Abstract
AbstractIn this paper, we present new regularized Shannon sampling formulas which use localized sampling with special window functions, namely Gaussian, $$\mathrm B$$
B
-spline, and $$\sinh $$
sinh
-type window functions. In contrast to the classical Shannon sampling series, the regularized Shannon sampling formulas possess an exponential decay and are numerically robust in the presence of noise. Several numerical experiments illustrate the theoretical results.
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Radiology, Nuclear Medicine and imaging,Signal Processing,Algebra and Number Theory,Analysis
Reference21 articles.
1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)
2. Chui, C.K.: An Introduction to Wavelets. Academic Press, Boston (1992)
3. Constantin, A.: Fourier Analysis, Part I: Theory. Cambridge University Press, Cambridge (2016)
4. Daubechies, I., DeVore, R.: Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order. Ann. Math. 2(158), 679–710 (2003)
5. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, New York (1980)
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