Multivariate vector sampling expansions in shift invariant subspaces
Qingyue Zhang
TL;DR
This paper investigates the conditions under which multivariate vector sampling expansions are valid in general shift-invariant subspaces, providing a theoretical foundation for sampling in multivariate signal processing.
Contribution
It establishes necessary and sufficient conditions for multivariate vector sampling theorems in finitely generated shift-invariant subspaces, advancing the theoretical understanding of sampling in these spaces.
Findings
Derived necessary and sufficient conditions for sampling theorems.
Extended sampling theory to multivariate vector settings.
Provided a theoretical framework for sampling in shift-invariant subspaces.
Abstract
In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Holomorphic and Operator Theory