Signal recovery under noise for not necessarily band-limited functions

We consider the problem of estimating a class of smooth functions defined everywhere on a real line using reconstruction techniques motivated by the Whittaker-Shannon sampling theorem. Such functions may be considered as signals and are common in communication. Furthermore, they have finite energy, bounded frequency content and are often jammed by noise. We examine the expected L₂-error of a class of estimators based on Whittaker-Shannon interpolation series and smoothing. Not band-limited signals are approximated in L₂(R) by an increasing ladder of band-limited subspaces (multiresolution approach)