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Fourier Transforms

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Fourier Transforms

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Author : Eric W. Hansen
language : en
Publisher: John Wiley & Sons
Release Date : 2014-10-01

Fourier Transforms written by Eric W. Hansen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-01 with Mathematics categories.

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

Fourier Transforms

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Author : Robert M. Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Fourier Transforms written by Robert M. Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

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.

Transforms And Applications Handbook

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Author : Alexander D. Poularikas
language : en
Publisher: CRC Press
Release Date : 2018-09-03

Transforms And Applications Handbook written by Alexander D. Poularikas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.

Fourier Transforms In Spectroscopy

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Author : Jyrki Kauppinen
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-10

Fourier Transforms In Spectroscopy written by Jyrki Kauppinen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Science categories.

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.

Lectures On The Fourier Transform And Its Applications

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Author : Brad G. Osgood
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-18

Lectures On The Fourier Transform And Its Applications written by Brad G. Osgood and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-18 with Mathematics categories.

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.

Fourier Transforms

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Author : Eric W. Hansen
language : en
Publisher: John Wiley & Sons
Release Date : 2014-09-22

Discrete And Continuous Fourier Transforms

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Author : Eleanor Chu
language : en
Publisher: CRC Press
Release Date : 2008-03-19

Discrete And Continuous Fourier Transforms written by Eleanor Chu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-19 with Mathematics categories.

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

Quaternion And Clifford Fourier Transforms

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Author : Eckhard Hitzer
language : en
Publisher: CRC Press
Release Date : 2021-09-21

Quaternion And Clifford Fourier Transforms written by Eckhard Hitzer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Mathematics categories.

Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth. The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists, and engineers (signal and color image processing, electrical engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.). Features Intuitive real geometric approach to higher-dimensional Fourier transformations A comprehensive reference, suitable for graduate students and researchers Includes detailed definitions, properties, and many full step-by-step proofs Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information

Fourier Series And Transforms

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Author : R.D Harding
language : en
Publisher: CRC Press
Release Date : 1985-01-01

Fourier Series And Transforms written by R.D Harding and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.

Fourier Series and Transforms, a software and text package, complements standard textbooks and lecture courses by providing a solid overview of the topic. The software provides more extensive illustrations than a conventional text with interactive programs that have been designed to be open to modifications. The emphasis on qualitative aspects and flexibility with regard to program modification make the package useful to a wide range of students. The book assumes some mathematical expertise as well as basic computer language knowledge.

Convergence And Summability Of Fourier Transforms And Hardy Spaces

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Author : Ferenc Weisz
language : en
Publisher: Birkhäuser
Release Date : 2017-12-27

Convergence And Summability Of Fourier Transforms And Hardy Spaces written by Ferenc Weisz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-27 with Mathematics categories.

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

Fourier Transforms

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