Recovery of Finite Missing Samples in Two-channel Oversampling

Abstract

When a band-limited signal is oversampled at a rate higher than the minimum Nyquist rate, the samples thus obtained are not independent but has some redunduncy. Hence, through oversampling, any finite missing samples can be recovered from the remaining known samples([1,2,7,9]). See also [5] for an abstract setting of the oversampling and recovering of missing samples in general reproducing kernel Hilbert spaces. Recently, Santos and Ferreira[9] considered the problem of recovering missing samples in two-channel oversampling involving a signal and its derivative. In [9], it is shown that any finite missing samples can always be recovered if these missing samples occur either in the signal itself or its derivative. In this work, we consider arbitrary two-channeling of a band-limited signal and find sufficient conditions under which we can recover any finite missing samples when they occur in a single channel or both channels. We also give several examples illustrating our results.