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A new multidimensional crystallographic fast Fourier transform.

机译：一种新的多维晶体学快速傅里叶变换。

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摘要

The Fast Fourier Transform (FFT) describes a well known set of algorithms that allows a fast evaluation of the Discrete Fourier Transform (DFT). In FFTs, the original sequence is replaced by the sum of a shorter sequence of transforms [1]. This results in an optimal reduction in the number of computations. However, some applications present repeated sequences of data inside the input dataset. These are the so-called symmetries. By eliminating these repetitions storage and Input/Output operations might be reduced significantly. Compact symmetric FFTs [2] show the potential of this approach and appears as an attractive methodology for the implementation of a highly-efficient symmetric FFT.;An extension of Compact Symmetric FFTs [2] to multidimensional FFTs is presented in [3]. However, attempts to develop actual implementations from these high-level specifications have been, so far, unsuccessful. The main implementation problem is the recursiveness of the divide-and-conquer methodology proposed in [3].;This work aims at solving this difficulty by rewriting the algorithm in [3] as a non recursive method, implementable in terms of O( N3log N) passes through a fixed, non-redundant data set. Such a variant results from a slight but nontrivial modification of the mathematical framework proposed in [3]. This variant is restricted to symmetries that are representable by unimodular matrices, a condition satisfied by crystal symmetries.;The resulting algorithm is intended for use in the Shake-and-Bake method [4], for solving Crystal Structures from X-ray diffraction data.
机译：快速傅立叶变换（FFT）描述了一组众所周知的算法，可以快速评估离散傅立叶变换（DFT）。在FFT中，原始序列被较短的变换序列之和[1]代替。这导致计算数量的最佳减少。但是，某些应用程序会在输入数据集中显示重复的数据序列。这些就是所谓的对称性。通过消除这些重复，可以大大减少存储和输入/输出操作。紧凑对称FFT [2]展示了这种方法的潜力，并成为实现高效对称FFT的一种有吸引力的方法。[3]介绍了紧凑对称FFT [2]对多维FFT的扩展。但是，到目前为止，从这些高级规范开发实际实现的尝试均未成功。主要的实现问题是[3]中提出的分治法的递归性。这项工作旨在通过将[3]中的算法重写为一种非递归方法来解决此难题，该方法可以根据O（N3log N）通过固定的非冗余数据集。此类变体是由[3]中提出的对数学框架的轻微但不平凡的修改导致的。该变体仅限于由单模矩阵表示的对称性，这是晶体对称性所满足的条件。所得算法旨在用于“摇一拍”方法[4]，用于根据X射线衍射数据求解晶体结构。

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  • 作者

    David-Venegas, Ivan A.;

  • 作者单位

    University of Puerto Rico, Mayaguez (Puerto Rico).;

  • 授予单位 University of Puerto Rico, Mayaguez (Puerto Rico).;
  • 学科 Computer Science.
  • 学位 M.S.
  • 年度 2004
  • 页码 61 p.
  • 总页数 61
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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