L2 sampled signal reconstruction with causality constraints - Part II: Theory

This paper provides the theoretic foundation for the design of optimal reconstructors (also known as interpolators/holds) with a prescribed degree of causality. A compact frequency- domain solution is derived that mimics known interpolation tech- niques for ordinary transfer functions. In parallel, an extensive state space solution is documented. It complements the frequency- domain solution in that it constructively proves the various claims, and it also makes the solution concrete. The state space solution re- quires the solution of one Riccati and one Lyapunov matrix equation.