摘要
本文研究平行六边形区域上的非均匀节点离散傅立叶变换的快速算法及其实现.首先在晶格(Lattice)的框架下建立了平行六边形区域上的非均匀节点离散傅立叶变换(NDFTH).在此基础上设计了平行六边形区域上的非均匀节点快速傅立叶变换(NFFTH)算法.其核心思想是以局部性态良好的窗口函数为基底,以平行六边形区域上均匀节点快速傅立叶变换(FFTH)为时空域和频域转换工具,通过在时空域和频域上截取其展开级数的少量几项来快速近似计算,最终降低其计算复杂度.数值计算结果表明,本文算法是合理、稳定、高效的.
In this paper, the nonequispaced discrete Fourier transform on a parallel hexagon （NDFTH） is established in the frame of Lattice, then a fast algorithm named NFFTH is devised and its implementation is studied in detail for evaluating NDFTH. The main idea is to use standard FFTHs and a window function which is well localized in the spatial domain and in the fre- quency domain. Numerical results demonstrate the NFFTH is accurate, stable, and highly efficient.
出处
《数值计算与计算机应用》
CSCD
北大核心
2009年第1期58-69,共12页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(No.10601056
No.60173021
No.10431050)资助.
关键词
非均匀节点快速傅立叶变换
平行六边形
快速算法及实现
数值实验
fast algorithm
nonequispaced discrete Fourier transform
parallel hexagon
implementation
numerical results
