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 thereal world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functins 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 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."

This text gives a clear introduction to the ideas and methods of wavelet analysis, making concepts understandable by relating them to methods in mathematics and engineering. It shows how to apply wavelet analysis to digital signal processing and presents a wide variety of applications.

0. 1. Junge Leute, die sich heutzutage zu einem Studium entschlie en, sollten in ihren Studienjahren mindestens zwei Dinge erreichen. Sie sollten sich erstens eine gewisse Kompetenz in einem Spezialgebiet aneignen, so d sie spater eine entsprechende Stellung in der Gesellschaft fmden konnen. Zweitens soIl ten sie sich der anderen Krafte und Stromungen in der Gesellschaft bewu t werden, die den Lauf und die Qualitiit ihres Lebens beeinflussen, und sie verstehen lemen. Urn dieses zweite Ziel zu erreichen, sind in den letzten Jahren an den amerikanischen Colleges Vorlesungen eingerichtet worden, die ein Verstandnis fUr Wesen und Aufgaben anderer Fachgebiete vermitteln, die nicht unmittelbar in das Spezialgebiet des Studenten fallen. Dieses Buch ist fur alle diejenigen gedacht, die die Stellung der Mathematik in Wissenschaft und Gesellschaft verstehen mochten. Es vermittelt keine mathematischen Techniken, noch bereitet es den Leser darauf vor, Mathematik emsthaft anzuwenden. Die einzigen mathematischen Voraus- setzungen sind: hinreichende Kenntnisse in der Arithmetik von Briichen und Dezimal- zahlen, in elementarer ebener Geometrie, in den Anfangsgriinden algebraischer Verfahren und in der Trigonometrie. Eine Moglichkeit, den uneingeweihten Leser mit der Mathematik bekanntzumachen, bestiinde darin, ihm Beispiele vorzufiihren, die gegenwartig fUr Mathematiker von Interesse sind, und ihm auf diese Weise zu zeigen, was Mathematik ist und wie Mathematiker denken.