Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions
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.
scientific article; zbMATH DE number 1251469