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Abstract
In this paper, the ill-posedness of derivative interpolation is discussed, and a regularized derivative interpolation for band-limited signals is presented. The ill-posedness is analyzed by the Shannon sampling theorem. The convergence of the regularized derivative interpolation is studied by the combination of a regularized Fourier transform and the Shannon sampling theorem. The error estimation is given, and high-order derivatives are also considered. The algorithm of the regularized derivative interpolation is compared with derivative interpolation using some other algorithms.
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1 Department of Mathematics and Statistics, Minnesota State University, Mankato, USA