Mathematics of Multidimensional Fourier Transform Algorithms

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Springer Science & Business Media, Dec 6, 2012 - Technology & Engineering - 233 pages
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The Fourier transform of large multidimensional data sets is an essen tial computation in many scientific and engineering fields, including seismology, X-ray crystallography, radar, sonar and medical imaging. Such fields require multidimensional arrays for complete and faithful modelling. Classically, a set of data is processed one dimension at a time, permitting control over the size of the computation and calling on well-established I-dimensional programs. The rapidly increasing availability of powerful computing chips, vector processors, multinode boards and parallel machines has provided new tools for carrying out multidimensional computations. Multidimensional processing offers a wider range of possible implementations as compared to I-dimensional the greater flexibility of movement in the data in processing, due to dexing set. This increased freedom, along with the massive size data sets typically found in multidimensional applications, places intensive demands on the communication aspects of the computation. The writ ing of code that takes into account all the algorithmic possibilities and matches these possibilities to the communication capabilities of the tar get architecture is an extremely time-consuming task. A major goal of this text is to provide a sufficiently abstra
 

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Contents

Multidimensional Tensor Product and FFT
29
Finite Abelian Groups
45
Bibliography
61
Bibliography
75
Lines 89
88
Bibliography
112
Bibliography
131
Reduced Transform Algorithms 135
134
Field Algorithm
159
Implementation on RISC Architectures 179
178
Implementation on Parallel Architectures
203
Index
230
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