On two-dimensional classical and Hermite sampling

  title={On two-dimensional classical and Hermite sampling},
  author={Rashad M. Asharabi and J{\"u}rgen Prestin},
  journal={Ima Journal of Numerical Analysis},
We investigate some modifications of the two-dimensional sampling series with a Gaussian function for wider classes of bandlimited functions including unbounded entire functions on R and analytic functions on a bivariate strip. The first modification is given for the twodimensional version of the Whittaker-Kotelnikov-Shannon sampling (classical sampling) and the second is given for two-dimensional sampling involving values of all partial derivatives of order α ≤ 2 (Hermite sampling). These… 

Figures and Tables from this paper

Double sampling derivatives and truncation error estimates

This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and

Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions

The bivariate sinc-Gauss sampling formula is introduced in Asharabi and Prestin (IMA J. Numer. Anal. 36:851–871, 2016) to approximate analytic functions of two variables which satisfy certain growth


The Hermite-Gauss sampling operator was introduced by Asharabi and Prestin (2015) to approximate a function from a wide class of entire functions, using few samples from the function and its first

A bivariate sampling series involving mixed partial derivatives

Abstract: Recently Fang and Li established a sampling formula that involves only samples from the function and its first partial derivatives for functions from Bernstein space, B σ(R) . In this

Generalized bivariate Hermite–Gauss sampling

Recently, Asharabi and Al-Haddad in (Turk J Math 41: 387–403, 2017) have established a generalized bivariate sampling series involving samples from the function and its mixed and non-mixed partial

Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula

The bivariate sinc-Gauss sampling formula that was proposed in [ 6 ] is used to construct a new sampling method to compute eigenpairs of a two-parameter Sturm-Liouville system and the amplitude error is estimated, which gives the possibility to establish the rigorous error analysis of this method.

Multivariate and some other extensions of sampling Theory for Signal Processing a historic perspective

  • A. J. Jerri
  • Computer Science
    2017 International Conference on Sampling Theory and Applications (SampTA)
  • 2017
This talk centers on a tutorial review of the various aspects of the multivariate sampling for the past sixty years, since it was suggested by Parzen in 1956.

Generalized bivariate Hermite–Gauss sampling

  • R. M. Asharabi
  • Materials Science
    Computational and Applied Mathematics
  • 2019
Recently, Asharabi and Al-Haddad in (Turk J Math 41: 387–403, 2017) have established a generalized bivariate sampling series involving samples from the function and its mixed and non-mixed partial


Abstract. Using complex analysis, we present new error estimates for multidimensional sinc-Gauss sampling formulas for multivariate analytic functions and their partial derivatives, which are valid



A Modification of Hermite Sampling with a Gaussian Multiplier

Two modifications of Hermite sampling with a Gaussian multiplier are introduced to approximate bandlimited and non-bandlimited functions and it is demonstrated that the approximation is highly efficient.

Complex-analytic approach to the sinc-Gauss sampling formula

This paper is concerned with theoretical error estimates for a sampling formula with the sinc-Gaussian kernel. Qian et al. have recently given an error estimate for the class of band-limited

K-order Sampling of N-dimensional Band-limited Functions†

ABSTRACT The work of II previous paper, utilizing the gradient in sampling theory, is generalized further to include the sampling of a function and its partial derivatives up to order K ≥ 1. The

Sinc Approximation with a Gaussian Multiplier

Recently, it was shown with the help of Fourier analysis that by incorporating a Gaussian multiplier into the truncated classical sampling series, one can approximate bandlimited signals of nite

Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion

Let BΩp, 1 ≤ p < ∞, be the space of all bounded functions from Lp(ℝ) which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated


This note gives a method of proof of the sampling theorem, both for the case where the interval I is centered at the origin and where it is not, which is somewhat simpler than the previously given proofs, and at the same time is more rigorous, and yields several useful generalizations to functions of several variables and random functions.

Advances in Shannon's Sampling Theory

Introduction and a Historical Overview. Shannon Sampling Theorem and Band-Limited Signals. Generalizations of Shannon Sampling Theorems. Sampling Theorems Associated with Sturm-Liouville

Approximation of Functions of Several Variables and Embedding Theorems

Abstract : The theory of embeddings of classes of differentiable functions of several variables has been intensively expanded during the past two decades, and a number of its fundamental problems