Optimized Compact-Support Interpolation Kernels

In this paper, we investigate the problem of designing compact-support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an nonlinear infinite dimensional problem to a linear finite dimensional case, and then find the optimum compact-support function that best approximates a given filter in the least square sense (ℓ₂ norm). The benefit of compact-support interpolants is the low computational complexity in the interpolation process while the optimum compact-support interpolant guarantees the highest achievable signal-to-noise ratio (SNR). Our simulation results confirm the superior performance of the proposed kernel compared to other conventional compact-support interpolants such as cubic spline.