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.

在本文中，我们研究了非等距快速傅立叶变换 (NFFT) 的误差行为。这种近似算法主要基于紧凑支持的窗函数的方便选择。在这里，我们考虑具有相同支持度和相同形状参数的连续 Kaiser-Bessel、连续 exp 型、sinh 型和连续 Cosh 型窗函数。我们使用这样的窗口函数为 NFFT 提出了新颖的显式误差估计，并推导出了 NFFT 中涉及的参数的最佳选择规则。窗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函数，误差常数相对于截断参数呈指数衰减。