Download or read book Digital Fourier Analysis Fundamentals written by Ken'iti Kido and published by Springer. This book was released on 2014-06-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fourier Analysis in Several Complex Variables written by Leon Ehrenpreis and published by Courier Corporation. This book was released on 2011-11-30 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fundamentals and Applications of Fourier Transform Mass Spectrometry written by Philippe Schmitt-Kopplin and published by Elsevier. This book was released on 2019-08-11 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Fundamentals of Fourier Transform Infrared Spectroscopy written by Brian C. Smith and published by CRC Press. This book was released on 2011-03-09 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Fundamentals of Fourier Analysis written by Loukas Grafakos and published by Springer. This book was released on 2024-05-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Fourier Analysis and Its Applications written by Anders Vretblad and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fourier Analysis on Number Fields written by Dinakar Ramakrishnan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fourier Methods in Imaging written by Roger L. Easton Jr. and published by John Wiley & Sons. This book was released on 2010-11-18 with total page 1005 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles and Applications of Fourier Optics written by Robert K. Tyson and published by Inst of Physics Pub Incorporated. This book was released on 2014-08-22 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier optics, being a staple of optical design and analysis for over 50 years, has produced many new applications in recent years. In this text, Bob Tyson presents the fundamentals of Fourier optics with sufficient detail to educate the reader, typically an advanced student or working scientist or engineer, to the level of applying the knowledge to a specific set of design or analysis problems. Well aware that many of the mathematical techniques used in the field can now be solved digitally, the book will point to those methods or applicable computer software available to the reader.

Download or read book Discrete and Continuous Fourier Transforms written by Eleanor Chu and published by CRC Press. This book was released on 2008-03-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform

Download or read book Fourier Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-02-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fundamentals of Music Processing written by Meinard Müller and published by Springer Nature. This book was released on 2021-04-09 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: The textbook provides both profound technological knowledge and a comprehensive treatment of essential topics in music processing and music information retrieval (MIR). Including numerous examples, figures, and exercises, this book is suited for students, lecturers, and researchers working in audio engineering, signal processing, computer science, digital humanities, and musicology. The book consists of eight chapters. The first two cover foundations of music representations and the Fourier transform—concepts used throughout the book. Each of the subsequent chapters starts with a general description of a concrete music processing task and then discusses—in a mathematically rigorous way—essential techniques and algorithms applicable to a wide range of analysis, classification, and retrieval problems. By mixing theory and practice, the book’s goal is to offer detailed technological insights and a deep understanding of music processing applications. As a substantial extension, the textbook’s second edition introduces the FMP (fundamentals of music processing) notebooks, which provide additional audio-visual material and Python code examples that implement all computational approaches step by step. Using Jupyter notebooks and open-source web applications, the FMP notebooks yield an interactive framework that allows students to experiment with their music examples, explore the effect of parameter settings, and understand the computed results by suitable visualizations and sonifications. The FMP notebooks are available from the author’s institutional web page at the International Audio Laboratories Erlangen.

Download or read book From Fourier Analysis to Wavelets written by Jonas Gomes and published by Springer. This book was released on 2015-09-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

Download or read book Introduction to Fourier Optics written by Joseph W. Goodman and published by McGraw-Hill Companies. This book was released on 1968 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.