Average sampling theorems for shift invariant subspaces

摘要

The sampling theorem is one of the most powerful results in signalanalysis. In this pa- per we study the average sampling on shiftinvariant subspaces, e.g. wavelet subspaces. We show that if asubspace satisfies certain conditions, then every function in thesubspace is uniquely deter- mined and can be reconstructed by itslocal averages near certain sampling points. Examples are given.