On planar sampling with Gaussian kernel in spaces of bandlimited functions

Abstract

Let $I=(a,b)\times (c,d)\subset {\mathbb{R}}_{+}^2$ be an index set and let $\{G_{\alpha }(x){\}}_{\alpha \in I}$ be a collection of Gaussian functions, i.e. $G_{\alpha }(x)=\exp (-{\alpha }_1{x}_1^2-{\alpha }_2{x}_2^2)$, where $\alpha =({\alpha }_1,{\alpha }_2)\in I,x=(x_1,x_2)\in {\mathbb{R}}^2$. We present a complete description of the uniformly discrete sets $\Lambda \subset {\mathbb{R}}^2$ such that every bandlimited signal $f$ admits a stable reconstruction from the samples $\{f\ast G_{\alpha }(\lambda ){\}}_{\lambda \in \Lambda }$.

22 pages, 1 figure

References in corpus (2)

• Reconstruction of Bandlimited Functions from Space-Time Samples
• On 2-dimensional mobile sampling