Kevin Wagner

What did dreams mean to Egyptian Christians of the first to the sixth centuries? Alexandrian philosophers, starting with Philo, Clement and Origen, developed a new approach to dreams that was to have profound effects on the spirituality of the medieval West and Byzantium. Their approach, founded on the principles of Platonism, was based on the convictions that God could send prophetic dreams and that these could be interpreted by people of sufficient virtue. In the fourth century, the Alexandrian approach was expanded by Athanasius and Evagrius to include a more holistic psychological understanding of what dreams meant for spiritual progress. The ideas that God could be known in dreams and that dreams were linked to virtue flourished in the context of Egyptian desert monasticism. This volume traces that development and its influence on early Egyptian experiences of the divine in dreams.

The topic of this book is proportionate-type normalized least mean squares (PtNLMS) adaptive filtering algorithms, which attempt to estimate an unknown impulse response by adaptively giving gains proportionate to an estimate of the impulse response and the current measured error. These algorithms offer low computational complexity and fast convergence times for sparse impulse responses in network and acoustic echo cancellation applications. New PtNLMS algorithms are developed by choosing gains that optimize user-defined criteria, such as mean square error, at all times. PtNLMS algorithms are extended from real-valued signals to complex-valued signals. The computational complexity of the presented algorithms is examined. Contents 1. Introduction to PtNLMS Algorithms2. LMS Analysis Techniques3. PtNLMS Analysis Techniques4. Algorithms Designed Based on Minimization of User Defined Criteria5. Probability Density of WD for PtLMS Algorithms6. Adaptive Step-size PtNLMS Algorithms7. Complex PtNLMS Algorithms8. Computational Complexity for PtNLMS Algorithms About the Authors Kevin Wagner has been a physicist with the Radar Division of the Naval Research Laboratory, Washington, DC, USA since 2001. His research interests are in the area of adaptive signal processing and non-convex optimization. Milos Doroslovacki has been with the Department of Electrical and Computer Engineering at George Washington University, USA since 1995, where he is now an Associate Professor. His main research interests are in the fields of adaptive signal processing, communication signals and systems, discrete-time signal and system theory, and wavelets and their applications.