Download or read book Fast Polynomial Transforms written by Jens Keiner and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical orthogonal polynomials and the related associated functions are real classics in approximation theory. They share a rich history of research that has uncovered their many relationships to topics of fundamental importance. This text develops a new aspect of the so-called connection problem. This problem asks how a given expansion in a specific sequence of polynomials or functions may be converted into an equivalent one using a different sequence - often within reason, that is, within the same classical family. A new theory relates this problem to the class of semiseparable matrices. This implies efficient algorithms that have the capacity to cover the connection problem not only numerically efficient, but at the same time, numerically stable. The result has implications for numerical problems whose treatment involves these transformations. One such example, described in more detail, are generalizations of the fast Fourier transform to geometries like the two-sphere or the rotation group SO(3).
Download or read book Binary Polynomial Transforms and Non Linear Digital Filters written by S. Agaian and published by CRC Press. This book was released on 1995-04-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. The book also: introduces the Rademacher logical functions; considers fast algorithms for computing Rademacher and polynomial logical functions; focuses attention on general auto- and cross-correlation functions; and more.;The work is intended for applied mathematicians; electrical, electronics and other engineers; computer scientists; and upper-level undergraduate and graduate students in these disciplines.
Download or read book Integral and Discrete Transforms with Applications and Error Analysis written by Abdul Jerri and published by CRC Press. This book was released on 1992-06-11 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.
Download or read book Weighted Polynomial Approximation and Numerical Methods for Integral Equations written by Peter Junghanns and published by Springer Nature. This book was released on 2021-08-10 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
Download or read book Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.
Download or read book Principles of Electron Optics written by Peter W. Hawkes and published by Academic Press. This book was released on 2012-12-02 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes in the PRINCIPLES OF ELECTRON OPTICS Series constitute the first comprehensive treatment of electron optics in over forty years. While Volumes 1 and 2 are devoted to geometrical optics, Volume 3 is concerned with wave optics and effects due to wave length. Subjects covered include:Derivation of the laws of electron propagation from SchrUdinger's equationImage formation and the notion of resolutionThe interaction between specimens and electronsImage processingElectron holography and interferenceCoherence, brightness, and the spectral functionTogether, these works comprise a unique and informative treatment of the subject. Volume 3, like its predecessors, will provide readers with both a textbook and an invaluable reference source.
Download or read book The DFT written by William L. Briggs and published by SIAM. This book was released on 1995-01-01 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.
Download or read book Numerical Fourier Analysis written by Gerlind Plonka and published by Springer. This book was released on 2019-02-05 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Download or read book IBM Journal of Research and Development written by and published by . This book was released on 1978 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Atti Del Congresso Internazionale Dei Matematici written by and published by . This book was released on 1928 with total page 961 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Transforms written by J.M. Firth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree course in which transform techniques will have a significant application. In other disciplines the readership will be past the second year undergraduate stage. In either case, the text is also intended for earlier graduates whose degree courses did not include this type of material and who now find themselves, in a professional capacity, requiring a knowledge of discrete transform methods.
Download or read book Encyclopedia of Optical Engineering Las Pho pages 1025 2048 written by Ronald G. Driggers and published by CRC Press. This book was released on 2003 with total page 1130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compiled by 330 of the most widely respected names in the electro-optical sciences, the Encyclopedia is destined to serve as the premiere guide in the field with nearly 2000 figures, 560 photographs, 260 tables, and 3800 equations. From astronomy to x-ray optics, this reference contains more than 230 vivid entries examining the most intriguing technological advances and perspectives from distinguished professionals around the globe. The contributors have selected topics of utmost importance in areas including digital image enhancement, biological modeling, biomedical spectroscopy, and ocean optics, providing thorough coverage of recent applications in this continually expanding field.
Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
Download or read book Fast Fourier Transform and Convolution Algorithms written by H.J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm.
Download or read book Two dimensional Digital Signal Processing II written by Thomas S. Huang and published by Springer. This book was released on 1981 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Tech Briefs written by and published by . This book was released on 1985 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomial Transforms written by John E. Haggerty and published by . This book was released on 1994 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this thesis is to provide a tutorial of the discrete polynomial transforms and to show some applications of these transforms in the fields of signal processing and image processing.
