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/discontinuous Kaiser--Bessel, continuous $\exp$-type, and continuous $\cosh$-type window functions. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice from 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 window functions, the error constants have an exponential decay with respect to the truncation parameter.

翻译：在本文中, 我们研究无孔隙快速 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函数。 这里我们考虑的是连续/ 连续的 Kaiser- Bessel 、 连续的 $\ exple$- 类型和连续的 $\ cosh$- 类型的窗口函数。 我们为具有此窗口函数的 NFFT 提出了新的明确错误估计, 并从 NFFT 所涉参数中得出最佳选择规则。 窗口函数的错误常数主要取决于过度抽样系数和短跑参数。 对于所考虑的窗口函数来说, 错误常数与短跑参数相比会发生指数衰减 。