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Author: Mark S Nixon
Publisher: World Scientific
ISBN: 1800611129
Category : Mathematics
Languages : en
Pages : 305
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Book Description
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: Mark S Nixon
Publisher: World Scientific
ISBN: 1800611129
Category : Mathematics
Languages : en
Pages : 305
Get Book Here
Book Description
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: Brad G. Osgood
Publisher: American Mathematical Soc.
ISBN: 1470441918
Category : Fourier transformations
Languages : en
Pages : 689
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Book Description
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: Robert J Marks II
Publisher: Oxford University Press
ISBN: 0198044305
Category : Technology & Engineering
Languages : en
Pages : 799
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Book Description
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.
Author: Ronald Newbold Bracewell
Publisher: McGraw-Hill Companies
ISBN:
Category : Mathematics
Languages : en
Pages : 510
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Book Description
Groundwork. Convolution. Notation for some useful functions. The impulse symbol. The basic theorems. Doing transforms. The two domains. Electrical waveforms, spectra, and filters. Sampling and series. The laplace transform. Relatives of the fourier transform. Antennas. Television image formation. Convolution in statistics. Noise waveforms. Heat conduction and diffusion. The discrete fourier transform. The discrete hartley transform. The fast hartley transform. Pictorial dictionary of fourier transforms. Supplementary problems. Tables.
Author: Schucker Thomas
Publisher: World Scientific Publishing Company
ISBN: 9813104406
Category : Science
Languages : en
Pages : 180
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Book Description
In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.
Author: Valery Serov
Publisher:
ISBN:
Category :
Languages : en
Pages : 517
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Book Description
Fourier Series, Fourier Transform and Their Applications to Mathematical Physics : Applied Mathematical Sciences by Valery SerovThe modern theory of analysis and differential equations in general certainly in-cludes the Fourier transform, Fourier series, integral operators, spectral theory ofdifferential operators, harmonic analysis and much more. This book combines allthese subjects based on a unified approach that uses modern view on all thesethemes. The book consists of four parts: Fourier series and the discrete Fouriertransform, Fourier transform and distributions, Operator theory and integral equa-tions and Introduction to partial differential equations and it outgrew from the half-semester courses of the same name given by the author at University of Oulu, Fin-land during 2005-2015.Each part forms a self-contained text (although they are linked by a commonapproach) and can be read independently. The book is designed to be a modernintroduction to qualitative methods used in harmonic analysis and partial differentialequations (PDEs). It can be noted that a survey of the state of the art for all parts ofthis book can be found in a very recent and fundamental work of B. Simon [35].This book contains about 250 exercises that are an integral part of the text. Eachpart contains its own collection of exercises with own numeration. They are not onlyan integral part of the book, but also indispensable for the understanding of all partswhose collection is the content of this book. It can be expected that a careful readerwill complete all these exercises.This book is intended for graduate level students majoring in pure and appliedmathematics but even an advanced researcher can find here very useful informationwhich previously could only be detected in scientific articles or monographs.Each part of the book begins with its own introduction which contains the facts(mostly) from functional analysis used thereinafter. Some of them are proved whilethe others are not.The first part, Fourier series and the discrete Fourier transform, is devoted tothe classical one-dimensional trigonometric Fourier series with some applicationsto PDEs and signal processing. This part provides a self-contained treatment of allwell known results (but not only) at the beginning graduate level. Compared withsome known texts (see [12, 18, 29, 35, 38, 44, 45]) this part uses many functionspaces such as Sobolev, Besov, Nikol'skii and Holder spaces. All these spaces are introduced by special manner via the Fourier coefficients and they are used in theproofs of main results. Same definition of Sobolev spaces can be found in [35]. Theadvantage of such approach is that we are able to prove quite easily the precise em-beddings for these spaces that are the same as in classical function theory (see [1, 3,26, 42]). In the frame of this part some very delicate properties of the trigonometricFourier series (Chapter 10) are considered using quite elementary proofs (see also[46]). The unified approach allows us also to consider naturally the discrete Fouriertransform and establish its deep connections with the continuous Fourier transform.As a consequence we prove the famous Whittaker-Shannon-Boas theorem about thereconstruction of band-limited signal via the trigonometric Fourier series (see Chap-ter 13). Many applications of the trigonometric Fourier series to the one-dimensionalheat, wave and Laplace equation are presented in Chapter 14. It is accompanied by alarge number of very useful exercises and examples with applications in PDEs (seealso [10, 17]).The second part, Fourier transform and distributions, probably takes a central rolein this book and it is concerned with distribution theory of L. Schwartz and its ap-plications to the Schrodinger and magnetic Schr ̈ odinger operators (see Chapter ̈ 32).
Author: G. B. Folland
Publisher: Thomson Brooks/Cole
ISBN:
Category : Mathematics
Languages : en
Pages : 460
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Book Description
Presenting Fourier methods as a set of tools for solving applied problems, this introduction also gives the student advanced theoretical treatments that are a part of pure mathematics.
Author: P.L. Butzer
Publisher: Birkhäuser
ISBN: 3034874480
Category : Mathematics
Languages : en
Pages : 565
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Book Description
At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.
Author: D. Sundararajan
Publisher: World Scientific
ISBN: 9789812810298
Category : Mathematics
Languages : en
Pages : 400
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Book Description
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."
Author: Mark Cartwright
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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Book Description
