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Author : Charles Van Loan
Publisher : SIAM
Page : 285 pages
File Size : 44,8 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 9780898712858
The author captures the interplay between mathematics and the design of effective numerical algorithms.
Author : Eleanor Chu,Alan George
Publisher : CRC Press
Page : 346 pages
File Size : 52,6 Mb
Release : 1999-11-11
Category : Mathematics
ISBN : 1420049968
Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.
Author : C. Sidney Burrus
Publisher : Lulu.com
Page : 256 pages
File Size : 40,5 Mb
Release : 2024-05-22
Category : Computer science
ISBN : 9781300461647
Author : Daisuke Takahashi
Publisher : Springer Nature
Page : 120 pages
File Size : 51,7 Mb
Release : 2019-10-05
Category : Computers
ISBN : 9789811399657
Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity analysis, this book offers a valuable reference guide for graduate students, engineers, and scientists in the field who wish to apply FFT to large-scale problems. Parallel computation is becoming indispensable in solving the large-scale problems increasingly arising in a wide range of applications. The performance of parallel supercomputers is steadily improving, and it is expected that a massively parallel system with hundreds of thousands of compute nodes equipped with multi-core processors and accelerators will be available in the near future. Accordingly, the book also provides up-to-date computational techniques relevant to the FFT in state-of-the-art parallel computers. Following the introductory chapter, Chapter 2 introduces readers to the DFT and the basic idea of the FFT. Chapter 3 explains mixed-radix FFT algorithms, while Chapter 4 describes split-radix FFT algorithms. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms, and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers. In closing, Chapter 8 describes parallel FFT algorithms for distributed-memory parallel computers.
Author : Keith Jones
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 53,8 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9789048139170
Most real-world spectrum analysis problems involve the computation of the real-data discrete Fourier transform (DFT), a unitary transform that maps elements N of the linear space of real-valued N-tuples, R , to elements of its complex-valued N counterpart, C , and when carried out in hardware it is conventionally achieved via a real-from-complex strategy using a complex-data version of the fast Fourier transform (FFT), the generic name given to the class of fast algorithms used for the ef?cient computation of the DFT. Such algorithms are typically derived by explo- ing the property of symmetry, whether it exists just in the transform kernel or, in certain circumstances, in the input data and/or output data as well. In order to make effective use of a complex-data FFT, however, via the chosen real-from-complex N strategy, the input data to the DFT must ?rst be converted from elements of R to N elements of C . The reason for choosing the computational domain of real-data problems such N N as this to be C , rather than R , is due in part to the fact that computing equ- ment manufacturers have invested so heavily in producing digital signal processing (DSP) devices built around the design of the complex-data fast multiplier and accumulator (MAC), an arithmetic unit ideally suited to the implementation of the complex-data radix-2 butter?y, the computational unit used by the familiar class of recursive radix-2 FFT algorithms.
Author : William L. Briggs,Van Emden Henson
Publisher : SIAM
Page : 446 pages
File Size : 44,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713428
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.
Author : Rob H. Bisseling
Publisher : Oxford University Press, USA
Page : 410 pages
File Size : 42,6 Mb
Release : 2020-09-30
Category : Computers
ISBN : 9780198788348
Parallel Scientific Computation presents a methodology for designing parallel algorithms and writing parallel computer programs for modern computer architectures with multiple processors.
Author : James S. Walker
Publisher : CRC Press
Page : 242 pages
File Size : 51,5 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351448871
This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
Author : Richard Tolimieri,Myoung An,Chao Lu
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461219484
Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.
Author : Ronald Perrott,Barbara Chapman,Jaspal Subhlok,Rodrigo Fernandes de Mello,Laurence T. Yang
Publisher : Springer
Page : 823 pages
File Size : 53,9 Mb
Release : 2007-09-08
Category : Computers
ISBN : 9783540754442
This book constitutes the refereed proceedings of the Third International Conference on High Performance Computing and Communications, HPCC 2007. The 75 revised full papers address all current issues of parallel and distributed systems and high performance computing and communication, including networking protocols, embedded systems, wireless, mobile and pervasive computing, Web services and internet computing, and programming interfaces for parallel systems.
Author : Peter Sloot
Publisher : Springer Science & Business Media
Page : 1188 pages
File Size : 50,7 Mb
Release : 2003-05-22
Category : Computers
ISBN : 9783540401971
The four-volume set LNCS 2657, LNCS 2658, LNCS 2659, and LNCS 2660 constitutes the refereed proceedings of the Third International Conference on Computational Science, ICCS 2003, held concurrently in Melbourne, Australia and in St. Petersburg, Russia in June 2003. The four volumes present more than 460 reviewed contributed and invited papers and span the whole range of computational science, from foundational issues in computer science and algorithmic mathematics to advanced applications in virtually all application fields making use of computational techniques. These proceedings give a unique account of recent results in the field.
Author : K.R. Rao,Do Nyeon Kim,Jae Jeong Hwang
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 44,6 Mb
Release : 2011-02-21
Category : Mathematics
ISBN : 9781402066290
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
Author : Vassil Alexandrov
Publisher : Springer Science & Business Media
Page : 1294 pages
File Size : 48,6 Mb
Release : 2001-05-24
Category : Computers
ISBN : 9783540422327
LNCS volumes 2073 and 2074 contain the proceedings of the International Conference on Computational Science, ICCS 2001, held in San Francisco, California, May 27 -31, 2001. The two volumes consist of more than 230 contributed and invited papers that reflect the aims of the conference to bring together researchers and scientists from mathematics and computer science as basic computing disciplines, researchers from various application areas who are pioneering advanced application of computational methods to sciences such as physics, chemistry, life sciences, and engineering, arts and humanitarian fields, along with software developers and vendors, to discuss problems and solutions in the area, to identify new issues, and to shape future directions for research, as well as to help industrial users apply various advanced computational techniques.
Author : Anonim
Publisher : Springer Science & Business Media
Page : 1070 pages
File Size : 54,9 Mb
Release : 2008
Category : Computational complexity
ISBN : 9783540693833
Author : R L May,A K Easton
Publisher : World Scientific
Page : 896 pages
File Size : 41,9 Mb
Release : 1996-08-30
Category : Electronic
ISBN : 9789814547284
This proceedings contains seven invited papers and 100 contributed papers. The topics covered range from studies of theoretical aspects of computational methods through to simulations of large-scale industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will find much of interest in this volume. Contents:Some Case Studies in Industrial Mathematics (F R de Hoog & N I Robinson)An Inverse Problem in Environmental Protection (J M Barry)Computational Techniques for Structural Assessment of Bridges (T Chalko et al)A Computationally Fast Method to Model Thin Strip Rolling (A E Dixon & W Y D Yuen)Comparison of Boundary Element Representations for Potential Fields (M J Drumm & T G Phemister)On the Computation of Stability Limits for Fusion Experiments (P R Garabedian & H J Gardner)The Finite Lattice Method of Series Expansions (I Jensen et al)A Comparison of Finite Difference and Lagrangian-Stochastic Methods for Oil Slick Tracking (G D Lewis et al)Numerical Modelling Techniques for Simulating the Microwave Heating of Polymer Materials Inside a Ridge Waveguide (F Liu & I Turner)Transport of Mucus (A H Pincombe & G D Tansley)Iterative Schemes for Series Solutions to Laplacian Free Boundary Problems (W W Read et al)A Systematic Approach to Calibrating Hydrodynamic Numerical Models (M D Teubner et al)Computation of Turbulent Combustion Flows with a Finite-Element Method (Z Zhu & N Stokes)and other papers Readership: Scientists in numerical and computational methods, applied mathematics, computational physics, supercomputing/parallel processing and fluid mechanics. keywords: