Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.

While people are now using peer-to-peer (P2P) applications for various processes, such as file sharing and video streaming, many research and engineering issues still need to be tackled in order to further advance P2P technologies. Peer-to-Peer Computing: Applications, Architecture, Protocols, and Challenges provides comprehensive theoretical and practical coverage of the major features of contemporary P2P systems and examines the obstacles to further success. Setting the stage for understanding important research issues in P2P systems, the book first introduces various P2P network architectures. It then details the topology control research problem as well as existing technologies for handling topology control issues. The author describes novel and interesting incentive schemes for enticing peers to cooperate and explores recent innovations on trust issues. He also examines security problems in a P2P network. The final chapter addresses the future of the field. Throughout the text, the highly popular P2P IPTV application, PPLive, is used as a case study to illustrate the practical aspects of the concepts covered. Addressing the unique challenges of P2P systems, this book presents practical applications of recent theoretical results in P2P computing. It also stimulates further research on critical issues, including performance and security problems.

Torah thoughts based on and adapted from the teaching of Rabbi Abraham Pam.

The growth of the Internet has fueled the demand for enhanced watermarking and data hiding technologies and has stimulated research into new ways to implement watermarking systems in the real world. This book presents the principles of watermarking system design and discusses technologies in information concealment and recovery. It highlights the requirements and challenges of applications in security, image/video indexing, hidden communications, image captioning, and transmission error recovery and concealment. It explains digital watermarking technologies and offers an understanding of new approaches and applications, laying the groundwork for further developments in the field.