The ill-posedness of derivative interpolation and regularized derivative interpolation for band-limited functions by sampling

EURASIP journal on advances in signal processing

article

Chen, Weidong¹ 

[1] Department of Mathematics and Statistics, Minnesota State University

关键词: Band-limited function;    Derivative interpolation;    Ill-posedness;    Regularization;   

DOI  :  10.1186/s13634-020-00668-5

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY