Simple Errorless Formulas when Missing Samples
B. Lacaze · The Open Electrical & Electronic Engineering Journal · 2009
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 , n Z} is free and complete in L (-, ).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.