Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions
type: Item
instance of: scholarly article
title: Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions
zbMATH Open document ID: 0982.94008
author: Paul L. Butzer
author: Junjiang Lei
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1999-04-27T00:00:00Z
review text: The authors study the approximation error obtained by approximating a function \[ f\in \text{Lip}_L (1;C(\mathbb{R})) \] by its truncated sampling series with measured sampled values \[ S_{w,\lambda,n}f(t):= \sum_{k=-n}^n \lambda_k f(\cdot+k/w) \text{sinc} (wt-k), \] where \(\{\lambda_k \}_{k\in \mathbb{Z}}\) is any sequence of continuous linear functionals \(C_0(\mathbb{R})\to \mathbb{C}\). This model covers various errors appearing in the approximation of a signal by its sampling series as truncation errors, aliasing errors, jitter errors, amplitude errors and errors arising from sampled values obtained by averaging a signal. The authors generalize their results to the multivariate setting.
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 42B08
zbMATH DE Number: 1251469
zbMATH Keywords: sampling theorem
zbMATH Keywords: multivariate sampling
zbMATH Keywords: truncated sampling series
zbMATH Keywords: truncation errors
zbMATH Keywords: aliasing errors
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1251469