AN ANALYSIS METHOD FOR SAMPLING IN SHIFT-INVARIANT SPACES

Abstract

A subspace V of L 2 (ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function. As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x 0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x 0 + k + δ k )) k∈ℤ , either when all δ k = 0 or in the irregular sampling case with an upper bound sup k |δ k | < δ.