A new approach to the interpolation of sampled data

A new class of interpolation kernels that are locally compact in signal space and "almost band-limited" in Fourier space is presented. The kernels are easy to calculate and lend themselves to problems in which the kernels must be analytically manipulated with other operations or operators such as convolutions and projection integrals. The interpolation kernels are comprised of a linear sum of a Gaussian function and its second derivative (and, when extended to higher order, its higher even derivatives). A numerical Gaussian quadrature method is derived that can be used with integrals involving the kernels that cannot be analytically evaluated. Potential extensions to higher order implementations of the kernels are discussed and examined. The emphasis of the manuscript is on the simplicity of the interpolation kernel and some of its mathematical properties.