Parallelization of the Hypercomplex Discrete Fourier Transform

M. V. Aliev; A. M. Belov; A. V. Yershov; M. A. Chicheva

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Parallelization of the Hypercomplex Discrete Fourier Transform

机译：超复杂离散傅立叶变换的并行化

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The techniques for parallelization of the multidimensional hypercomplex discrete Fourier trans-form are considered. The main idea consists in using the properties of hypercomplex algebra involved in this transformation. The intrinsic parallelism of the multidimensional Cooley–Tukey scheme offers additional opportunities to enhance efficiency of the algorithm.

机译：考虑了用于多维超复杂离散傅立叶变换的并行化技术。主要思想在于使用涉及此变换的超复杂代数的性质。多维Cooley-Tukey方案的固有并行性为提高算法效率提供了更多机会。

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《Pattern recognition and image analysis: advances in mathematical theory and applications in the USSR》 |2005年第1期|共3页
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M. V. Aliev; A. M. Belov; A. V. Yershov; M. A. Chicheva;
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正文语种 eng
中图分类计算技术、计算机技术;
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1. Parallelization of the Hypercomplex Discrete Fourier Transform [J] . M. V. Aliev, A. M. Belov, A. V. Yershov, Pattern recognition and image analysis: advances in mathematical theory and applications in the USSR . 2005,第1期

机译：超复杂离散傅立叶变换的并行化
2. Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler's formula [J] . Sangwine S.J., Ell T.A. Applied mathematics and computation . 2012,第2期

机译：基于欧拉公式的矩阵指数形式的复数和超复数离散傅里叶变换
3. Fast algorithms for a multidimensional hypercomplex discrete Fourier transform with radix-3 decomposition [J] . M. V. Aliev, M. A. Chicheva Pattern recognition and image analysis: advances in mathematical theory and applications in the USSR . 2007,第1期

机译：具有基数3分解的多维超复杂离散傅立叶变换的快速算法
4. Parallelization Techniques for Multidimensional Hypercomplex Discrete Fourier Transform [C] . Marina Chicheva, Marat Aliev, Alexey Yershov International Conference on Parallel Computing Technologies(PaCT 2005); 20050905-09; Krasnoyarsk(RU) . 2005

机译：多维超复杂离散傅立叶变换的并行化技术
5. Parallel implementation and benchmarking in cluster architectures of one-dimensional discrete fourier transforms: A comparison using the row-column algorithm versus a novel formulation based on the bluestein/pseudocirculant algorithm. [D] . Velez Rodriguez, William. 2014

机译：一维离散傅里叶变换的群集体系结构中的并行实现和基准测试：使用行列算法与基于bluestein / pseudocirculant算法的新颖公式进行比较。
6. A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals [O] . Pablo Soto-Quiros 2015

机译：矢量值离散时间信号的具有离散傅立叶变换的块矩阵的并行框架
7. Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler's formula [O] . Sangwine, SJ, Ell, TA 2012

机译：基于欧拉公式的矩阵指数形式的复数和超复数离散傅里叶变换
8. Comparison of Arithmetic Requirements for the PFA (Prime Factor Algorithm), WFTA (Winograd Fourier Transform Algorithm), SWIFT, MFFT (Mixed Radix Fast Fourier Transform), FFT (Fast Fourier Transform) and DFT (Discrete Fourier Transform) Algorithms. [R] . Hicks, R. C. 1982

机译：pFa（素因子算法），WFTa（Winograd傅立叶变换算法），sWIFT，mFFT（混合基线快速傅里叶变换），FFT（快速傅立叶变换）和DFT（离散傅立叶变换）算法的算术要求的比较。

Parallelization of the Hypercomplex Discrete Fourier Transform

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