The ILL-Posedness of Derivative and Regularized Interpolation for Non-band limited Functions

In this paper, the ill-posedness of derivative interpolation is discussed, and a regularized derivative interpolation for non-bandlimited signals is presented. The regularized derivative interpolation's convergence is investigated. The numerical results are presented, and the Tikhonov regularization method is used to compare them to derivative interpolation. In this study, the regularized derivative interpolation is more accurate in computing. The regularized derivative interpolation by sampling can be applied. The convergence property is proved and tested by some examples. The numerical results are better than Tikhonov regularization method.