An approximation for discrete B-splines in time domain

A simple discrete version of B-splines defined as a multifold discrete convolution of sampled rectangles is proposed in the analogy of B-splines being multifold convolution integrals of rectangular functions. Then it is proven that its staircase interpolation tends to the B-spline when the sampling interval goes to zero. This version can be regarded as an approximation for the discrete B-splines established in the literature, and it is faster in numerical evaluation.