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Sampled Signal Reconstruction Via H2Optimization

In this paper the sampled signal reconstruction problem is formulated and solved as the sampled-data H2 smoothing problem, in which an analog reconstruction error is minimized. Both infinite (non-causal reconstructors) and finite (reconstructors with relaxed causality) preview cases are considered. The optimal reconstructors are in the form of the cascade of a discrete-time smoother and a generalized hold (interpolator). In the particular case of reconstructing polynomial signals with infinite preview, the proposed procedure recovers the cardinal B-spline reconstructors