一种可编程实现的Ramanujan和计算方法(英文)  

A Programmable Approach to Evaluate Ramanujan Sums

作　　者：郭旭静[1] 周丽娜[1] 尚佳栋[1] 王祖林[1] 

机构地区：[1]北京航空航天大学电子信息工程学院

出　　处：《新型工业化》2013年第2期61-70,共10页The Journal of New Industrialization

基　　金：National Natural Science Foundation of China(No.61071070);the Specialized Research Fund for the Doctoral Program of High Education of China(No.20091102120010)

摘　　要：广泛应用在数学领域的Ramanujan和正在信号处理领域和通信领域获得越来越多的关注。使用传统的数学公式进行Ramanujan和的计算方式因涉及因数分解而不适用于硬件实时生成。本文仅使用余弦函数和四则基本运算,使Ramanujan和的计算方法可以在FPGA程序中实现。文中给出了简化的证明,并对余弦函数值的采样点数和量化位数对Ramanujan和的影响进行了探讨。Ramanujan sums, which have been widely researched in mathematics, recently began to attract more attentions in signal processing and communications. The traditional methods to get the values of Ramanujan sums follow the definition and formulas in number theory, both of which need factorization information. As it is complex and the amount of time needed is unpredictable in hardware programming, a programmable approach base on the primitive roots of unity is proposed in this paper. Only simple arithmetic computing and cosine function is involved. Considering that each value of Ramanujan sums is an integer, the number of sample points required is no more than the period of Ramanujan sums, and quantification bits required are no more than 16 bits, as the simulation results demonstrated.

关 键 词：Ramanujan和 可编程实现 单位本原根 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术] TN9[电子电信—信息与通信工程]