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, continuous window functions, namely B-spline, $$\sinh $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>sinh</mml:mo> </mml:math> -type, and continuous Kaiser–Bessel window functions. In contrast to the known 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.