具有非等距空间与频率数据的非均匀快速傅里叶变换及快速 sinc 变换
Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms
AI总结：
本文研究基于 NFFT 的 NNFFT 算法，采用两个紧支撑连续窗函数并证明其误差随截断参数指数衰减，进而提出快速 sinc 变换并给出误差估计。
摘要：
本文研究具有非等距空间与频率数据的非均匀快速傅里叶变换（NNFFT）及其应用——快速 sinc 变换。NNFFT 的计算主要基于具有非等距空间节点和等距频率的非均匀快速傅里叶变换（NFFT）。NNFFT 采用两个紧支撑的连续窗函数。对于固定的非谐波带宽，证明了采用两个 sinh 型窗函数的 NNFFT 的误差关于所用窗函数的截断参数呈指数衰减。作为 NNFFT 的一个重要应用，我们给出了快速 sinc 变换。同时估计了快速 sinc 变换的误差。
英文摘要：
In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, it is shown that the error of the NNFFT with two sinh-type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
