The influence of the non-uniform spline basis on the approximation signal

This paper is concerned with the problem of recovering a discrete signal from a set of irregularly spaced samples. The approximation method is based on spline functions using non-uniform B-splines. According to the various knot sequence configurations, several bases can be used. We study the important issue of selecting an adequate basis of the spline function. The analysis shows that the choice of the elements and dimension of the basis has a strong influence on the quality of the signal approximation. For a given degree of the spline and for a particular knot sequence configuration, the smallest dimension of the basis provides good performances compared to the basis spline of higher dimension. Moreover this basis, with the smallest dimension, requires only two consecutive knots for the construction of its elements. The theoretical results are illustrated with examples.