Application of the convergence of the control points of B-splines to wavelet decomposition at rational scales and rational location

We first recall the relation between discrete B-splines and the control points of B-splines. We then use some convergence properties of the control points of B-splines to derive a new algorithm that approximates the wavelet decomposition at rational scales and rational location. We conclude the paper by some numerical experiments illustrating the behavior of our algorithm and by a discussion on an efficient implementation of the proposed method.