Adaptive filters are systems that adjust themselves to a changing environment. They are designed to meet certain performance specifications and are expected to perform reasonably well under the operating conditions for which they have been designed. | Sayed . Rupp M. Robustness Issues in Adaptive Filtering Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 20 Robustness Issues in Adaptive Filtering Ali H. Sayed University of California Los Angeles Markus Rupp Bell Laboratories Lucent Technologies Motivation and Example Adaptive Filter Structure Performance and Robustness Issues Error and Energy Measures Robust Adaptive Filtering Energy Bounds and Passivity Relations Min-Max Optimality of Adaptive Gradient Algorithms Comparison of LMS and RLS Algorithms Time-Domain Feedback Analysis Time-Domain Analysis Stability and the Small Gain Condition Energy Propagation in the Feedback Cascade A Deterministic Convergence Analysis Gradient Algorithms References and Concluding Remarks Adaptive filters are systems that adjust themselves to a changing environment. They are designed to meet certain performance specifications and are expected to perform reasonably well under the operating conditions for which they have been designed. In practice however factors that may have been ignored or overlooked in the design phase of the system can affect the performance of the adaptive scheme that has been chosen for the system. Such factors include unmodeled dynamics modeling errors measurement noise and quantization errors among others and their effect on the performance of an adaptive filter could be critical to the proposed application. Moreover technological advancements in digital circuit and VLSI design have spurred an increase in the range of new adaptive filtering applications in fields ranging from biomedical engineering to wireless communications. For these new areas it is increasingly important to design adaptive schemes that are tolerant to unknown or nontraditional factors and effects. The aim of this chapter is to explore and determine the robustness properties of some
