基于查表插值法的余弦函数离散值算法
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摘要
现场可编程逻辑门阵列(FPGA)以其灵活性、可靠性和集成度高而在智能电网相关继电保护及自动化设备中得到广泛应用。由于计算精度与存储容量的突出矛盾,在存储资源有限的FPGA芯片中,常用的查找表实现余弦函数离散值的方法已没有优势。提出了一种查找表与拉格朗日插值相结合的算法,结合两者的优势,在保证精度的前提下优化了算法的输出时延和资源消耗,并在Xilinx公司的Artix7芯片上完成了算法的设计和硬件验证。
Field programmable gate array( FPGA) is widely used in smart grid related relay protection and automation equipment for its flexibility,reliability and integration. Due to the prominent contradiction between the calculation accuracy and the storage capacity,the commonly used table lookup method has no advantage in calculating the cosine function discrete value in the FPGA chip which has limited storage space. Therefore,an algorithm which combines the table lookup with the Lagrange interpolation is proposed. Combining the advantages of the two algorithms,the output delay and resource consumption of the algorithm are optimized on the premise of ensuring the accuracy. The design of the algorithm and hardware verification is completed on Xilinx's Artix7 chip.
Field programmable gate array( FPGA) is widely used in smart grid related relay protection and automation equipment for its flexibility,reliability and integration. Due to the prominent contradiction between the calculation accuracy and the storage capacity,the commonly used table lookup method has no advantage in calculating the cosine function discrete value in the FPGA chip which has limited storage space. Therefore,an algorithm which combines the table lookup with the Lagrange interpolation is proposed. Combining the advantages of the two algorithms,the output delay and resource consumption of the algorithm are optimized on the premise of ensuring the accuracy. The design of the algorithm and hardware verification is completed on Xilinx's Artix7 chip.
引文
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[2]黄聚永,袁慧梅,吴向阳,等.基于查找表和Newton插值算法的正余弦函数的FPGA实现[J].继电器,2007,35(16):33-36.
[3]盛利元,孔德元,简远鸣,等.正弦和余弦函数的一种混合式CORDIC算法实现[J].郑州大学学报(工学版),2008,29(2):84-86.
[4]姜萍,蒋立平,谭雪琴.正弦函数计算器的设计与实现[J].现代电子技术,2007,30(18):5-6,12.
[5]陈石平,李全,付佃华,等. 32位浮点正余弦函数的FPGA实现[J].微计算机信息,2008,24(2):176-178.
[6]周晓青,李合生,陶荣辉,等.基于CORDIC算法的双曲正余弦函数FPGA实现[J].信息与电子工程,2010,8(2):211-214.
[7]刘小明,洪一.基于查找表和Taylor展开的正余弦函数的实现[J].现代电子技术,2009,32(13):165-170.
[8]孙宇峰,陈国军,王大鸣,等.一种高精度正余弦函数的FPGA实现方法[J].信息工程大学学报,2007,8(3):368-370.