High-throughput, reduced hardware systolic solution to prime factor discrete Fourier transform algorithm

Jones K.J.

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High-throughput, reduced hardware systolic solution to prime factor discrete Fourier transform algorithm

机译：高通量，简化的硬件收缩解决方案，用于素因子离散傅里叶变换算法

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The paper discusses a novel systolic implementation of the row-column method for solving the prime factor discrete Fourier transform (DFT) algorithm. It deals, in particular, with the two-factor decomposition where the transform length N is an odd multiple of 4. By processing the four-point row-DFTs coefficient by coefficient, rather than DFT by DFT, as is conventionally done, it is seen how pipelined implementations of the row-DFT and column-DFT processes can be performed simultaneously, without need for matrix transposition of the row-DFT output, resulting in a fully pipelined concurrent solution. Hardware efficiency and simplicity is achieved via the computationally attractive Cordic (co-ordinate digital computer) arithmetic, with O(N) throughput requiring (asymptotically) one-quarter of the hardware requirements of established N-processor solutions.

机译：本文讨论了解决素数离散傅里叶变换（DFT）算法的行-列方法的一种新的收缩实现。它特别处理两因子分解，其中变换长度N是4的奇数倍。通过按系数处理四点行DFT而不是按常规方法进行DFT处理，它是看到如何在无需行DFT输出的矩阵转置的情况下同时执行行DFT和列DFT过程的流水线实现，从而获得了完全流水线的并发解决方案。硬件效率和简单性是通过具有计算吸引力的Cordic（坐标数字计算机）算法实现的，O（N）吞吐量（渐近地）要求已建立的N处理器解决方案的硬件需求的四分之一。

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《IEE Proceedings. Part E》 |1990年第3期|P.191-196|共6页
作者
Jones K.J.;
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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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专利

1. Efficient systolic solution for a new prime factor discrete Hartley transform algorithm [J] . Meher P.K., Satapathy J.K. IEE Proceedings. Part G, Circuits, Devices and Systems . 1993,第2期

机译：一种新的素因数离散Hartley变换算法的有效心跳解决方案
2. Bidiagonal factorization of Fourier matrices and systolic algorithms for computing discrete Fourier transforms [J] . Gader P.D. IEEE Transactions on Acoustics, Speech, and Signal Processing . 1989,第8期

机译：离散傅里叶变换的傅里叶矩阵的对角分解和脉动算法
3. Fast, prime factor, discrete Fourier transform algorithms over GF(2(m)) for 8 <=, m <= 10 [J] . Truong TK, Chen PD, Wang LJ, Information Sciences: An International Journal . 2006,第1期

机译：对于8 <=，m <= 10的GF（2（m））上的快速素因子离散傅里叶变换算法
4. Reduced Hardware Systolic Solutions to the Discrete Hartley Transform [C] . Wang, L., Hartimo, . 2001

机译：离散Hartley变换的简化的硬件收缩解决方案
5. Discrete cosine transform-only and discrete sine transform-only windowed update algorithms for shifting data with hardware implementation. [D] . Karwal, Vikram. 2009

机译：仅离散余弦变换和仅离散正弦变换的窗口更新算法，用于通过硬件实现来移位数据。
6. Photonic scheme of discrete quantum Fourier transform for quantum algorithms via quantum dots [O] . Jino Heo, Kitak Won, Hyung-Jin Yang, -1

机译：量子点的量子算法的离散量子傅里叶变换的光子方案
7. An Efficient Prime-Factor Algorithm for the Discrete Cosine Transform and Its Hardware Implementations [O] . Peizong Lee, Fang-Yu Huang 1993

机译：离散余弦变换的有效素因子算法及其硬件实现
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。

High-throughput, reduced hardware systolic solution to prime factor discrete Fourier transform algorithm

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