Fast Fourier Transform Algorithms for Parallel Computers
Fast Fourier Transform Algorithms for Parallel Computers

Author: Daisuke Takahashi

Publisher: Springer Nature

Published: 2019-10-05

Total Pages: 120

ISBN-13: 9811399654

DOWNLOAD EBOOK

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.

Inside the FFT Black Box
Inside the FFT Black Box

Author: Eleanor Chu

Publisher: CRC Press

Published: 1999-11-11

Total Pages: 346

ISBN-13: 9781420049961

DOWNLOAD EBOOK

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.

Fast Fourier Transform - Algorithms and Applications
Fast Fourier Transform - Algorithms and Applications

Author: K.R. Rao

Publisher: Springer Science & Business Media

Published: 2011-02-21

Total Pages: 437

ISBN-13: 1402066295

DOWNLOAD EBOOK

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.

Parallel Computations
Parallel Computations

Author: Garry Rodrigue

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 416

ISBN-13: 1483276643

DOWNLOAD EBOOK

Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.

Mathematics of Multidimensional Fourier Transform Algorithms
Mathematics of Multidimensional Fourier Transform Algorithms

Author: Richard Tolimieri

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 241

ISBN-13: 1468402056

DOWNLOAD EBOOK

The main emphasis of this book is the development of algorithms for processing multi-dimensional digital signals, and particularly algorithms for multi-dimensional Fourier transforms, in a form that is convenient for writing highly efficient code on a variety of vector and parallel computers.

Algorithms for Discrete Fourier Transform and Convolution
Algorithms for Discrete Fourier Transform and Convolution

Author: Richard Tolimieri

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 363

ISBN-13: 1475738544

DOWNLOAD EBOOK

This easily accessible book provides a broad view of the latest developments in the field of fast digital signal processing algorithms. It bridges the gap between DSP algorithms and their implementation on a variety of serial and super computers.

Algorithms and Parallel Computing
Algorithms and Parallel Computing

Author: Fayez Gebali

Publisher: John Wiley & Sons

Published: 2011-03-29

Total Pages: 372

ISBN-13: 0470934638

DOWNLOAD EBOOK

There is a software gap between the hardware potential and the performance that can be attained using today's software parallel program development tools. The tools need manual intervention by the programmer to parallelize the code. Programming a parallel computer requires closely studying the target algorithm or application, more so than in the traditional sequential programming we have all learned. The programmer must be aware of the communication and data dependencies of the algorithm or application. This book provides the techniques to explore the possible ways to program a parallel computer for a given application.

High Performance Computing - HiPC 2007
High Performance Computing - HiPC 2007

Author: Srinivas Aluru

Publisher: Springer

Published: 2008-01-22

Total Pages: 687

ISBN-13: 3540772200

DOWNLOAD EBOOK

This book constitutes the refereed proceedings of the 14th International Conference on High-Performance Computing, HiPC 2007, held in Goa, India, in December 2007. The 53 revised full papers presented together with the abstracts of five keynote talks were carefully reviewed and selected from 253 submissions. The papers are organized in topical sections on a broad range of applications including I/O and FPGAs, and microarchitecture and multiprocessor architecture.

Applied Parallel Computing
Applied Parallel Computing

Author: Yuefan Deng

Publisher: World Scientific

Published: 2013

Total Pages: 218

ISBN-13: 9814307602

DOWNLOAD EBOOK

The book provides a practical guide to computational scientists and engineers to help advance their research by exploiting the superpower of supercomputers with many processors and complex networks. This book focuses on the design and analysis of basic parallel algorithms, the key components for composing larger packages for a wide range of applications.