An Introduction To Fourier Analysis

Author : Russell L. Herman
Publisher : CRC Press
Page : 527 pages
File Size : 40,8 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 : Robert T. Seeley
Publisher : Courier Corporation
Page : 116 pages
File Size : 43,8 Mb
Release : 2014-02-20
Category : Mathematics
ISBN : 9780486151793

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An Introduction to Fourier Series and Integrals by Robert T. Seeley Pdf

A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 47,7 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 : Elias M. Stein,Guido Weiss
Publisher : Princeton University Press
Page : 312 pages
File Size : 50,8 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883899

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Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by Elias M. Stein,Guido Weiss Pdf

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Author : Peter Bloomfield
Publisher : John Wiley & Sons
Page : 285 pages
File Size : 49,7 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471653998

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Fourier Analysis of Time Series by Peter Bloomfield Pdf

A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition: * Devotes an entire chapter to complex demodulation * Treats harmonic regression in two separate chapters * Features a more succinct discussion of the fast Fourier transform * Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility * Includes Web addresses for all time series data used in the examples An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.

Author : M. W. Wong
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 48,5 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 : Sir M J Lighthill
Publisher : Hassell Street Press
Page : 92 pages
File Size : 40,5 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1013715624

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Introduction to Fourier Analysis and Generalised Functions by Sir M J Lighthill Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Howard J. Wilcox,David L. Myers
Publisher : Courier Corporation
Page : 194 pages
File Size : 49,9 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486137476

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An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox,David L. Myers Pdf

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 42,8 Mb
Release : 2008
Category : Fourier analysis
ISBN : 9780821847978

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Introduction to Fourier Analysis and Wavelets by Mark A. Pinsky Pdf

This text provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. It contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.

Author : Robert D. Stuart
Publisher : Chapman & Hall
Page : 134 pages
File Size : 44,7 Mb
Release : 1977
Category : Mathematics
ISBN : UVA:X002314883

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An Introduction to Fourier Analysis by Robert D. Stuart Pdf

Fourier series; Analysis of periodic waveforms; Fourier integrals; Analysis of transients; Application to circuit analysis; Application to wave motion analysis.

Author : Eric Stade
Publisher : John Wiley & Sons
Page : 519 pages
File Size : 50,7 Mb
Release : 2011-10-07
Category : Mathematics
ISBN : 9781118165515

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Fourier Analysis by Eric Stade Pdf

A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach, illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts Conveys information in a lucid, readable style, inspiring further reading and research on the subject Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real-world situations.

Author : Harry Dym,Henry Pratt McKean,Henry P. McKean
Publisher : Unknown
Page : 312 pages
File Size : 49,6 Mb
Release : 1972
Category : Mathematics
ISBN : MINN:31951000508928G

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Fourier Series and Integrals by Harry Dym,Henry Pratt McKean,Henry P. McKean Pdf

Author : Robert M. Gray,Joseph W. Goodman
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461523598

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Fourier Transforms by Robert M. Gray,Joseph W. Goodman Pdf

The Fourier transform is one of the most important mathematical tools in a wide variety of fields in science and engineering. In the abstract it can be viewed as the transformation of a signal in one domain (typically time or space) into another domain, the frequency domain. Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "primitive" components, provide shortcuts to the computation of complicated sums and integrals, and often reveal hidden structure in data. Fourier analysis lies at the base of many theories of science and plays a fundamental role in practical engineering design. The origins of Fourier analysis in science can be found in Ptolemy's decomposing celestial orbits into cycles and epicycles and Pythagorus' de composing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J. Fourier in his 1822 Theorie analytique de la Chaleur [16] (still available as a Dover reprint) was the first to claim that arbitrary periodic functions could be expanded in a trigonometric (later called a Fourier) series, a claim that was eventually shown to be incorrect, although not too far from the truth. It is an amusing historical sidelight that this work won a prize from the French Academy, in spite of serious concerns expressed by the judges (Laplace, Lagrange, and Legendre) re garding Fourier's lack of rigor.

Author : Robert Bell
Publisher : Elsevier
Page : 401 pages
File Size : 50,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323152105

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Introductory Fourier Transform Spectroscopy by Robert Bell Pdf

Introductory Fourier Transform Spectroscopy discusses the subject of Fourier transform spectroscopy from a level that requires knowledge of only introductory optics and mathematics. The subject is approached through optical principles, not through abstract mathematics. The book approaches the subject matter in two ways. The first is through simple optics and physical intuition, and the second is through Fourier analysis and the concepts of convolution and autocorrelation. This dual treatment bridges the gap between the introductory material in the book and the advanced material in the journals. The book also discusses information theory, Fourier analysis, and mathematical theorems to complete derivations or to give alternate views of an individual subject. The text presents the development of optical theory and equations to the extent required by the advanced student or researcher. The book is intended as a guide for students taking advanced research programs in spectroscopy. Material is included for the physicists, chemists, astronomers, and others who are interested in spectroscopy.

Author : P.P.G. Dyke
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105053

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An Introduction to Laplace Transforms and Fourier Series by P.P.G. Dyke Pdf

This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.