Min-max interpolators and Lagrange interpolation formula

For oversampled band-limited signals, min-max optimal interpolators have been proposed under assumptions upon either the signal to be interpolated itself (e.g. finite energy) or its Fourier transform. In this paper, we consider the case where the signal is assumed to be bounded. For band-limited signals this is a more realistic assumption that is weaker than those previously considered. We propose an approximate solution that leads to closed form expressions for the interpolator coefficients. It relies upon an extension of the Lagrange interpolation formula.