Nonlinear and Adaptive Signal Processing

Most real-world systems exhibit at least some amount of nonlinearity and time variation in their characteristics. My students and I, during the last twenty five years, have contributed in many ways to the understanding of nonlinear and adaptive systems and their applications. Some of our contributions are:

1. We have developed a class of adaptive nonlinear filters that are known to be the most computationally efficient among recursive least-squares adaptive polynomial filters. They exhibit fast convergence behavior, robustness to spectral dynamics of the input signal and finite precision errors.
2. We have developed a class of adaptive nonlinear filters with recursive system models that are guaranteed to operate in a stable manner and converge to the global minimum of the error surface.
3. We have developed systematic methods of approximating polynomial systems using multiplicative and parallel combinations of lower order nonlinearities.
4. We have developed methods to compensate for the distortions caused by a large class of nonlinear systems. Our methods can be implemented using systolic arrays and operates in a stable manner. The methods we have developed are among the simplest to implement of the many approaches available in the literature.
5. We have developed a systematic theory of analyzing a class of polynomial systems for its stability properties.
6. We have applied adaptive and nonlinear signal processing techniques to problems in high-speed communication systems and image processing. In the communications arena, our recent works dealt with multi-user CDMA systems and tracking fast variations in MIMO channels using adaptive algorithms employing time-varying channel models.
   

Our work in this area has been funded over the years by grants and contracts from the National Science Foundation, IBM, NATO, Analog Devices, and University of Utah Research Foundation.  We have also collaborated on this work with researchers at Trieste University, Italy (Professors Giovanni Sicuranza and Gianni Ramponi) and the University of Athens (Professor Nick Kalouptsidis).

Graduate Students With Research Emphasis in Adaptive and/or Nonlinear Signal Processing

• Sung Ho Cho, Convergence Analysis for Efficient Adaptive Filtering Algorithms and Structures, Ph. D., University of Utah, July 1989.
• Mushtaq A. Syed, QR-Decomposition Based Algorithms for Nonlinear and Multichannel Adaptive Filtering, Ph. D., University of Utah, June 1992.
  
• Junghsi Lee, Adaptive Polynomial Filtering Algorithms, Ph. D., University of Utah, August 1992.
• Peter J. Hahn, Adaptive Methods of Time Delay Estimation for a Passive Sonar Array, M. S., University of Utah, August 1996.
• Shan Mo, Adaptive Quadratic Preprocessing of Document Images for Binarization, M. S., University of Utah August 1997.
  
• Thomas Panicker, Parallel-Cascade Realizations of Truncated Volterra Systems, Ph. D., University of Utah, March 1998.
• Alberto Carini, Adaptive and Nonlinear Signal Processing, Ph. D., University of Trieste, Italy (Visiting scholar to the University of Utah), 1998.
  
• Shan Mo, Adaptive Receivers for Spread Spectrum Multiple Access Communications, Ph. D., University of Utah, December 2001.
• Janez Jeraj, Adaptive Estimation and Equalization of Nonlinear Systems, Ph. D., May 2005.

Publications in Nonlinear and Adaptive Signal Processing

1. V. J. Mathews and G. L. Sicuranza, Polynomial Signal Processing ,  John Wiley  & Sons, New York, 2001.

2. D. H. Youn, S. N. Chiou and V. J. Mathews, "Adaptive Phase Transform Processors for Time Delay Estimation," J. Acoust. Soc. America, Vol. 80, No. 1, pp. 188-194, July 1986 in Coherence and Time Delay Estimation, edited by G. C. Carter, IEEE Press, 1993.

3. C. F. N. Cowan, E. J. Coyle, M. Gabbouj, V. J. Mathews, I. Pitas and G. L. Sicuranza, "Fundamentals of Nonlinear Digital Signal Processing," in Circuit and Systems Tutorials, edited by C. Toumazou, pp. 1-70, IEEE ISCAS, 1994.

4. V. J. Mathews and J. K. Tugnait, "Detection and Estimation with Fixed Lag for Abruptly Changing Systems,'' IEEE Transactions on Aerospace, Electronic Systems, Vol. AES-19, No. 5, pp. 730-739, September 1983
5. D. H. Youn and V. J. Mathews, "Adaptive Realizations of the Maximum Likelihood Processor for Time Delay Estimation,'' IEEE Trans. Acoust., Speech, Signal Proc., Vol. ASSP-32, No. 4, pp. 938-940, August 1984.
6. D. H. Youn, V. J. Mathews and S. H. Cho, "An Efficient Lattice Filtering Algorithm for Instantaneous Frequency Estimation,'' Signal Processing , Vol. 10, No. 1, pp. 75-81, January 1986.
7. D. H. Youn, S. N. Chiou and V. J. Mathews, "Adaptive Phase Transform Processors for Time Delay Estimation,'' J. Acoust. Soc. America, Vol. 80, No. 1, pp. 188-194, July 1986.
8. V. J. Mathews and S. H. Cho, "Improved Convergence Analysis of Stochastic Gradient Adaptive Filters Using the Sign Algorithm,'' IEEE Trans. Acoust., Speech, Signal Proc., Vol. ASSP-35, No. 4, pp. 450-454, April 1987.
9. V. J. Mathews, "An Efficient FIR Adaptive Filter Using DPCM and the Sign Algorithm,'' IEEE Trans. Acoust., Speech, Signal Proc., Vol. ASSP-37, No. 1, pp. 128-133, January 1989.
10. V. J. Mathews and Z. Xie, "Fixed Point Error Analysis of Stochastic Gradient Adaptive Lattice Filters,'' IEEE Trans. Acoust., Speech, Signal Proc., Vol. ASSP-38, No. 1, pp. 70-80, January 1990.
11. S. H. Cho and V. J. Mathews, "Tracking Analysis of the Sign Algorithm in Non-Stationary Environments,'' IEEE Trans. Acoust., Speech, Signal Proc ., Vol. ASSP-38, No. 12, pp. 2046-2057, December 1990.
12. V. J. Mathews, "Performance Analysis of Adaptive Filters Equipped with the Dual Sign Algorithm,'' IEEE Trans. Signal Proc., Vol. 39, No. 1, pp. 85-91, January 1991.
13. V. J. Mathews, "Adaptive Polynomial Filters,'' IEEE Signal Processing Magazine, Vol. 8, No. 3, pp. 10-26, July 1991.
14. M. A. Syed and V. J. Mathews, "Finite Precision Error Analysis of a QR-Decomposition Based Lattice Predictor,'' Optical Engineering, Vol. 31, No. 6, pp. 1170-1180, June 1992.
15. H. K. Baik and V. J. Mathews, "Adaptive Bilinear Lattice Filters,'' IEEE Trans. Signal Proc., Vol. 41, No. 6, pp. 2033-2046, June 1993.
16. J. Lee and V. J. Mathews, "A Fast Recursive Least Squares Adaptive Second Order Volterra Filter and its Performance Analysis,'' IEEE Trans. Signal Proc., Vol. 41, No. 3, pp. 1087-1102, March 1993.
17. M. A. Syed and V. J. Mathews, "QR-Decomposition Based Algorithms for Adaptive Volterra Filtering,'' IEEE Trans. Circuits and Systems - I: Fundamental Theory and Applications , Vol. 40, No. 6, pp. 372-382, June 1993.
18. V. J. Mathews and Z. Xie, " Stochastic Gradient Adaptive Filters with Gradient Adaptive Step Sizes ,'' IEEE Trans. Signal Proc., Vol. 41, No. 6, pp. 2075-2087, June 1993.
19. J. Lee and V. J. Mathews, "A Stability Condition for Certain Bilinear Systems,'' IEEE Trans. Signal Proc., Vol. 41, No. 7, pp. 1871-1873, July 1994.
20. M. A. Syed and V. J. Mathews, "Lattice Algorithms for Recursive Least Squares Adaptive Volterra Filtering,'' IEEE Trans. Circuits and Systems - II: Analog and Digital Signal Processing , Vol. 41, No. 3, pp. 202-214, March 1994.
21. J. Lee and V. J. Mathews, "A Stability Result for RLS Adaptive Bilinear Filters,'' IEEE Signal Processing Letters, Vol. 1, No. 12, December 1994.
22. V. J. Mathews, "Orthogonalization of Correlated Gaussian Signals for Volterra System Identification ,'' IEEE Signal Processing Letters, Vol. 2, No. 10, pp. 188-190, October 1995.
23. V. J. Mathews, "Adaptive Volterra Filters Using Orthogonal Structures,'' IEEE Signal Processing Letters, Vol. 3, No. 12, pp. 307-309, December 1996.
24. A. Carini, G. L. Sicuranza and V. J. Mathews, "On the Inversion of Certain Nonlinear Systems,'' IEEE Signal Processing Letters, vol. 4, No. 12, pp. 334-336, December 1997.
25. S. Mo and V. J. Mathews, "Adaptive, Quadratic Preprocessing of Document Images for Binarization,''  IEEE Trans. Image Processing, Vol. 7, No. 7, pp. 992-999, July 1998.
26. T. M. Panicker, V. J. Mathews and G. L. Sicuranza, "Adaptive Parallel Cascade Truncated Volterra Filters,'' IEEE Trans. Signal Processing ,  Vol. 46, No. 10, pp. 2664-2673, October 1998.
27. T. M. Panicker and V. J. Mathews, "Parallel-Cascade Realizations and Approximations of Truncated Volterra Systems,'' IEEE Trans. Signal Proc ., Vol. 46, No. 10, pp. 2829-2832, October 1998.
28. L. Li and V. J. Mathews, "Frequency-Domain Realizations of Adaptive Parallel-Cascade Quadratic Filters,'' IEEE Trans. Circuits and Systems II -- Analog and Digital Signal Processing , Vol. 46, No. 4, pp. 468-472, April 1999.
29. A. Carini, V. J. Mathews and G. L. Sicuranza, "Sufficient Stability Bounds for Slowly-Varying Discrete-Time Recursive Linear Filters and Their Applications in Adaptive IIR Filtering,'' IEEE Trans. Signal Proc., Vol. 47, No. 9, pp. 2561-2567, September 1999.
30. A. Carini, V. J. Mathews and G. L. Sicuranza, "Equalization of Recursive Polynomial Systems,'' IEEE Signal Processing Letters, Vol. 6, No. 12, pp. 312-314, December 1999.
    
31. A. Polesel, G. Ramponi and V. J. Mathews, "Image Enhancement via Adaptive Unsharp Masking,'' IEEE Trans. Image Processing , Vol. 9, No. 3, pp. 505-510, March 2000.
32. N. Kalouptsidis, P. Koukoulas, and V. J. Mathews, "Blind Identification of Bilinear Systems,'' IEEE Trans. Signal Processing,  Vol. 51, No. 2, pp. 484-499, Feb 2003.
33. J. Jeraj and V. J. Mathews, "A stable adaptive Hammerstein filter employing partial orthogonalization of the input signal," IEEE Trans. Signal Processing, vol. 54, no. 4, pp. 1412-1420, April 2006.
34. J. Jeraj and V. J. Mathews, "Stochastic mean-square performance analysis of an adaptive Hammerstein filter," IEEE Trans. Signal Processing, vol. 54, no. 4, pp. 2168-2177, June 2006.

35. V. J. Mathews and J. K. Tugnait, "Detection and Estimation with Fixed Lag for Abruptly Changing Systems, " Proc. 20th Annual Allerton Conf. Control, Communication and Computing, pp. 545-554, Urbana-Champaign, Illinois, October 6-8, 1982.
36. D. H. Youn, S. N. Chiou and V. J. Mathews, "Adaptive Realizations of Phase Transform for Time Delay Estimation, Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., pp. 15.10.1-4, San Diego, California, March 1984.
37.  D. H. Youn, K. K. Yu and V. J. Mathews, "Adaptive Nonlinear Digital Filter with Sequential Regression Algorithm," Proc. 22nd Annual Allerton Conf. Control, Communication and Computing, pp. 152-161, Urbana-Champaign, Illinois, October 3-5, 1984.
38. D. H. Youn, V. J. Mathews and S. H. Cho, "An Efficient Algorithm for Lattice Filter/Prediction," Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., pp. 1181-1184, Tampa, Florida, March 26-29, 1985.
39. V. J. Mathews and S. H. Cho, "Convergence Analysis for LMS Adaptive Filters Using the Sign Algorithm," Proc. Platinum Jubilee Conf. Systems and Signal Proc., pp. 63-66, Indian Institute of Science, Bangalore, India, December 11-13, 1986.
40. V. J. Mathews, "Adaptive Filters Requiring Zero Multiplications," Proc. Midwest Symp. Circuits, Systems, pp. 471-474, Syracuse, New York, August 17-18, 1987.
41. V. J. Mathews, "A Fast, Recursive Least Squares Nonlinear Adaptive Filter," Proc. 21st Annual Asilomar Conf. Signals, Systems and Computers , pp. 156-160, Pacific Grove, California, November 1987.
42. V. J. Mathews and J. Lee, "A Fast Recursive Least Squares Second Order Volterra Filter," Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc ., New York, pp. 1383-1386, April 11-14, 1988.
43. S. H. Cho and V. J. Mathews, "Multiplication-Free Adaptive Filters," Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., pp. 1576-1579, New York, April 11-14, 1988.
44. S. H. Cho and V. J. Mathews, "Tracking Analysis of the Sign Algorithm in Non-Stationary Environments," Proceedings of the 32nd Midwest Symposium on Circuits and Systems, pp. 869-872, Urbana-Champaign, Illinois, August 14-15, 1989.
45. V. J. Mathew and Z. Xie, "Stochastic Gradient Adaptive Filters with Gradient Adaptive Step Sizes," Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc, pp. 1385-1388, Albuquerque, New Mexico, April 3-6, 1990.
46. M. A. Syed and V. J. Mathews, "Lattice and QR-Decomposition Based Algorithms for Recursive Least Squares Adaptive Nonlinear Filters," Proc. IEEE Int. Symp. Circuits and Systems, New Orleans, Louisiana, May 1990.
47. H. K. Baik, V. J. Mathews and R. T. Short, "Adaptive Lattice Bilinear Filter," Proceedings of the SPIE Conference on Advanced Signal Processing Algorithms, Architectures and Implementations, San Diego, June 1990.
48. H. K. Baik and V. J. Mathews, "Adaptive Algorithms for Identifying Recursive Nonlinear Systems," Proc IEEE Int. Conf. Acoust., Speech, Signal Proc., Toronto, Canada, pp. 2077-2080, May 1991.
49. V. J. Mathews and T. K. Moon, "Parameter Estimation for a Bilinear Time Series Model," Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc ., Toronto, Canada, pp. 3513-3516, May 1991.
50. M. A. Syed and V. J. Mathews, "Finite Precision Error Analysis of a QR-Decomposition Based Lattice Predictor," Proc. SPIE Conf. on Adaptive Signal Processing, San Diego, California, July 1991.
51. J. Lee and V. J. Mathews, "Output-Error Adaptive Bilinear Filters," Proc. Twenty Fifth Asilomar Conf. Signals, Systems and Computers , Pacific Grove, California, pp. 207-211, November 1991.
52. M. A. Syed and V. J. Mathews, "QR-Decomposition Based Algorithms for Adaptive Volterra Filtering," Proceedings of IEEE Int. Symp. Circuits and Systems, pp. 2625-2628, San Diego, California, May 1992.
53. J. Lee and V. J. Mathews, "A Stability Theorem for Bilinear Systems," Proc. IEEE Winter Workshop on Nonlinear Digital Signal Processing , Tampere, Finland, January 1993.
54. V. J. Mathews and G. L. Sicuranza, "Volterra and General Polynomial Filtering," Proc. IEEE Winter Workshop on Nonlinear Digital Signal Processing , Tampere, Finland, January 1993. (Plenary Talk)
55. J. Lee and V. J. Mathews, "On Extended Least Squares Bilinear Filtering Algorithms," Proc. IEEE Int. Conf. Acoustics, Speech, Signal Proc., Minneapolis, April 1993.
56. V. J. Mathews and J. Lee, "Techniques for Bilinear Time Series Analysis," Proc. Twenty Seventh Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, November 1993.
57. J. Lee and V. J. Mathews, "Adaptive Bilinear Predictors," Proc. ICASSP '94, Adelaide, Australia, April 1994.
58. G. K. Ma, J. Lee and V. J. Mathews, "A Fast RLS Bilinear Filter for Channel Equalization," Proc. ICASSP '94, Adelaide, Australia, April 1994.
59. V. J. Mathews and J. Lee, "Adaptive Algorithms for Bilinear Filtering," Proc. SPIE Annual Meeting; Conference on Advanced Signal Processing: Algorithms, Architectures and Implementations V, San Diego, July 24-29, 1994.
60. J. Lee and V. J. Mathews, "A Stability Condition for Time Varying Bilinear Systems," Proc. EUSIPCO 94, Edinburgh, September 1994.
61. V. J. Mathews, "Adaptive Volterra Filters Using Orthogonal Structures," Proceedings of ICASSP 95, Detroit, May 1995.
62. S. Mo and V. J. Mathews, "Adaptive Binarization of Document Images," Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing , Neos-Marmaras, Halkidiki, Greece, June 1995.
63. T. M. Panicker and V. J. Mathews, "Parallel-cascade realizations and approximations of truncated Volterra systems," Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing , Atlanta, May 1996.
64. P. J. Hahn, V. J. Mathews and T. D. Tran, "Adaptive realization of a maximum likelihood time delay estimator," Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Atlanta, May 1996.
65. T. M. Panicker, V. J. Mathews and G. L. Sicuranza, "Parallel-Cascade Adaptive Volterra Filters," Proc. EUSIPCO 1996, Trieste, Italy, September 1996.
66. T. M. Panicker and V. J. Mathews, "A Fast Gauss-Newton Parallel-Cascade Adaptive Truncated Volterra Filter," Proc. ICASSP 97, Munich, April 1997.
67. A. Carini, V. J. Mathews and G. L. Sicuranza, "Sufficient Stability Bounds for Slowly-Varying Discrete-Time Recursive Linear Filters," Proc. ICASSP 97, Munich, April 1997.
68. A. Carini, G. L. Sicuranza and V. J. Mathews, "On the Inversion of Certain Nonlinear Systems," IEEE Nonlinear Signal and Image Processing Workshop, Mackinac Island, Michigan, September 1997.
69. T. M. Panicker and V. J. Mathews, "An Extended Kalman Filter for Parallel-Cascade Truncated Volterra Systems," Proc. Thirty First Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, November 1997.
70. A. Carini, G. L. Sicuranza and V. J. Mathews, "Equalization and Linearization of Nonlinear Systems," Proc. ICASSP '98, Seattle, May 1998.
71. L. Li and V. J. Mathews, "Frequency-Domain Realization of Adaptive Parallel-Cascade Quadratic Filters," Proc. ICASSP '98, Seattle, May 1998.
72. A. Carini, V. J. Mathews and G. L. Sicuranza, "Exact and p th Order Equalization and Linearization of Recursive Polynomial Systems," Proc. Thirty Second Annual Asilomar Conference on Signals, Systems and Computers , Pacific Grove, California, November 1998.
73. N. Kalouptsidis, P. Kakoulas and V. J. Mathews, "Blind Identification of Bilinear Systems,'' IEEE International Conference on Acoustics, Speech and Signal Processing, Salt Lake City, May 2001.
74. S. Mo and V. J. Mathews, "An Adaptive Channel Estimator for CDMA Systems in Multipath Fading Channels,'' IEEE International Conference on Acoustics, Speech and Signal Processing, Salt Lake City, May 2001.
75. J. Jeraj, V. J. Mathews and J. Dubow, "A Stable Adaptive Hammerstine Filter Employing Partial Orthogonalization of the Input Signals," IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 2, pp. 1349-1352, May 2002.
76. J. Jeraj and V. J. Mathews, "Stochastic mean-square performance analysis of an adaptive Hammerstine filter," Proc. IEEE International Conf. Acoustics, Speech, and Signal Processing, vol. 2, pp. 725-728, Montreal, Canada, May 2004.
77. J. Jeraj and V. J. Mathews, "Identification of nonlinear, memoryless systems using Chebyshev nodes," Proc. IEEE International Conf. Acoustics, Speech, and Signal Processing, vol. 4, pp. 93-96, Philadelphia, March 2005.