Sampling Theorems for Multivariate Shift Invariant Subspaces ∗
نویسندگان
چکیده
Regular and irregular sampling theorems for multivariate shift invariant subspaces are studied. We give a characterization of regular points and an irregular sampling theorem, which covers many known results, e.g., Kadec’s 1/4-theorem. We show that some subspaces may not have a regular point. We also present a reconstruction algorithm which is slightly different from the known one but is more efficient. We study the aliasing error and prove that every smooth square integrable function can be approximated by its sampling series.
منابع مشابه
Multivariate vector sampling expansions in shift invariant subspaces
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.
متن کاملShift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملPerturbations and Irregular Sampling Theorems for Frames
This paper gives a perturbation theorem for frames in a Hilbert space which is a generalization of a result by Casazza and Christensen. Then this result is applied to the Perturbation of regular sampling in shift-invariant spaces. Irregular sampling theorems for frames in wavelet subspaces are established for which it is easy to derive explicit formulas and algorithms to calculate the ranges of...
متن کاملSupprrium of Perturbation for Sampling in Shift Invariant Subspaces
In the more general framework ' shift invariant subspace", the paper obtains a different estimate of sampling in function subspace to our former work, by using the Frame Theory. The derived formula is easy to be calculated, and the estimate is relaxed in some shift invariant subspaces.
متن کاملA sampling theorem for shift-invariant subspace
A sampling theorem for regular sampling in shift invariant subspaces is established. The sufficient-necessary condition for which it holds is found. Then, the theorem is modified to the shift sampling in shiftinvariant subspaces by using the Zak transform. Finally, some examples are presented to show the generality of the theorem.
متن کامل