Abstract
Even if it is an idealization, the band-limited process is widely taken as model in signal processing and in communications. The classical Shannon formula is exact for the unit rate sampling and a spectral support of 2� -length. It is no longer error-free when one sample is lost and replaced by an estimation, because the set of functions {e in� , nZ} is free and complete in L� (-� ,� ). Then, an exact reconstruction can occur only when the process is oversampled. In this con- text, iterative procedures exist (1), but not analytic formulas, from apart these in (2), which have an uncontrolled conver- gence. In this paper, we give simple formulas when one or two samples are missing, but which can be generalized to a number of erased samples larger than two. We show that the reintroduction of ignored samples can improve the conver- gence of the formulas. The links with the Lagrange interpolation formula are highlighted.
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