B-spline interpolation technique for digital signal processing

The problem of interpolation a set of data is an old one, but the demanding of flexibility and high speed in operating on-line and in real time processing need to find new methods and improve the old ones [1]. The main properties of B-spline functions offer the possibility to implement algorithms of interpolation in a faster and optimal manner. A function can be represented by B-spline functions with a set of coefficients. For interpolative signal reconstruction it is necessary to calculate those coefficients. In this paper, for cubic spline interpolation it is analyzed a known algorithm and some of his deficiencies. Also there are relieved some possibilities for developing new algorithms that could eliminate those problems. It is presented another way to determine the initial coefficients by using the polynomial representation on short intervals of the spline function and his derivatives. Based on this results are made several observations for further use in improving the algorithm.