Applied Fourier Analysis

Author : Tim Olson
Publisher : Birkhäuser
Page : 302 pages
File Size : 43,6 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9781493973934

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Applied Fourier Analysis by Tim Olson Pdf

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.

Author : Jayakumar Ramanathan
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217565

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Methods of Applied Fourier Analysis by Jayakumar Ramanathan Pdf

Author : Hsu
Publisher : Unknown
Page : 128 pages
File Size : 47,7 Mb
Release : 1993-01-01
Category : Electronic
ISBN : 0155005057

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Applied Fourier Analysis by Hsu Pdf

Author : Elena Prestini
Publisher : Birkhäuser
Page : 356 pages
File Size : 54,6 Mb
Release : 2016-12-01
Category : Mathematics
ISBN : 9781489979896

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The Evolution of Applied Harmonic Analysis by Elena Prestini Pdf

A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews

Author : G. B. Folland
Publisher : American Mathematical Soc.
Page : 447 pages
File Size : 50,7 Mb
Release : 2009
Category : Fourier analysis
ISBN : 9780821847909

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Fourier Analysis and Its Applications by G. B. Folland Pdf

This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.

Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 49,8 Mb
Release : 2014-12-10
Category : Mathematics
ISBN : 9781470415600

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Early Fourier Analysis by Hugh L. Montgomery Pdf

Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line. The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.

Author : Bao Luong
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 55,5 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780817649166

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Fourier Analysis on Finite Abelian Groups by Bao Luong Pdf

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

Author : Claude Gasquet,Patrick Witomski
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 48,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461215981

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Fourier Analysis and Applications by Claude Gasquet,Patrick Witomski Pdf

The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.

Author : M. W. Wong
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 52,6 Mb
Release : 2011-05-30
Category : Mathematics
ISBN : 9783034801164

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Discrete Fourier Analysis by M. W. Wong Pdf

This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Author : Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Publisher : Springer
Page : 618 pages
File Size : 55,9 Mb
Release : 2019-02-05
Category : Mathematics
ISBN : 9783030043063

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Numerical Fourier Analysis by Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche Pdf

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.

Author : Charles K. Chui,Qingtang Jiang
Publisher : Springer Science & Business Media
Page : 567 pages
File Size : 41,6 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9789462390096

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Applied Mathematics by Charles K. Chui,Qingtang Jiang Pdf

This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and “frequency” of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of “wavelets” in connection with the “multi-scale” structure of data-sets. The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.

Author : Russell L. Herman
Publisher : CRC Press
Page : 527 pages
File Size : 52,9 Mb
Release : 2016-09-19
Category : Mathematics
ISBN : 9781498773720

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An Introduction to Fourier Analysis by Russell L. Herman Pdf

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

Author : David W. Kammler
Publisher : Cambridge University Press
Page : 39 pages
File Size : 50,6 Mb
Release : 2008-01-17
Category : Mathematics
ISBN : 9781139469036

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A First Course in Fourier Analysis by David W. Kammler Pdf

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Author : Hwei Piao Hsu
Publisher : Houghton Mifflin Harcourt P
Page : 234 pages
File Size : 54,6 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015017302368

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Applied Fourier Analysis by Hwei Piao Hsu Pdf

Author : T. W. Körner
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,6 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009230070

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Fourier Analysis by T. W. Körner Pdf

Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.