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Author : Daniel Potts
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (596 download)
Download or read book Fast Algorithms for Discrete Polynomial Transforms written by Daniel Potts and published by . This book was released on 1996 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Potts
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (897 download)
Download or read book Fast Algorithm for Discrete Polynomial Transforms written by D. Potts and published by . This book was released on 1996 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H.J. Nussbaumer
Publisher : Springer Science & Business Media
ISBN 13 : 3662005514
Total Pages : 260 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Guoan Bi
Publisher : Springer Science & Business Media
ISBN 13 : 0817682201
Total Pages : 439 pages
Book Rating : 4.8/5 (176 download)
Download or read book Transforms and Fast Algorithms for Signal Analysis and Representations written by Guoan Bi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive presentation of recent results and developments on several widely used transforms and their fast algorithms. In many cases, new options are provided for improved or new fast algorithms, some of which are not well known in the digital signal processing community. The book is suitable as a textbook for senior undergraduate and graduate courses in digital signal processing. It may also serve as an excellent self-study reference for electrical engineers and applied mathematicians whose work is related to the fields of electronics, signal processing, image and speech processing, or digital design and communication.
Author : Jens Keiner
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832528504
Total Pages : 231 pages
Book Rating : 4.8/5 (325 download)
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).
Author : Douglas F. Elliott
Publisher : Elsevier
ISBN 13 : 0080918069
Total Pages : 511 pages
Book Rating : 4.0/5 (89 download)
Download or read book Fast Transforms Algorithms, Analyses, Applications written by Douglas F. Elliott and published by Elsevier. This book was released on 1983-03-09 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.
Author : International Business Machines Corporation. Research Division
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (123 download)
Download or read book Fast Algorithms for the Discrete Cosine Transform written by International Business Machines Corporation. Research Division and published by . This book was released on 1990 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard E. Blahut
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 466 pages
Book Rating : 4.3/5 (91 download)
Download or read book Fast Algorithms for Digital Signal Processing written by Richard E. Blahut and published by Addison Wesley Publishing Company. This book was released on 1985 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to abstract algebra. Fast algorithms for short convolutions. Fast algorithms for the discrete Fourier transform. Number theory and algebraic field theory. Computation in surrogate fields. Fast algorithms and multidimensional convolutions. Fast algorithms and multidimensional transforms. Architecture of filters and transforms. Fast algorithms based on doubling strategies. Fast algorithms for solving Toeplitz systems. Fast algorithms for Trellis and tree search. A collection of cyclic convolution algorithms. A collection of Winograd small FFT algorithms.
Author : Henri J Nussbaumer
Publisher :
ISBN 13 : 9783642818981
Total Pages : 292 pages
Book Rating : 4.8/5 (189 download)
Download or read book Fast Fourier Transform and Convolution Algorithms written by Henri J Nussbaumer and published by . This book was released on 1982-09-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. Sidney Burrus
Publisher : Lulu.com
ISBN 13 : 1300461640
Total Pages : 256 pages
Book Rating : 4.3/5 (4 download)
Download or read book Fast Fourier Transforms written by C. Sidney Burrus and published by Lulu.com. This book was released on 2012-11-30 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
Author : Richard Tolimieri
Publisher : Springer Science & Business Media
ISBN 13 : 1475727674
Total Pages : 273 pages
Book Rating : 4.4/5 (757 download)
Download or read book Algorithms for Discrete Fourier Transform and Convolution written by Richard Tolimieri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.
Author : Richard E. Blahut
Publisher : Cambridge University Press
ISBN 13 : 1139487957
Total Pages : 469 pages
Book Rating : 4.1/5 (394 download)
Download or read book Fast Algorithms for Signal Processing written by Richard E. Blahut and published by Cambridge University Press. This book was released on 2010-06-24 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-end applications of signal processing, and extend the reach of high-end applications.
Author : Artyom M. Grigoryan
Publisher : CRC Press
ISBN 13 : 1482276321
Total Pages : 540 pages
Book Rating : 4.4/5 (822 download)
Download or read book Multidimensional Discrete Unitary Transforms written by Artyom M. Grigoryan and published by CRC Press. This book was released on 2003-07-31 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm sele
Author : Vladimir Britanak
Publisher : Elsevier
ISBN 13 : 0080464645
Total Pages : 364 pages
Book Rating : 4.0/5 (84 download)
Download or read book Discrete Cosine and Sine Transforms written by Vladimir Britanak and published by Elsevier. This book was released on 2010-07-28 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Loéve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. - Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Loéve transform (KLT) - Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases - Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations - Comprehensive list of additional references reflecting recent/latest developments in the efficient implementations of DCTs and DSTs mainly one-, two-, three- and multi-dimensional fast DCT/DST algorithms including the recent active research topics for the time period from 1990 up to now
Author : Michael M. Resch
Publisher : Springer
ISBN 13 : 3319467352
Total Pages : 191 pages
Book Rating : 4.3/5 (194 download)
Download or read book Sustained Simulation Performance 2016 written by Michael M. Resch and published by Springer. This book was released on 2016-11-30 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the state of the art in high-performance computing and simulation on modern supercomputer architectures. It explores general trends in hardware and software development, and then focuses specifically on the future of high-performance systems and heterogeneous architectures. It also covers applications such as computational fluid dynamics, material science, medical applications and climate research and discusses innovative fields like coupled multi-physics or multi-scale simulations. The papers included were selected from the presentations given at the 20th Workshop on Sustained Simulation Performance at the HLRS, University of Stuttgart, Germany in December 2015, and the subsequent Workshop on Sustained Simulation Performance at Tohoku University in February 2016.
Author : Gerlind Plonka
Publisher : Springer
ISBN 13 : 3030043061
Total Pages : 618 pages
Book Rating : 4.0/5 (3 download)
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 618 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.
Author : Peter Junghanns
Publisher : Springer Nature
ISBN 13 : 303077497X
Total Pages : 662 pages
Book Rating : 4.0/5 (37 download)
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.
