Generalized non-uniform B-spline functions for discrete signal interpolation

This paper is concerned with the problem of recovering a discrete signal from a set of irregular spaced samples at known locations. We propose a local interpolation method based on non-uniform B-spline functions. Under specific constraints (multiplicity order imposed on each knot), we generalize the non-uniform B-spline functions for any degree of the interpolation function. We show that whatever the degree of the interpolation function, only few knots are enough to reconstruct the discrete signal. We provide a new and general scheme for the implementation of the reconstruction method. The results of simulation are satisfactory.