电子学报 ›› 2018, Vol. 46 ›› Issue (12): 2978-2984.DOI: 10.3969/j.issn.0372-2112.2018.12.022

• 学术论文 • 上一篇    下一篇

基于CORDIC的精确快速幅相解算方法

孙悦, 王传伟, 康龙飞, 叶超, 张信   

  1. 中国工程物理研究院流体物理研究所, 四川绵阳 621999
  • 收稿日期:2017-12-29 修回日期:2018-08-30 出版日期:2018-12-25
    • 通讯作者:
    • 王传伟
    • 作者简介:
    • 孙悦 女,1991年出生于安徽阜阳.硕士,研究实习员,主要研究方向为嵌入式测控技术、数据采集处理技术.E-mail:15151823877@163.com

High Precision & Speed Amplitude and Phase Solving Algorithm Based on CORDIC

SUN Yue, WANG Chuan-wei, KANG Long-fei, YE Chao, ZHANG Xin   

  1. Institute of Fluid Physics, CAEP, Mianyang, Sichuan 621999, China
  • Received:2017-12-29 Revised:2018-08-30 Online:2018-12-25 Published:2018-12-25

摘要: 针对传统CORDIC算法进行高精度幅度相位解算时迭代次数过多、时延较长、相位收敛较慢等局限,提出了一种基于最佳一致逼近方法的幅度与相位补偿算法,即利用传统CORDIC算法迭代一定次数后得到的向量信息,采用最佳一致逼近方法对幅度和相位分区间进行一阶多项式补偿,有效提高了计算精度.仿真及实测结果表明,对传统CORDIC算法4次迭代后的结果进行补偿,幅度相对误差可达到10-5量级、相位绝对误差可达到10-5度量级,最大输出时延不大于100ns.在使用部分专用乘法器的条件下,寄存器消耗降低了42.5%,查找表消耗降低了15.5%.采用该补偿算法,每多一次CORDIC迭代其相位精度可提高约一个数量级.因此,本文提出的补偿CORDIC算法在迭代次数、计算精度等方面优于传统CORDIC算法,适合于高精度计算的场合.

关键词: CORDIC, 相位补偿, 最佳一致逼近, FPGA

Abstract: An amplitude and phase compensation algorithm based on the best uniform approximation method is proposed.It overcomes the limitations of the traditional CORDIC when used in high-precision calculation of the amplitude and phase,such as too many iterations,long delay time,and slow phase convergence.By utilizing the vector information obtained from several iterations of traditional CORDIC,sectionalized first-order polynomial of best uniform approximation compensating for the amplitude and phase results is constructed,thus efficiently improving the computation accuracy.Simulation and test results show that,by using the proposed algorithm with 4 iterations of traditional CORDIC,the relative error of amplitude can reach 10-5 level,and the absolute error of phase can reach 10-5 degree level.At the same time,the maximum delay time is no more than 100 ns.And with the use of some dedicated multipliers,the registers and LUTs are reduced by 42.5% and 15.5% respectively.Moreover,the phase precision can be increased approximately one order with one more iteration.Hence,compared to conventional CORDIC algorithm,the proposed algorithm improves in iterations and computation precision,and is suitable for high-precision computation applications.

Key words: coordinate rotation digital computer(CORDIC), phase compensation, best uniform approximation, FPGA

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