An Introduction to Finite Tight Frames

Beschreibung

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing.

Key features and topics:

* First book entirely devoted to finite frames

* Extensive exercises and MATLAB examples for classroom use

* Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames

* Later chapters delve into general theory details and recent research results

* Many illustrations showing the special aspects of the geometry of finite frames

* Provides an overview of the field of finite tight frames

* Discusses future research directions in the field

Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.

First book entirely devoted to finite frames

Replete with exercises, illustrations, and MATLAB examples

Well suited as a textbook for a graduate course or seminar on finite frames

Real-world applications to signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing

For a broad readership in pure and applied mathematics, engineering, mathematical physics, and signal processing

Autor*in

Shayne F. D. Waldron

Themen in »An Introduction to Finite Tight Frames«

Heisenberg frames MATLAB finite tight frames harmonic frames multivariate orthogonal polynomials quantum information theory remote sensing signal processing tight frames

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“This book gives a well-written and accessible introduction to the rapidly developing area of finite tight frames. ... this book is more than a textbook since it presents many advanced results that give an overview of the current state of the art, which will be useful for researchers who study finite tight frames.” (Pierluigi Vellucci, zbMATH 1388.42078, 2018)

“This book is a recent addition to the literature on frame theory. … This book could serve as a text for an undergraduate course or for a graduate course that aims to propel students to the frontier of research.”(Bernhard G. Bodmann, Mathematical Reviews, February, 2019)

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