Dual frames in L~2(0,1) connected with generalized sampling in shift-invariant spaces

摘要

The aim of this article is to derive stable generalized sampling in a shift-invariant space by using some special dual frames in L~2(0,2). These sampling formulas involve samples of filtered versions of the functions in the shift-invariant space. The involved samples are expressed as the frame coefficients of an appropriate function in L~2(0,1) with respect to some particular frame in L~2(0,1). Since any shift-invariant space with stable generator is the image of L~2 (0,1) by means of a bounded invertible operator, our generalized sampling is derived from some dual frame expansions in L~2(0,1).