Digital Fourier Analysis: Fundamentals
Digital Fourier Analysis: Fundamentals

Author: Ken'iti Kido

Publisher: Springer

Published: 2014-06-26

Total Pages: 210

ISBN-13: 1461492602

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This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader can test various cases and view the results until they fully understand the principle. Additionally, the applet source code in Visual Basic is provided online, allowing this book to be used for teaching simple programming techniques. A complete, intuitive guide to the basics, "Digital Fourier Analysis - Fundamentals" is an essential reference for undergraduate students in science and engineering.

Fourier Analysis in Several Complex Variables
Fourier Analysis in Several Complex Variables

Author: Leon Ehrenpreis

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 532

ISBN-13: 0486153037

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Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.

Fundamentals and Applications of Fourier Transform Mass Spectrometry
Fundamentals and Applications of Fourier Transform Mass Spectrometry

Author: Philippe Schmitt-Kopplin

Publisher: Elsevier

Published: 2019-08-11

Total Pages: 778

ISBN-13: 0128140143

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Fundamentals and Applications of Fourier Transform Mass Spectrometry is the first book to delve into the underlying principles on the topic and their linkage to industrial applications. Drs. Schmitt-Kopplin and Kanawati have brought together a team of leading experts in their respective fields to present this technique from many different perspectives, describing, at length, the pros and cons of FT-ICR and Orbitrap. Numerous examples help researchers decide which instruments to use for their particular scientific problem and which data analysis methods should be applied to get the most out of their data. Covers FT-ICR-MS and Orbitrap’s fundamentals, enhancing researcher knowledge Includes details on ion sources, data processing, chemical analysis and imaging Provides examples across the wide spectrum of applications, including omics, environmental, chemical, pharmaceutical and food analysis

Fundamentals of Fourier Transform Infrared Spectroscopy
Fundamentals of Fourier Transform Infrared Spectroscopy

Author: Brian C. Smith

Publisher: CRC Press

Published: 2011-03-09

Total Pages: 207

ISBN-13: 9781420069303

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Reflecting the myriad changes and advancements in the technologies involved in FTIR, particularly the development of diamond ATRs, this second edition of Fundamentals of Fourier Transform Infrared Spectroscopy has been extensively rewritten and expanded to include new topics and figures as well as updates of existing chapters. Designed for those ne

Fourier Analysis and Approximation of Functions
Fourier Analysis and Approximation of Functions

Author: Roald M. Trigub

Publisher: Springer Science & Business Media

Published: 2004-09-07

Total Pages: 610

ISBN-13: 9781402023415

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In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.

Fundamentals of Fourier Analysis
Fundamentals of Fourier Analysis

Author: Loukas Grafakos

Publisher: Springer

Published: 2024-05-28

Total Pages: 0

ISBN-13: 9783031564994

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This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts. Compared with the author’s other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood–Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters.

Classical Fourier Analysis
Classical Fourier Analysis

Author: Loukas Grafakos

Publisher: Springer Science & Business Media

Published: 2008-09-18

Total Pages: 494

ISBN-13: 0387094326

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The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online

Principles of Fourier Analysis
Principles of Fourier Analysis

Author: Kenneth B. Howell

Publisher: CRC Press

Published: 2016-12-12

Total Pages: 742

ISBN-13: 1498734138

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Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

Fourier Analysis on Number Fields
Fourier Analysis on Number Fields

Author: Dinakar Ramakrishnan

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 372

ISBN-13: 1475730853

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A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Introduction to Fourier Optics
Introduction to Fourier Optics

Author: Joseph W. Goodman

Publisher: McGraw-Hill Companies

Published: 1968

Total Pages: 312

ISBN-13:

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This renowned text applies the powerful mathematical methods of fourier analysis to the analysis and synthesis of optical systems. These ubiquitous mathematical tools provide unique insights into the capabilities and limitations of optical systems in both imaging and information processing and lead to many fascinating applications, including the field of holography.