GENERALIZED HERMITE INTERPOLATION AND SAMPLING THEOREM INVOLVING DERIVATIVES

Title & Authors
GENERALIZED HERMITE INTERPOLATION AND SAMPLING THEOREM INVOLVING DERIVATIVES
Shin, Chang-Eon;

Abstract
We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\small{\leq}$ A exp($\small{\sigma}$｜y｜) for some A, $\small{\sigma}$ > 0 and any ｚ
Keywords
generalized Hermite interpolation;sampling theorem;contour integral;
Language
English
Cited by
1.
A Modification of Hermite Sampling with a Gaussian Multiplier, Numerical Functional Analysis and Optimization, 2015, 36, 4, 419
2.
Generalized sinc-Gaussian sampling involving derivatives, Numerical Algorithms, 2016, 73, 4, 1055
3.
Truncation error estimates for generalized Hermite sampling, Numerical Algorithms, 2017, 74, 2, 481
References
1.
Interpolation and Approximation,

2.
Foundations,

3.
I.R.E. Trans. Inform. Theory, vol.IT-2. pp.139-146

4.
Inform. Control, vol.3. pp.26-31

5.
Birkhoff Interpolation,

6.
Theory and Practice,

7.
Inform. Control, pp.172-182

8.
Theor. Probability Appl., vol.12. pp.647-657

9.
IEEE Trans. Inform. Theory, vol.IT-35. 6, pp.1223-1227

10.
General Sampling Theorem Using Contour Integral,

11.