Foundation of Digital Signal Processing: Signal Spaces, System Representation, and Quantization Effects

Abstract

A main driving force for the development of our current information society is digital signal processing, the central idea of which is to implement analog systems using digital methods. Future applications require high bandwidth signals and fast A/D conversion, and thus approach the limits of today’s digital signal processing hardware. Even the exponential progress in hardware performance that is made according to Moore’s law is not sufficient to meet this increasing demand. Classically, the necessary theory has been developed for linear systems and signals in PW2 (Paley-Wiener class), i.e., for bandlimited signals that are square integrable. However, for several applications a rigorous theory for other classes of function spaces is needed.

In this talk an axiomatic approach will be used to analyze implementation aspects of systems on bounded bandlimited signals. In particular the existence of systems with certain properties will be discussed. The fundamental question is: what spaces are compatible with the basic operations that naturally arise in sampling, reconstruction, and signal processing? The appropriate classes for addressing our questions turn out to be the Bernstein and Paley–Wiener classes. This talk will close by addressing several practically relevant open problems.

Biography

 Holger Boche received the Dipl.-Ing., Dipl.- Math., and Dr.-Ing. degrees in electrical engineering and mathematics from the Technische Universität Dresden, Dresden, Germany, in 1990, 1992, and 1994, and Dr.rer.nat degree in pure mathematics from the Technische Universität Berlin, Berlin, Germany, in 1998. Starting in 2002, 2003, and 2004 he was Full Professor for Mobile Communication Networks at Technische Universität Berlin, Director of the Fraunhofer German-Sino Lab for Mobile Communications, Berlin and Director of the Fraunhofer Institute for Telecommunications (HHI), Berlin, Germany respectively. Since October 2010 he has been with the Institute of Theoretical Information Technology and Full Professor at the Technische Universität München, Munich, Germany.

 He was elected a Member of the German Academy of Sciences (Leopoldina) in 2008 and of the Berlin Brandenburg Academy of Sciences and Humanities in 2009. He received the Research Award "Technische Kommunikation" from the Alcatel SEL Foundation in October 2003, the "Innovation Award" from the Vodafone Foundation in June 2006, and the Gottfried Wilhelm Leibniz Prize from the Deutsche Forschungsgemeinschaft (German Research Foundation) in 2008. He was co-recipient of the 2006 IEEE Signal Processing Society Best Paper Award and recipient of the 2007 IEEE Signal Processing Society Best Paper Award. Since 2011 he is a fellow of the IEEE.

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