Efficient evaluation of oversampled functions

摘要

It has been known since long that an oversampled function can be represented by a generalized sinc series which converges much faster than the usual one. We show that the speed of convergence is exponential and give numerical approximations to the kernel function involved in the generalized series. The practical consequence is that a bandlimited function which is oversampled can be evaluated at any point with accuracy O(L e−L) using O(L) operations.