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 Fourier Transforms written by Ian Naismith Sneddon and published by Courier Corporation. This book was released on 1995-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on applications of Fourier transforms and related topics rather than theory, this accessible treatment is suitable for students and researchers interested in boundary value problems of physics and engineering. 1951 edition.
Download or read book Fourier Transforms written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tables of Fourier Transforms and Fourier Transforms of Distributions written by Fritz Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.
Download or read book A First Course in Wavelets with Fourier Analysis written by Albert Boggess and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Download or read book The Analytical Theory of Heat written by Jean-Baptiste-Joseph Fourier and published by . This book was released on 1878 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Transforms written by Eric W. Hansen and published by John Wiley & Sons. This book was released on 2014-10-01 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Data Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author captures the interplay between mathematics and the design of effective numerical algorithms.
Download or read book A Student s Guide to Fourier Transforms written by John Francis James and published by Cambridge University Press. This book was released on 2002-09-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular 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-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.
Download or read book Fourier and Laplace Transforms written by and published by Cambridge University Press. This book was released on 2003-08-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.
Download or read book Introductory Fourier Transform Spectroscopy written by Robert Bell and published by Elsevier. This book was released on 2012-12-02 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Fourier Transform Spectroscopy discusses the subject of Fourier transform spectroscopy from a level that requires knowledge of only introductory optics and mathematics. The subject is approached through optical principles, not through abstract mathematics. The book approaches the subject matter in two ways. The first is through simple optics and physical intuition, and the second is through Fourier analysis and the concepts of convolution and autocorrelation. This dual treatment bridges the gap between the introductory material in the book and the advanced material in the journals. The book also discusses information theory, Fourier analysis, and mathematical theorems to complete derivations or to give alternate views of an individual subject. The text presents the development of optical theory and equations to the extent required by the advanced student or researcher. The book is intended as a guide for students taking advanced research programs in spectroscopy. Material is included for the physicists, chemists, astronomers, and others who are interested in spectroscopy.
Download or read book Decay of the Fourier Transform written by Alex Iosevich and published by Springer. This book was released on 2014-10-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Download or read book Fourier Series Fourier Transform and Their Applications to Mathematical Physics written by Valery Serov and published by Springer. This book was released on 2018-08-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.
Download or read book The Fast Fourier Transform and Its Applications written by E. Oran Brigham and published by Pearson. This book was released on 1988 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fourier Transforms in Spectroscopy written by Jyrki Kauppinen and published by John Wiley & Sons. This book was released on 2011-02-10 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical point of view. Some aspects, linear prediction for example, are explained here thoroughly for the first time.
