Regularized Shannon sampling formulas related to the special affine Fourier transform

Abstract: 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.