Mathematics of Multidimensional Fourier Transform Algorithms

Richard Tolimieri

ISBN 10: 0387982604 / ISBN 13: 9780387982601

Editore: Springer Jul 1997, 1997

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Neuware - 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.

Codice articolo 9780387982601

Dati bibliografici

• Titolo: Mathematics of Multidimensional Fourier Transform Algorithms
• Editore: Springer Jul 1997
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0387982604
• ISBN 13: 9780387982601
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 17 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 17 millimetri di profondità
• Peso: 477 grammi

Descrizione articolo

Riassunto

Fourier transforms of large multidimensional data sets arise in many fields --ranging from seismology to medical imaging. The rapidly increasing power of computer chips, the increased availability of vector and array processors, and the increasing size of the data sets to be analyzed make it both possible and necessary to analyze the data more than one dimension at a time. The increased freedom provided by multidimensional processing, however, also places intesive demands on the communication aspects of the computation, making it difficult to write code that takes all the algorithmic possiblities into account and matches these to the target architecture. This book develops algorithms for multi-dimensional Fourier transforms that yield highly efficient code on a variety of vector and parallel computers. By emphasizing the unified basis for the many approaches to one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimizing implementations. This book will be of 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. Topics covered include: tensor products and the fast Fourier transform; finite Abelian groups and their Fourier transforms; Cooley- Tukey and Good-Thomas algorithms; lines and planes; reduced transform algorithms; field algorithms; implementation on Risc and parallel

Contenuti

Tensor Product.- Multi-dimensional Tensor Product and FFT.- Finite Abelian Groups.- Fourier Transform of Finite Abelian Groups.- Cooley-Tukey and Good-Thomas.- Lines.- Duality of Lines and Planes.- Reduced Transform Algorithms.- Field Algorithm.- Implementation on Risc Architectures.- Implementation on Parallel Architectures.