Causal Spline Interpolation by H# Optimization

Spline interpolation systems generally contain non-causal filters, and hence such systems are difficult to use for real-time processing. Our objective is to design a causal system which approximates spline interpolation. This is formulated as a problem of designing a stable inverse of a system with unstable zeros. For this purpose, we adopt H00 optimization. We give a closed form solution to the H^∞ optimization in the case of the cubic spline. For higher order splines, the optimal filter can be effectively solved by a numerical computation. We also show that the optimal FIR (finite impulse response) filter can be designed by an LMI (linear matrix inequality), which can also be effectively solved numerically. A design example is presented to illustrate the result.