【摘要】 算术傅立叶变换 (AFT)是一种非常重要的傅立叶分析技术 .AFT的乘法量少 (仅为O(N) ) ,算法结构简单 ,非常适合VLSI设计 ,具有广泛的应用 .但AFT的加法量很大 ,为O(N2 ) ,因此减少AFT的加法运算量是很重要的工作 .本文通过分析AFT的采样特点 ,给出了奇函数和偶函数的AFT的改进算法 .然后在此基础上给出了一般函数的AFT的改进算法 .改进算法比原算法的加法运算量降低了一半 ,因此计算速度快了一倍 .本文改进的偶函数和奇函数的AFT算法还分别可以用来计算离散余弦变换 (DCT)和离散正弦变换 (DST) .更多还原

【Abstract】 The arithmetic Fourier transform(AFT) is a very important Fourier analysis technique.AFT needs only O(N) multiplications and has simple computational structure,so it is very suitable for VLSI design.It arises in many applications.But AFT needs many additions ( O(N 2 )),so it is very important to reduce its number of additions.By analyzing sampling characteristics of AFT,this paper gives improved algorithms of AFT for odd and even functions,and based on these algorithms,gives an improved AFT algorithm for general functions.The improved algorithms reduce the numbers of additions of AFT algorithms to a half and increase the computational speeds to double.The improved AFT algorithms for even and odd functions can also be used for computing discrete cosine transform (DCT) and discrete sine transform (DST),respectively.更多还原