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 ($ell_{2}$ 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.

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