Noncausal sampled signal reconstruction from noisy measurements: A system-theoretic approach

The paper studies the problem of reconstructing a not necessarily bandlimited analog signal from its noisy sampled measurements. Both A/D (analog-to-digital) and D/A (digital-to-analog) devices are treated as design parameters and no causality constraints are imposed on the reconstructor. We derive closed- form formulae for both L²middot and L^infinmiddot optimal reconstructors as well as expressions for the optimal achievable performance in both cases.