Determination of Derivative – and Regularized Derivative Interpolation for Band-limited Functions
This chapter looks at the ill-posedness of derivative interpolation as well as a regularised derivative interpolation for band-limited signals. To check for ill-posedness, the Shannon Sampling Theorem is applied. A regularised Fourier transform and the Shannon Sampling Theorem are used to investigate the convergence of regularised derivative interpolation. The error estimation is provided, as well as high order derivatives. The regularised derivative interpolation algorithm is compared to various methods of derivative interpolation. To prove and test the convergence property, certain instances are given. The numerical results show that the regularised sampling algorithm’s derivative interpolation is more successful in reducing noise for band-limited signals.
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