一种减少算术傅立叶变换采样点的方法

算术傅立叶变换是为了克服快速傅立叶变换的缺陷而在 1988年被提出的计算傅立叶系数的有效方法 .它的优点是不需要复数乘法 ,并且适合于作并行处理 ;但采样点过多是它的很大缺陷 .此文提出的一种方法 ,通过对采样点进行归类 ,重新划分 ,不但减少了采样点 ,而且精度状况良好 ,是对算术傅立叶变换的一次有效改进

A Design for reducing the number of the AFT sampling

In 1988, in order to overcome the disadvantage of the FFT, which required too much complex number multiplication, a new algorithm based on the number theoretic Mobius inversion formula was proposed by Tufts and Sadasiv. This new algorithm was named AFT (arithmetic Fourier transform), which is mainly additions with only a little real-multiplication and can be performed in parallel. However AFT also has its disadvantages, which requires too many samplings. In this paper, a design for reducing the number of samplings is developed. By comparing the values of the different algorithm and the numbers of the computing, the design is verified as an efficient algorithm.