Ramanujan和,广义Mius变换与算术Fourier变换

Ramanujan s sum,generalized M■ius transform and arithmetic Fourier transform

在广义Mobius变换与Ramanujan和的基础上,采用算术Fourier变换(AFT)计算离散Fourier变换(DFT),直接提取了DFT的Cosine系数.将数论方法应用在计算数学领域.

Based on generalized Mbius transform and Ramanujan s sum,arithmetic Fourier transform(AFT) is used to compute discrete Fourier transform(DFT) in this paper.This new method can extract directly the Cosine coefficients of DFT.This is a new direction that number theory methods are applied into computation mathematics.