Blanco, C.;Cabrelli, Carlos A.;Heineken, Sigrid B.

Functions in Sampling Spaces

Sampl. Theory Signal Image Process Vol.5 No.3 (2005) p.275-295

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abstract

Sampling theory in spaces other than the space of band-limited
functions has recently received considerable attention. This is in
part because the band-limitedness assumption is not very
realistic in many applications. In addition, band-limited
functions have very slow decay which translates in poor
reconstruction. In this article we study the sampling problem in
general shift invariant spaces. We characterize the functions in
these spaces and provide necessary and sufficient conditions for a
function in $L^2(R)$ to belong to a sampling space. Furthermore
we obtain decompositions of a sampling space in sampling
subspaces. These decompositions are related with determining sets.
Some examples are provided.

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