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This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
An Introduction to Frames is an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox, spurred by a host of recent applications requiring some level of redundancy. It asks the question: Why and where should one use frames? And answers emphatically: Anywhere where redundancy is a must. It then goes on to discuss a host of applications that richly illustrate that answer. An Introduction to Frames is geared primarily toward engineering students and those without extensive mathematical training. It is also intended to help researchers and practitioners decide whether frames are the right tool for their application.
"The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
A hands-on, step-by-step tutorial, this comprehensive resource teaches new programmers and those new to JavaScript.
For courses on web development that focus on more than one application. Platinum Edition Using XHTML, XML & Java 2 is a complete Web programming reference guide that covers each of the technologies and shows how they can work together. It teaches students the features and benefits of each technology. The coverage includes XHTML, XML, JavaScript, Dynamic HTML, CGI Programming with Perl, Server-Side Programming with ASP, ColdFusion and PHP, and Java 2. It also shows the value in combining technologies to create more powerful Web solutions.
This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006.
Frames and Framing in Documentary Comics explores how graphic narratives reframe global crises while also interrogating practices of fact-finding. An analog print phenomenon in an era shaped by digitalization, documentary comics formulates a distinct counterapproach to conventional journalism. In what ways are ‘facts’ being presented and framed? What is documentary honesty in a world of fake news and post-truth politics? How can the stories of marginalized peoples and neglected crises be told? The author investigates documentary comics in its unique relationship to framing: graphic narratives are essentially shaped by a reciprocal relationship between the manifest frames on the page and the attention to the cognitive frames that they generate. To account for both the textuality of comics and its strategic use as rhetoric, the author combines theories of framing analysis and cognitive narratology with comics studies and its attention toward the medium’s visual frames.
It is often the case - perhaps more often than not - that new ideas arrive long before there is the me ans to clothe and deli ver them. We can think ofLeonardo da Vinci's drawings of helicopters and submarines among many other examples. Computer-Assisted Learning (CAL) is an example of an idea which has had a particularly long gestation. As I will illustrate early in the book, the principles of CAL were really first discovered by Socrates. As a formal method of teaching, the Socratic method disappeared for over two millennia until the 1950s. It was then revived in the form ofProgrammed Learning (PL) which resulted from the researches ofB. F. Skinner at Harvard University. Even then, PL was premature. In the 1950s and 60s, methods were devised, such as teaching machines and various sorts ofPL text books, and there was a mushrooming of PL publishing at that time. For a complex of reason- economic, logistical and technical-PL also largely disappeared from the mid- 60s, although it continued in a few specialized areas ofteaching and industrial training. However, during the same period, PL quietly transformed itselfinto CAL. But the computerized form was not capable of mass dissemination until recently hecause personal microcomputers did not have sufficient internal memory sizes. That situation has now changed very dramatically and 128K microcomputers are becoming cheap and widely available. Cheap memory chips of256K and 1024K cannot be far away, either.
Rules and List of members included in some volumes.