Simple Errorless Formulas when Missing Samples

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 2π-length. It is no longer error-free when one sample is lost and replaced by an estimation, because the set of functions {einω, nєZ} is free and complete in L2(-π,π). Then, an exact reconstruction can occur only when the process is oversampled. In this context, iterative procedures exist [1], but not analytic formulas, from apart these in [2], which have an uncontrolled convergence. 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 convergence of the formulas. The links with the Lagrange interpolation formula are highlighted.

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