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Regularized shannon sampling formulas related to the special affine fourier transform.
J. Fourier Anal. Appl. 31:40 (2025)
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-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.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Compactly Supported Window Function ; Error Estimates ; Numerical Robustness ; Regularized Shannon Sampling Formula Related To Saft ; Saft ; Shannon Sampling Theorem ; Special Affine Fourier Transform; Signals; Reconstruction
ISSN (print) / ISBN
1069-5869
Quellenangaben
Volume: 31,
Issue: 3,
Article Number: 40
Publisher
Springer
Publishing Place
233 Spring Street, 6th Floor, New York, Ny 10013 Usa
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
Grants
Helmholtz Association
Helmholtz Zentrum Mnchen - Deutsches Forschungszentrum fr Gesundheit und Umwelt (GmbH) (4209)
Helmholtz Zentrum Mnchen - Deutsches Forschungszentrum fr Gesundheit und Umwelt (GmbH) (4209)