Determination of Derivative - and Regularized Derivative Interpolation for Band-limited Functions

Abstract

The ill-posedness of derivative interpolation is examined in this chapter, as well as a regularised derivative interpolation for band-limited signals. The Shannon Sampling Theorem is used to examine the ill-posedness. 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 regularised derivative interpolation algorithm is compared to derivative interpolation with other algorithms. Some examples are used to prove and test the convergence property. The numerical findings reveal that for band-limited signals, the regularised sampling algorithm's derivative interpolation is more effective in decreasing noise.