Delay Estimation Using the LMS Adaptive Filter—Static Behavior,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, 1981, pp. 561-571.

[11] B. Farhang-Boroujeny, “Fast LMS/Newton Algorithms Based on Autoregressive Modeling and Their Application to Acoustic Echo Cancellation,” IEEE Transactions on Signal Processing, Vol. 45, 1997, pp. 1987-2000.

[12] S. U. H. Qureshi, “Adaptive Equalization,” Proceedings of the IEEE, Vol. 73, 1985, pp. 1349-1387.

[13] P. C. Young, “Recursive Estimation and Time-Series Analysis,” 2nd Edition, Springer-Verlag, Berlin, 2011.

[14] S. Haykin and B. Widrow, “Least-Mean-Square Adaptive Filters (Adaptive and Learning Systems for Signal Processing, Communications and Control),” Wiley Interscience, 2003.

[15] E. Eweda, “Comparison of RLS, LMS, and Sign Algorithms for Tracking Randomly Time-Varying Channels,” IEEE Transactions on Signal Processing, Vol. 42, 1994, pp. 2937-2944.

[16] T. Aboulnasr and K. Mayyas, “A Robust Variable Step-Size LMS-Type Algorithm: Analysis and Simulations,” IEEE Transactions on Signal Processing, Vol. 45, 1997, pp. 631-639.

[17] R. C. Bilcu, P. Kuosmanen and K. Egiazarian, “A Transform Domain LMS Adaptive Filter with Variable Step-Size,” IEEE of Signal Processing Letters, Vol. 9, 2002, pp. 51-53.

[18] T. J. Moir, “Loop-Shaping Techniques Applied to the Least-Mean-Squares Algorithm,” Signal, Image and Video Processing, Vol. 5, 2011, pp. 231-243.

[19] A. G. J. MacFarlane, “Return-Difference and Return-Ratio Matrices and Their Use in Analysis and Design of Multivariable Feedback Control Systems,” Proceedings of the Institution of Electrical Engineers, Vol. 117, 1970, pp. 2037-2049.