Lectures On The Fourier Transform And Its Applications

Author : Brad G. Osgood
Publisher : American Mathematical Soc.
Page : 689 pages
File Size : 52,9 Mb
Release : 2019-01-18
Category : Fourier transformations
ISBN : 9781470441913

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Lectures on the Fourier Transform and Its Applications by Brad G. Osgood Pdf

This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

Author : Ronald Newbold Bracewell
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 1978
Category : Fourier transformations
ISBN : OCLC:220097501

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The Fourier Transform and Its Applications by Ronald Newbold Bracewell Pdf

Author : Prof. Brad Osgood
Publisher : Unknown
Page : 428 pages
File Size : 47,6 Mb
Release : 2014-12-18
Category : Electronic
ISBN : 150561449X

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Lecture Notes for EE 261 the Fourier Transform and Its Applications by Prof. Brad Osgood Pdf

Lecture Notes for EE 261 The Fourier Transform and its ApplicationsBy Prof. Brad Osgood

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 47,6 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

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Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Ronald Newbold Bracewell
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 648 pages
File Size : 43,9 Mb
Release : 2000
Category : Mathematics
ISBN : UCSD:31822031267685

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The Fourier Transform and Its Applications by Ronald Newbold Bracewell Pdf

This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms.The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.

Author : David W. Kammler
Publisher : Cambridge University Press
Page : 39 pages
File Size : 40,9 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 : Thomas H. Wolff
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 47,9 Mb
Release : 2003-09-17
Category : Mathematics
ISBN : 9780821834497

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Lectures on Harmonic Analysis by Thomas H. Wolff Pdf

This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.

Author : Norbert Wiener
Publisher : CUP Archive
Page : 228 pages
File Size : 43,6 Mb
Release : 1988-11-17
Category : Mathematics
ISBN : 0521358841

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The Fourier Integral and Certain of Its Applications by Norbert Wiener Pdf

The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from the presence of an application of the theory to the prime number theorems of Hadamard and de la Vallee Poussin. Both pure and applied mathematicians will welcome the reissue of this classic work. For this reissue, Professor Kahane's Foreword briefly describes the genesis of Wiener's work and its later significance to harmonic analysis and Brownian motion.

Author : R.C. Jennison
Publisher : Elsevier
Page : 129 pages
File Size : 54,9 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483155401

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Fourier Transforms by R.C. Jennison Pdf

Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of the Cavendish Laboratory. The book begins with an introduction to Fourier Transform. It provides a definition o Fourier Transform, describes its applications, and presents the formal mathematical statement of the transform. Separate chapters discuss the elementary transform, extended functions, and direct applications of Fourier transforms. The final two chapters deal with limitations, products, and convolutions; and the differentiation of Fourier transforms.

Author : Jyrki Kauppinen,Jari Partanen
Publisher : John Wiley & Sons
Page : 271 pages
File Size : 55,7 Mb
Release : 2011-02-10
Category : Science
ISBN : 9783527635016

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Fourier Transforms in Spectroscopy by Jyrki Kauppinen,Jari Partanen Pdf

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical point of view. Some aspects, linear prediction for example, are explained here thoroughly for the first time.

Author : Volker Michel
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 51,5 Mb
Release : 2012-12-12
Category : Mathematics
ISBN : 9780817684037

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Lectures on Constructive Approximation by Volker Michel Pdf

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Author : Mark S Nixon
Publisher : World Scientific
Page : 305 pages
File Size : 44,6 Mb
Release : 2022-03-10
Category : Mathematics
ISBN : 9781800611122

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D'oh! Fourier: Theory, Applications, And Derivatives by Mark S Nixon Pdf

D'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively.The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.

Author : Naum Il_ich Akhiezer
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 43,9 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 9780821845240

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Lectures on Integral Transforms by Naum Il_ich Akhiezer Pdf

Focuses on classical integral transforms, principally the Fourier transform, and their applications. This book develops the general theory of the Fourier transform for the space $L DEGREES1(E_n)$ of integrable functions of $n$ var

Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Page : 615 pages
File Size : 48,7 Mb
Release : 2022-05-05
Category : Computers
ISBN : 9781009098489

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Data-Driven Science and Engineering by Steven L. Brunton,J. Nathan Kutz Pdf

A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

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An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.