The sinc-approximating kernels of classical polynomial interpolation

A classical approach to interpolation of sampled data is polynomial interpolation. However, from the sampling theorem it follows that the ideal approach to interpolation is to convolve the given samples with the sinc function. In this paper we study the properties of the sinc-approximating kernels that can be derived from the Lagrange central interpolation scheme. Both the finite-extent properties and the convergence property are analyzed. The Lagrange central interpolation kernels of up to ninth order are compared to cardinal splines of corresponding orders, both by spectral analysis and by rotation experiments on real-life test-images. It is concluded that cardinal spline interpolation is by far superior