Monday, April 30, 2007 

Program: "Energy Conservation in Adaptive Filtering"
Ali H. Sayed, UCLA Electrical Engineering Department

Adaptive filters are systems that respond to variations in their environment by adapting their internal structure in order to meet certain performance specifications. Such systems are widely used in communications, biomedical applications, signal processing, and control. The performance of an adaptive filter is evaluated in terms of its transient behavior and its steady-state behavior. The former provides information about how fast a filter learns, while the latter provides information about how well a filter learns. Such performance analyses are usually challenging since adaptive filters are, by design, time-variant, nonlinear, and stochastic systems. For this reason, it has been common in the literature to study different adaptive schemes separately due to the differences that exist in their update equations. 

The purpose of this talk is to provide an overview of an energy conservation approach to the performance analysis of adaptive filters. The framework is based on studying the energy flow through successive iterations of an adaptive filter and on establishing a fundamental energy conservation relation; the relation bears resemblance with Snellís Law in optics and has far reaching consequences to the study of adaptive schemes. In this way, many new and old results can be pursued uniformly across different classes of algorithms. 

In particular, the talk will highlight some recently discovered phenomena pertaining to the learning ability of adaptive filters. It will be seen that adaptive filters generally learn at a rate that is better than that predicted by least-mean-squares theory; that is, they are "smarter" than originally thought! It will also be seen that adaptive filters actually have two distinct rates of convergence; they learn at a slower rate initially and at a faster rate later; perhaps in a manner that mimics the human learning process. 


Ali H. Sayed received his PhD in Electrical Engineering from Stanford University in 1992. He is Professor and Chairman of Electrical Engineering at UCLA where he directs the Adaptive Systems Laboratory ( He has published widely in the areas of adaptive filtering, estimation theory, and signal processing for communications with over 250 articles and 4 books. He is the author of the textbook Fundamentals of Adaptive Filtering (Wiley, NY, 2003). He is a Fellow of IEEE and served as the Editor-in-Chief of the IEEE Transactions on Signal Processing during 2003-2005. He now serves as Editor-in-Chief of the EURASIP Journal on Applied Signal Processing. His research has received several recognitions including the 1996 IEEE D. G. Fink Prize, a 2002 Best Paper Award and a 2005 Young Author Best Paper award, both from the IEEE Signal Processing Society, the 2003 Kuwait Prize, the 2005 Terman Award, and two Best Student Paper Awards at international meetings (1999,2001). He has served as a 2005 Distinguished Lecturer of the IEEE Signal Processing Society; as a member of the Publications and Award Boards of the IEEE Signal Processing Society; and is serving as General Chairman of ICASSP 2008.

The speaker is being provided as part of the University of Delaware Electrical Engineering Lecture series. He will be presenting a talk to the EE Dept earlier in the day with the title "Distributed Processing over Adaptive Networks."

You might want to review the topic "Adaptive Filters"; a simple review is contained in wikipedia; a section of which is shown below.

Suppose a hospital is recording a heart beat (an ECG), which is being corrupted by a 50 Hz noise (the frequency coming from the power supply in many countries).

One way to remove the noise is to filter the signal with a notch filter at 50 Hz. However, due to slight variations in the power supply to the hospital, the exact frequency of the power supply might (hypothetically) wander between 47 Hz and 53 Hz. A static filter would need to remove all the frequencies between 47 and 53 Hz, which could excessively degrade the quality of the ECG since the heart beat would also likely have frequency components in the rejected range.

To circumvent this potential loss of information, an adaptive filter could be used. The adaptive filter would take input both from the patient and from the power supply directly and would thus be able to track the actual frequency of the noise as it fluctuates. Such an adaptive technique generally allows for a filter with a smaller rejection range, which means, in our case, that the quality of the output signal is more accurate for medical diagnosis.