Average sampling in shift invariant subspaces with symmetric averaging functions ✩

In this paper, we study the reconstruction of functions in shift invariant subspaces from local averages with symmetric averaging functions. We present an average sampling theorem for shift invariant subspaces and give quantitative results on the aliasing error and the truncation error. We show that every square integrable function can be approximated by its average sampling series. As special cases we also obtain new error bounds for regular sampling. Examples are given.  2003 Elsevier Inc. All rights reserved.