Reproducing Polynomials with B-Splines
A B-Spline of order is known to be able to reproduce any polynomial up to order :
In words, a proper linear combination of shifted versions of a B-Spline can reproduce any polynomial up to order . This is needed for certain applications, for example, for the Sampling at Finite Rate of Innovation (FRI) framework where where any kernel reproducing polynomials, that is, satisfying the Strang-Fix conditions, can be used. However, among all possible kernels, the B-Splines have the smallest possible support.