volume | PIER Journals

Abstract

This research concerns offline identification of acoustic characteristics of enclosures with second-order resonant dynamics and their modeling as linear dynamic systems. The applied models can be described by basis function expansions. The practical problem of acoustic echo in enclosures is used as the target problem to be addressed. It has been found out that the classical filters are ineffective filter structures for approximating an echo generating system, due to their many required parameters. In order to reduce the number of estimated parameters, alternative methods for modeling the room impulse response need to be investigated. Out of various available techniques impulse response identification is utilized. With the help of given experimental data, the enclosures' impulse response is modeled using special orthonormal basis functions called Kautz functions. As another improved approximation, hybrid multistage system identifiers have been used in which the simplicity of classical filter structures and fast convergence of orthonormal structures is utilized as an advantage.

1. Beranek, L. L., Acoustics, Acoustical Society of America, Woodbury, NY, 1993.

2. Morse, P. M. and K. U. Ingard, Theoretical Acoustics, Princeton University Press, Princeton, NJ, 1987.

3. Cremer, L. and H. A. Muller, Principles and Applications of Room Acoustics, Vols. 1 and 2, 1982.

4. Gritton, C. W. K. and D. W. Lin, "Echo cancellation algorithms," IEEE Acoustics, Vol. 1, No. 2, 30-38, 1984.

5. Haneda, Y., S. Makino, and Y. Kaneda, "Common acoustical pole and zero modeling of room transfer functions," IEEE Transactions on Acoustics, Vol. 2, No. 2, 320-328, 1994.

6. Golub, G. H. and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1996.

7. Ljung, L., System Identification: Theory for the User, Prentice- Hall, Englewood Cliffs, NJ, 1999.

8. Mourjopoulos, J. and M. A. Paraskevas, "Pole and zero modeling of room transfer function," Journal of Sound and Vibration, Vol. 146, No. 2, 281-302, 1991.
doi:10.1016/0022-460X(91)90764-B

9. Kuttru, H., Room Acoustics, Elsevier Applied Science, London, Great Britain, 1991.

10. Ninness, B. and F. Gustafsson, "A unifying construction of orthonormal bases for system identification," IEEE Transactions on Automatic Control, Vol. 42, No. 4, 515-521, 1997.
doi:10.1109/9.566661

11. Davidson, G. W. and D. D. Falconer, "Reduced complexity echo cancellation using orthornormal functions," IEEE Transactions on Circuits and Systems, Vol. 38, No. 1, 20-28, 1991.
doi:10.1109/31.101300

12. Wahlberg, B. and P. M. Makila, "On approximation of stable linear dynamical systems using Laguerre and Kautz functions," Automatica, Vol. 32, No. 5, 693-708, 1996.
doi:10.1016/0005-1098(95)00198-0

13. Heuberger, P. S. C., P. M. J. Van den Hof, and O. H. Bosgra, "A generalized orthonormal basis for linear dynamical systems," IEEE Transactions on Automatic Control, Vol. 40, No. 3, 451-465, 1995.
doi:10.1109/9.376057

14. Makila, P. M. and J. R. Partington, "Laguerre and Kautz shift approximations of delay systems," International Journal of Control, Vol. 72, No. 10, 932-946, 1999.
doi:10.1080/002071799220678

15. Silva, T. O., "Optimality conditions for truncated Kautz networks with two periodically repeating complex conjugate poles," IEEE Transactions on Automatic Control, Vol. 40, No. 2, 342-346, 1995.
doi:10.1109/9.341807

16. Kaneda, Y., "A study of non-linear effect on acoustic impulse response measurement," Journal of Acoustical Society of Japan, Vol. 16, No. 3, 193-195, 1995.

17. Carayannis, G., D. G. Manolakis, and N. Kalouptsidis, "A fast sequential algorithm for least-squares filtering and prediction," IEEE Transactions on Acoustics, Vol. 31, No. 6, 1394-1402, 1983.
doi:10.1109/TASSP.1983.1164224

18. Tanguy, N., R. Morvan, P. Vilbe, and L. C. Calvez, "Improved method for optimum choice of free parameter in orthogonal approximations," IEEE Transactions on Acoustics, Vol. 47, No. 9, 2576-2578, 1999.

19. den Brinker, A. C., "Optimality conditions for a specific class of truncated Kautz series," IEEE Transactions on Circuits and Systems-II, Vol. 43, No. 8, 597-600, 1996.
doi:10.1109/82.532006

20. Murano, K., S. Unagami, and F. Amano, "Echo cancellation and applications," IEEE Communication Magazine, Vol. 28, No. 1, 49-55, 1990.
doi:10.1109/35.46671

Professor Shabbir Chaudhry

Dr. Alina Chaudhr