论文标题
NFFT的连续窗口功能
Continuous window functions for NFFT
论文作者
论文摘要
在本文中，我们研究了无需快速傅立叶变换（NFFT）的错误行为。该近似算法主要基于紧凑型窗口功能的便利选择。在这里，我们考虑连续的kaiser- bessel，连续$ \ exp $ -type，$ \ sinh $ -type和连续的$ \ cosh $ -type窗口窗口功能具有相同的支持和相同的形状参数。我们提出了具有这样的窗口函数的NFFT的新型显式误差估计，并得出了针对NFFT参数的最佳选择的规则。窗口函数的误差常数主要取决于过采样因子和截断参数。对于所考虑的连续窗口函数，误差常数相对于截断参数具有指数衰减。
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here we consider the continuous Kaiser--Bessel, continuous $\exp$-type, $\sinh$-type, and continuous $\cosh$-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.
