New reconstruction formulas for oversampled processes and functions

This paper addresses the reconstruction of band-limited oversampled stationary processes and functions. The reconstruction is performed from a multiperiodic subset of the periodic sampling sequence and from some isolated samples. Reconstruction performance can be characterized at the omitted sample points. The omission of some sample points provides a time-varying nature to the reconstruction formulas. This particular sampling scheme associated to specific interpolation functions result in an exact reconstruction with an arbitrarily tunable convergence rate. Moreover, the convergence properties hold when the reconstruction is performed in the neighbourhood of any lost sample. Indeed, the formulas can be fitted to any sample loss or deterioration by a simple time index translation. Specific expressions of the general reconstruction formula are derived for different process bandwidth ranges.