Fourier Techniques And Applications

Author : John F. Price
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461325253

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Fourier Techniques and Applications by John F. Price Pdf

The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua non of Fourier analysis and synthesis, has led to the routine use of the methods originating with Fourier in a great diversity of areas - astrophysics, computing, economics, electrical engineering, geophysics, information theory, medical engineering, optics, petroleum and mineral exploration, quan tum physics and spectroscopy, to name a few.

Author : Jianwei Zhu
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 46,8 Mb
Release : 2009-10-03
Category : Business & Economics
ISBN : 9783642018084

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Applications of Fourier Transform to Smile Modeling by Jianwei Zhu Pdf

This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.

Author : Sonali Bagchi,Sanjit K. Mitra
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461549253

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The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing by Sonali Bagchi,Sanjit K. Mitra Pdf

The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

Author : Ronald Newbold Bracewell
Publisher : Unknown
Page : 128 pages
File Size : 51,6 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 : E. Oran Brigham
Publisher : Pearson
Page : 474 pages
File Size : 49,9 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015047815561

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The Fast Fourier Transform and Its Applications by E. Oran Brigham Pdf

The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

Author : D. C. Champeney
Publisher : Unknown
Page : 280 pages
File Size : 52,6 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015060913202

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Fourier Transforms and Their Physical Applications by D. C. Champeney Pdf

Author : Anders Vretblad
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 49,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387217239

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Fourier Analysis and Its Applications by Anders Vretblad Pdf

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.

Author : Goran Nikolic,Dragan Cvetkovic,Milorad Cakic
Publisher : BoD – Books on Demand
Page : 264 pages
File Size : 51,8 Mb
Release : 2017-02-08
Category : Mathematics
ISBN : 9789535128939

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Fourier Transforms by Goran Nikolic,Dragan Cvetkovic,Milorad Cakic Pdf

The main purpose of this book is to provide a modern review about recent advances in Fourier transforms as the most powerful analytical tool for high-tech application in electrical, electronic, and computer engineering, as well as Fourier transform spectral techniques with a wide range of biological, biomedical, biotechnological, pharmaceutical, and nanotechnological applications. The confluence of Fourier transform methods with high tech opens new opportunities for detection and handling of atoms and molecules using nanodevices, with potential for a large variety of scientific and technological applications.

Author : Brad G. Osgood
Publisher : American Mathematical Soc.
Page : 689 pages
File Size : 50,8 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 : G. B. Folland
Publisher : American Mathematical Soc.
Page : 447 pages
File Size : 40,9 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 : J. F. James
Publisher : Cambridge University Press
Page : 161 pages
File Size : 43,8 Mb
Release : 2011-03-31
Category : Science
ISBN : 9781139493949

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A Student's Guide to Fourier Transforms by J. F. James Pdf

Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem, Babinet's principle and dipole arrays.

Author : Eric W. Hansen
Publisher : John Wiley & Sons
Page : 788 pages
File Size : 52,9 Mb
Release : 2014-09-22
Category : Mathematics
ISBN : 9781118479148

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Fourier Transforms by Eric W. Hansen Pdf

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, and 432 homework problems

Author : Radomir S. Stankovic,Claudio Moraga,Jaakko Astola
Publisher : John Wiley & Sons
Page : 230 pages
File Size : 55,7 Mb
Release : 2005-08-08
Category : Science
ISBN : 9780471745426

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Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design by Radomir S. Stankovic,Claudio Moraga,Jaakko Astola Pdf

Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.

Author : Matt Christopher
Publisher : Little, Brown Books for Young Readers
Page : 151 pages
File Size : 48,9 Mb
Release : 2009-12-19
Category : Juvenile Fiction
ISBN : 9780316096010

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The Kid Who Only Hit Homers by Matt Christopher Pdf

Over one million copies sold! A baseball fan learns the true meaning of success in this beloved classic that will capture the imaginations of a new generation of young readers. Sylvester loves baseball, but he isn't exactly what you'd call a good hitter. Even though he wants nothing more than to join his neighborhood team, the Hooper Redbirds, he's sure he'll never do anything more than warm the bench. But then he meets the mysterious Mr. Baruth who promises to make Sylvester one of the best players ever. Suddenly, Sylvester goes from the worst player on the team to the kid who can only hit homers. With his overnight success, however, come tough questions. Will Sylvester ever learn the true meaning of teamwork? And what will happen when he has to learn to stand on his own? This beloved story about baseball, confidence, perseverance, and being a good teammate is a modern classic and sure to win over a new generation of young sports fans.

Author : Robert M. Gray,Joseph W. Goodman
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 43,6 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.