[This page is no longer being updated.  Go to my homepage for my current contact information or to my list of publications to download papers.  -- SCD]


Adaptive Filters and Adaptive Signal Processing

Adaptive filters are computational devices that attempt to model the relationships between two or more signals in an iterative manner.  The success of adaptive filters in many practical signal processing problems is due in large part to the simplicity and robustness of gradient-based algorithms such as the least-mean-square (LMS) algorithm.  Despite being forty years old, the field is still going strong, and much research work continues to be published.

Adaptive filters could be considered my primary research area.  I am co-authoring with V. John Mathews of the University of Utah a book on adaptive filters, which is tentatively scheduled for publication in the next millenium--which is soon!  The text will be MATLAB-friendly, with .m files for all imporant algorithms, including fast least-squares methods.  I have also been a section editor for The Digital Signal Processing Handbook, published by CRC Press, which contains several very nice chapter ``capsules'' on analyses of adaptive filters, RLS adaptive filters, transform-domain adaptive filters, adaptive IIR filters, and blind equalization techniques.  If you are looking for a quick introduction to the field, these chapters are highly recommended.

My work in adaptive filters goes back to my Stanford Ph.D. days, where I studied the performance effects and improvements that can be obtained when nonlinearities are introduced within gradient-type algorithms.  The resulting generic analyses can be used to study the behaviors of many different algorithms, where only the exact forms of the signal expectations need to be specified for the chosen algorithm forms.  Alternatively, they can be used to optimize the algorithm to the underlying signal statistics.  This work is largely contained in three publications in IEEE Trans. Signal Processing in June 1992, June 1994, and June 1994, respectively.  An application of the methodology to an interesting airborne magnetic sensing task has also appeared in conference paper form.

Many of my published works pertain to the performance analysis of adaptive filters.  Using more-or-less traditional independence assumption methods, I've developed analyses of the multiple-error and block LMS algorithms, two leaky LMS algorithms, two partial update algorithms, and an anti-Hebbian algorithm, respectively.   Along with my student Weimin Pan, we also developed new algorithmic procedures for the exact analysis of the LMS adaptive filter without the independence assumption, with extensions to the sign-data LMS adaptive filter.  The main drawback of the exact analysis method is complexity--if you wish to obtain an exact analysis for a 32-tap equalizer using current symbolic computations methods, be prepared to wait a long time!

Some of my publications present analytical and practical extensions of the normalized LMS adaptive filter and other algorithms that can provide zero a posteriori error.  My publication in the March 1994 issue of IEEE Signal Processing Letters describes a family of normalized algorithms that includes an interesting algorithm that updates only one coefficient at each time instant while still performing quite well in some situations.  A sidelight of this effort has been the development of a data-adaptive procedure for calculating a running maximum, along with some analytical tools for analyzing such algorithms and systems.  More recently, I have been working with Markus Rupp of Lucent Technologies to develop methods that use the relationship between the a priori and a posteriori errors to predict algorithm robustness.  Also jointly with Markus, we have developed several useful methods for bias removal in equation-error adaptive IIR filters that provide good performance with a low complexity.  In addition, I have done some work on approximating the fast affine projection algorithm (FAP) using orthogonal frequency-domain-type transforms; these methods avoid the fast RLS algorithms imbedded in the FAP algorithm while providing nearly the same convergence performance as compared to that of the FAP algorithm.

My work on RLS and fast transversal filters (FTF) has been jointly with Jihee Soh, one of my Ph.D. students.  We have performed a linearized stability analysis of an approximate leaky FTF algorithm, providing conditions on the leakage factor to provide numerical stability of the algorithm.   We have also developed a novel leakage technique for sliding window computations that is both simple and numerically-stable, and we've applied it to the sliding DFT and DCT, the conventional sliding-window-covariance RLS adaptive filter, and a novel sliding-window-covariance FTF.

I have also done quite a bit of work on adaptive algorithms for active noise and vibration control; these publications are organized on a separate page.  One of the foci of that work has been on delay compensation methods, in which an adaptive algorithm with delay in the feedback loop is altered to provide exact delayless adaptation behavior without using the standard update equations.  We have developed a pipelined LMS adaptive filter architecture using this technique.

Finally, my most-recent adaptive filtering work has been on modified algorithms for blind equalization in which the equalizer is used as a prewhitening filter.  Probably the best description of this work is in the form of a technical report, although we have published a letter and a correspondence on the topic.  More work on blind deconvolution/equalization and the related task of blind source separation can be found on a separate page.
 


Publications on Adaptive Filters and Adaptive Signal Processing -- Scott C. Douglas

Book
  1. V.J. Mathews and S.C. Douglas, Adaptive Filters (Upper Saddle River, NJ:  Prentice-Hall, 2000, to be published).
Book Chapters
  1. S.C. Douglas, ``Introduction to Adaptive Filters,'' in The DSP Handbook, V.J. Madisetti and D. Williams, eds. (Boca Raton, FL:  CRC/IEEE Press, 1998), Chapter 18.
  2. S.C. Douglas and M. Rupp, ``Convergence Issues in the LMS Adaptive Filter,'' in The DSP Handbook, V.J. Madisetti and D. Williams, eds. (Boca Raton, FL:  CRC/IEEE Press, 1998), Chapter 19.
Technical Reports
    S.C. Douglas, A. Cichocki, and S. Amari, ``Self-Whitening Adaptive Equalization and Deconvolution Algorithms,'' Technical Report No. EE-99-001, Dept. of Electrical Engineering, Southern Methodist University, Dallas, TX, January 1999.(Postscript, 534K, 35 pages)
Journal Publications
  1. S.C. Douglas and T.H.-Y. Meng, ``The Optimum Scalar Data Nonlinearity in LMS Adaptation for Arbitrary I.I.D. Inputs,'' IEEE Trans. Signal Processing, vol. 40, no. 6, pp. 1566-1570, June 1992.
  2. S.C. Douglas, ``A Family of Normalized LMS Algorithms,'' IEEE Signal Processing Letters, vol. 1, no. 3, pp. 49-51, March 1994.(Postscript, 177K, 7 pages)
  3. S.C. Douglas and T.H.-Y. Meng, ``Normalized Data Nonlinearities for LMS Adaptation,'' IEEE Trans. Signal Processing, vol. 42, no. 6, pp. 1352-1365, June 1994.
  4. S.C. Douglas and T.H.-Y. Meng, ``Stochastic Gradient Adaptation Under General Error Criteria,'' IEEE Trans. Signal Processing, vol. 42, no. 6, pp. 1335-1351, June 1994.
  5. S.C. Douglas, ``Analysis of the Multiple-Error and Block Least-Mean-Square Adaptive Algorithms,'' IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 42, no. 2, pp. 92-101, February 1995.
  6. S.C. Douglas and W. Pan, ``Exact Expectation Analysis of the LMS Adaptive Filter,'' IEEE Trans. Signal Processing, vol. 43, no. 12, pp. 2863-2871, December 1995.(Postscript, 287K, 28 pages)
  7. S.C. Douglas, ``Analysis of an Anti-Hebbian Adaptive FIR Filtering Algorithm,'' IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 43, no. 11, pp. 777-780, November 1996.(Postscript, 412K, 16 pages)
  8. S.C. Douglas, ``Running Max/Min Calculation Using a Pruned Ordered List,'' IEEE Trans. Signal Processing, vol. 44, no. 11, pp. 2872-2877, November 1996. (Postscript, 258K, 18 pages)
  9. S.C. Douglas, A. Cichocki, and S. Amari, ``Fast-Convergence Filtered-Regressor Algorithms for Blind Equalisation,'' Electronics Letters, vol. 32, no. 23, pp. 2114-2115, 7th November 1996. (Postscript, 173K, 6 pages)
  10. S.C. Douglas, ``Adaptive Filters Employing Partial Updates,'' IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 44, no. 3, pp. 209-216, March 1997.(Postscript, 452K, 20 pages)
  11. S.C. Douglas, ``Performance Comparison of Two Implementations of the Leaky LMS Adaptive Filter,'' IEEE Trans. Signal Processing, vol. 45, no. 8, pp. 2125-2130, August 1997. (Postscript, 242K, 12 pages)
  12. S.C. Douglas, ``An Efficient Implementation of the Modified Filtered-X LMS Algor ithm,'' IEEE Signal Processing Letters, vol. 4, no. 10, pp. 286-288, October 1997. (Postscript, 102K, 6 pages)
  13. S.C. Douglas and A. Cichocki, ``On-Line Step Size Selection for Training Adaptive Systems,'' IEEE Signal Processing Mag., vol. 14, no. 6, pp. 45-46, November 1997.
  14. S.C. Douglas, Q. Zhu, and K.F. Smith, ``A Pipelined LMS Adaptive FIR Filter Architecture Without Adaptation Delay,'' IEEE Trans. Signal Processing, vol. 46, no. 3, pp. 775-779, March 1998.
  15. S.C. Douglas, A. Cichocki, and S. Amari, ``Self-Whitening Algorithms for Adaptive Equalization and Deconvolution,''  IEEE Trans. Signal Processing, vol. 47, no. 4, pp. 1161-1165, April 1999.(Postscript, 242K, 17 pages)

Conference Publications

  1. S.C. Douglas and T.H.-Y. Meng, ``Optimum Error Nonlinearities for LMS Adaptation,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Albuquerque, NM, vol. 3, pp. 1421-1424, April 1990.
  2. S.C. Douglas and T.H.-Y. Meng, ``Optimum Error Quantization for LMS Adaptation,'' Proc. IEEE Pacific Rim Conf. on Communications, Computers, and Signal Processing, Victoria, B.C., Canada, vol. 2, pp. 704-708, May 1991.
  3. S.C. Douglas and T.H.-Y. Meng, ``An Optimum NLMS Algorithm: Performance Improvement Over LMS,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Toronto, Canada, vol. 3, pp. 2125-2128, May 1991.
  4. S.C. Douglas and T.H.-Y. Meng, ``Linearized Least-Squares Training of Multilayer Feedforward Neural Networks,'' Proc. International Joint Conference on Neural Networks, Seattle, WA, vol. I, pp. 307-312, July 1991.
  5. S.C. Douglas and T.H.-Y. Meng, ``A Nonlinear Error Adaptive Notch Filter for Separating Two Sinusoidal Signals,'' Proc. 25th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, vol. 2, pp. 673-677, November 1991.
  6. S.C. Douglas and T.H.-Y. Meng, ``Exact Expectation Analysis of the LMS Adaptive Filter Without the Independence Assumption,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, San Francisco, CA, vol. 4, pp. 61-64, March 1992.
  7. S.C. Douglas, ``Exact Expectation Analysis of the Sign-Data LMS Algorithm for I.I.D. Input Data,'' Proc. 26th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, vol. 1, pp. 566-570, October 1992. (Postscript, 181K, 5 pages)
  8. S.C. Douglas and J.A. Olkin, ``Multiple-input, Multiple-output, Multiple-error Adaptive Feedforward Control Using the Filtered-X Normalized LMS Algorithm,'' Proc. Second Conference on Recent Advances in Active Control of Sound and Vibration, Blacksburg, VA, pp. 743-754, April 1993.
  9. S.C. Douglas, ``Exact Expectation Analysis of the LMS Adaptive Filter for Correlated Gaussian Input Data,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Minneapolis, MN, vol. 3, pp. 519-522, April 1993. (Postscript, 151K, 4 pages)
  10. N.L. Freire and S.C. Douglas, ``Adaptive Cancellation of Geomagnetic Background Noise Using a Sign-Error Normalized LMS Algorithm,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Minneapolis, MN, vol. 3, pp. 523-526, April 1993.(Postscript, 158K, 4 pages)
  11. S.C. Douglas,``Mean-Square Analysis of the Multiple-Error and Block LMS Adaptive Algorithms,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Adelaide, Australia, vol. 3, pp. 429-432, April 1994.(Postscript, 178K, 4 pages)
  12. S.C. Douglas, ``Simplified Stochastic Gradient Adaptive Filters Using Partial Updating,'' Proc. Sixth IEEE Digital Signal Processing Workshop, Yosemite, CA, pp. 265-268, October 1994.
  13. S.C. Douglas, ``Generalized Gradient Adaptive Step Sizes for Stochastic Gradient Adaptive Filters,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Detroit, MI, vol. 2, pp. 1396-1399, May 1995.(Postscript, 204K, 4 pages)
  14. S.C. Douglas and V.J. Mathews,``Stochastic Gradient Adaptive Step Size Algorithms for Adaptive Filtering,'' Proc. International Conference on Digital Signal Processing, Limassol, Cyprus, vol. 1, pp. 142-147, June 1995. (Postscript, 144K, 6 pages)
  15. S.C. Douglas, ``Analysis and Implementation of the Max-NLMS Adaptive Filter,'' Proc. 29th Annual Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 1, pp. 659-663, November 1995. (Postscript, 251K, 5 pages)
  16. S.C. Douglas, ``Efficient Approximate Implementations of the Fast Affine Projection Algorithm Using Orthogonal Transforms,'' Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, Atlanta, GA, vol. 3, pp. 1656-1659, May 1996.(Postscript, 217K, 4 pages)
  17. S.C. Douglas, ``An Efficient Algorithm for Running Max/Min Calculation,'' Proc. IEEE International Symposium on Circuits and Systems, Atlanta, GA, vol. 2, pp. 5-8, May 1996. (Postscript, 176K, 4 pages)
  18. S.C. Douglas and M. Rupp, ``On Bias Removal and Unit Norm Constraints in Equation-Error Adaptive IIR Filters,'' Proc. 30th Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 2, pp. 1093-1097, November 1996. (Postscript, 229K, 5 pages)
  19. J.K. Soh and S.C. Douglas, ``Analysis of the Stabilized FTF Algorithm With Leakage Correction,'' Proc. 30th Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 2, pp. 1088-1092, November 1996. (Postscript, 159K, 5 pages)
  20. S.C. Douglas, A. Cichocki, and S. Amari, ``Quasi-Newton Filtered-Regressor Algorithms for Adaptive Equalization and Deconvolution,'' Proc. IEEE Workshop on Signal Processing Advances in Wireless Communications, Paris, France, pp. 109-112, April 1997. (Postscript, 430K, 4 pages)
  21. M. Rupp and S.C. Douglas, ``Deterministic Stability Analyses of Unit-Norm Constrained Algorithms for Unbiased Adaptive IIR Filtering,'' Proc. IEEE International Conf. Acoust., Speech, Signal Processing, Munich, Germany, vol. 3, pp. 1937-1940, April 1997.
  22. Q. Zhu, S.C. Douglas, and K.F. Smith, ``A Pipelined Architecture for LMS Adaptive FIR Filters Without Adaptation Delay,'' Proc. IEEE International Conf. Acoust., Speech, Signal Processing, Munich, Germany, vol. 3, pp. 1934-1937, April 1997.
  23. S.C. Douglas and M. Rupp, ``A Posteriori Updates for Adaptive Filters,'' Proc. 31st Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 2, pp. 1641-1645, November 1997. (Postscript, 161K, 5 pages)
  24. S.C. Douglas and J.K. Soh, ``A Numerically-Stable Sliding-Window Estimator and Its Application to Adaptive Filtering,'' Proc. 31st Annual Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 1, pp. 111-115, November 1997. (Postscript, 192K, 5 pages)
  25. S.C. Douglas and J.K. Soh, ``Delay Compensation Methods for Stochastic Gradient Adaptive Filters,'' Proc. 8th IEEE Digital Signal Processing Workshop, Bryce Canyon, UT, paper no. 108, August 1998.(Postscript, 152K, 4 pages)
  26. J.K. Soh and S.C. Douglas, ``A Sliding-Window-Covariance Fast Transversal Filter Employing Periodic Leakage,'' Proc. 8th IEEE Digital Signal Processing Workshop, Bryce Canyon, UT, paper no. 109, August 1998.(Postscript, 163K, 4 pages)
  27. M. Rupp and S.C. Douglas, ``A Posteriori Analysis of Adaptive Blind Equalizers,'' Proc. 32nd Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, vol. 1, pp. 369-373, November 1998.(Postscript, 144K, 5 pages)
  28. J.K. Soh and S.C. Douglas, ``Efficient Implementations of the NLMS Algorithm With Decorrelation Filters for Acoustic Echo Cancellation,'' Proc. International Workshop on Acoustic Echo and Noise Control, Pocono Manor, PA, pp. 164-167, September 1999.(Postscript, 159K, 4 pages)
  29. X. Sun and S.C. Douglas, ``Adaptive Time Delay Estimation With Allpass Constraints,'' presented at 33rd Annual Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, October 24-27, 1999.(Postscript, 331K, 5 pages)
  30. S.C. Douglas, ``Numerically-Stable O(N^2) Algorithms for RLS Adaptive Filtering Using Least-Squares Prewhitening,'' to be presented at
  31. IEEE International Conf. Acoust., Speech, Signal Processing, Istanbul, Turkey, June 2000.(Postscript, 345K, 4 pages)

  32. X. Sun and S.C. Douglas, ``Phase Estimation Using Adaptive Allpass Filters,'' to be presented at IEEE International Conf. Acoust., Speech, Signal Processing, Istanbul, Turkey, June 2000.(Postscript, 198K, 4 pages)