Generalized average sampling and reconstruction for wavelet subspaces

Abstract

As an extension of the average sampling, we analyse generalized average sampling and reconstruction problem over some wavelet subspaces of \(L^{2}({{\mathbb {R}}})\). For closed subspaces \(V_{0}\) of \(L^{2}({{\mathbb {R}}})\), we present a necessary and sufficient condition under which there is the generalized average sampling expansion for every \(f \in V_{0}\).