Applied Fourier Analysis: From Signal Processing to Medical Imaging - Hardcover

Olson

Hardcover

ISBN 10: 1493973916 ISBN 13: 9781493973910

Verlag: Springer, 2017

Inhaltsangabe

<P>THE FIRST OF ITS KIND, THIS FOCUSED TEXTBOOK SERVES AS A SELF-CONTAINED RESOURCE FOR TEACHING FROM SCRATCH THE FUNDAMENTAL MATHEMATICS OF FOURIER ANALYSIS AND ILLUSTRATING SOME OF ITS MOST CURRENT, INTERESTING APPLICATIONS, INCLUDING MEDICAL IMAGING AND RADAR PROCESSING. DEVELOPED BY THE AUTHOR FROM EXTENSIVE CLASSROOM TEACHING EXPERIENCE, IT PROVIDES A BREADTH OF THEORY THAT ALLOWS STUDENTS TO APPRECIATE THE UTILITY OF THE SUBJECT, BUT AT AS ACCESSIBLE A DEPTH AS POSSIBLE. WITH MYRIAD APPLICATIONS INCLUDED, THIS BOOK CAN BE ADAPTED TO A ONE OR TWO SEMESTER COURSE IN FOURIER ANALYSIS OR SERVE AS THE BASIS FOR INDEPENDENT STUDY.</P><P><I>APPLIED FOURIER ANALYSIS </I>ASSUMES NO PRIOR KNOWLEDGE OF ANALYSIS FROM ITS READERS, AND BEGINS BY MAKING THE TRANSITION FROM LINEAR ALGEBRA TO FUNCTIONAL ANALYSIS. IT GOES ON TO COVER BASIC FOURIER SERIES AND FOURIER TRANSFORMS BEFORE DELVING INTO APPLICATIONS IN SAMPLING AND INTERPOLATION THEORY, DIGITAL COMMUNICATIONS, RADAR PROCESSING, MEDI</P><P></P>CAL IMAGING, AND HEAT AND WAVE EQUATIONS. FOR ALL APPLICATIONS, AMPLE PRACTICE EXERCISES ARE GIVEN THROUGHOUT, WITH COLLECTIONS OF MORE IN-DEPTH PROBLEMS BUILT UP INTO EXPLORATORY CHAPTER PROJECTS.   ILLUMINATING VIDEOS ARE AVAILABLE ON SPRINGER.COM AND LINK.SPRINGER.COM THAT PRESENT ANIMATED VISUALIZATIONS OF SEVERAL CONCEPTS.<P></P><P>THE CONTENT OF THE BOOK ITSELF IS LIMITED TO WHAT STUDENTS WILL NEED TO DEAL WITH IN THESE FIELDS, AND AVOIDS SPENDING UNDUE TIME STUDYING PROOFS OR BUILDING TOWARD MORE ABSTRACT CONCEPTS. THE BOOK IS PERHAPS BEST SUITED FOR COURSES AIMED AT UPPER DIVISION UNDERGRADUATES AND EARLY GRADUATES IN MATHEMATICS, ELECTRICAL ENGINEERING, MECHANICAL ENGINEERING, COMPUTER SCIENCE, PHYSICS, AND OTHER NATURAL SCIENCES, BUT IN GENERAL IT IS A HIGHLY VALUABLE RESOURCE FOR INTRODUCING A BROAD RANGE OF STUDENTS TO FOURIER ANALYSIS.<BR/></P>

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Reseña del editor

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study.

Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi

cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects.   Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts.

The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Biografía del autor

Tim Olson is an Associate Professor of Mathematics at the University of Florida. His research focuses on applications of Fourier Analysis to medical imaging and radar processing, electromagnetics, and other related fields.
He is also an experienced fly-fisherman and a fishing guide in the rivers of Montana.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2017
• ISBN 10: 1493973916
• ISBN 13: 9781493973910
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 320