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.
翻译:在本文中, 我们研究无间距快速 Fourier 变换( NFFFT) 的错误行为。 这种近似算法主要基于方便地选择一个紧凑支持的窗口功能。 这里我们考虑的是连续的 Kaiser- Bessel, 连续的$\ exple$- type, $\ sinh$- type, 和连续的 $\ cosh$- type 窗口函数, 其支持和形状参数相同。 我们为具有此窗口函数的 NFFT 提出了新的明确错误估计, 并为 NFFT 所涉参数的最佳选择提供了规则。 窗口函数的错误常数主要取决于过度采样系数和逃逸参数。 对于被考虑的连续窗口函数, 错误常数会与 truncation 参数发生指数衰减 。