Howard L. Resnikoff - Böcker

The past decade has witnessed the rapid development of a new mathematical tool, called wavlet analysis, for analyzing complex signals. It has begin to play a serious role in applications ranging from communications to geophysics, and from simulations to image processing. Like Fourier analysis (of which it is a generalization), or musical notation, wavelet analysis provides a method for representing a set of complex phenomena in a simpler, more compact, and thus more efficient manner. This text introduces the ideas and methods of wavelet analysis, relates them to previously known methods in mathematics and engineering, and shows how to apply wavelet analysis to digital signal processing. It begins by describing the multiscale (sometimes called "fractal") nature of information in many aspects of the real world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functions on a space.The discussion then turns from the continuous to the discrete and shows how a properly selected set of wavelets can be used to represent -- and even differentiate -- a wide range of signls efficiently and effectively. The last part of the book presents a wide variety of applications of wavelets to probllems in data compression and telecommunications.

The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature. How else can one ex­ plain the remarkable effectiveness of mathematics in describing and predicting the physical world? The projection of the mathematical method onto the subspace of human endeav­ 1 ors has long been a source of societal progress and commercial technology. The invention of the electronic digital computer (not the mechanical digital computer of Babbage) has made the role of mathematics in civilization even more central by making mathematics active in the operation of products. The writing of this book was intertwined with the development of a start-up company, Aware, Inc. Aware was founded in 1987 by one of the authors (H.L.R.), and the second author (R.O.W.) put his shoulder to the wheel as a consultant soon after.

The Illusion of Reality was conceived during my tenure as director of the newly established Division of Information Science and Technology at the National Science Foundation in 1979-1981 as a partial response to the need for a textbook for students, both in and out of government, that would pro­ vide a comprehensive view of information science as a fundamental constitu­ ent of other more established disciplines with a unity and coherence distinct from computer science, cognitive science, and library science although it is related to all of them. Driven by the advances of information technology, the perception of information science has progressed rapidly: today it seems well understood that information processing biological organisms and informa­ tion processing electronic machines have something basic in common that may subsume the theory of computation, as well as fundamental parts of physics. This book is primarily intended as a text for an advanced undergraduate or a graduate introduction to information science. The multidisciplinary nature of the subject has naturally led to the inclusion of a considerable amount of background material in various fields. The reader is likely to fmd the treat­ ment relatively oversimplified in fields with which he is familiar and, perhaps, somewhat heavier sailing in less familiar waters. The theme of common principles among seemingly unrelated applications provides the connective tissue for the diverse topics covered in the text and, I hope, justifies the variable level of presentation. Some of the material appears here for the first time.