2023/11/01 by Frank Filbir, Filbir, Frank, Manfred Tasche +3
Computer Science · Mathematics · #42A38 #65T50 #94A20 #Complex Variables (math.CV) #Digital Filter Design and Implementation #FOS: Electrical engineering #FOS: Mathematics #G.1.2 #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2311.00610
openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.