In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported window functions, namely B-spline, sinh-type, and continuous Kaiser-Bessel window functions. In contrast to the Shannon sampling series for SAFT, the regularized Shannon sampling formulas for SAFT possesses an exponential decay of the approximation error and are numerically robust in the presence of noise, if certain oversampling condition is fulfilled. Several numerical experiments illustrate the theoretical results.

翻译：本文提出了与特殊仿射傅里叶变换（SAFT）相关的新的正则化香农采样公式。这些采样公式采用具有特殊紧支撑窗函数（即B样条、双曲正弦型和连续Kaiser-Bessel窗函数）的局部化采样。与针对SAFT的香农采样级数相比，若满足特定过采样条件，SAFT的正则化香农采样公式具有近似误差的指数衰减特性，且在噪声存在时数值鲁棒性更强。若干数值实验验证了理论结果。