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Author: Sujaul Chowdhury Publisher: Springer Nature ISBN: 3031346645 Category : Science Languages : en Pages : 113
Book Description
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform. This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical data Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation
Author: Sujaul Chowdhury Publisher: Springer Nature ISBN: 3031346645 Category : Science Languages : en Pages : 113
Book Description
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform. This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical data Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation
Author: Gerlind Plonka Publisher: Springer Nature ISBN: 3031350057 Category : Mathematics Languages : en Pages : 676
Book Description
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Author: Claude Gasquet Publisher: Springer Science & Business Media ISBN: 1461215986 Category : Mathematics Languages : en Pages : 434
Book Description
The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.
Author: Luca Brandolini Publisher: Springer Science & Business Media ISBN: 0817681728 Category : Mathematics Languages : en Pages : 268
Book Description
Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians
Author: Russell L. Herman Publisher: CRC Press ISBN: 1498773729 Category : Mathematics Languages : en Pages : 541
Book Description
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: Brad G. Osgood Publisher: American Mathematical Soc. ISBN: 1470441918 Category : Fourier transformations Languages : en Pages : 689
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: Elena Prestini Publisher: Birkhäuser ISBN: 1489979891 Category : Mathematics Languages : en Pages : 377
Book Description
A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews
Author: Valery Serov Publisher: ISBN: Category : Languages : en Pages : 517
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: Sujaul Chowdhury
Author: Sujaul Chowdhury
Author: Gerlind Plonka
Author: Claude Gasquet
Author: Luca Brandolini
Author: Charles Van Loan
Author: Russell L. Herman
Author: Brad G. Osgood
Author: Jayakumar Ramanathan
Author: Elena Prestini
Author: Valery Serov