Determining the Coefficients in B-spline Interpolation by Using the Second Derivative

To resolve a problem in the context of generalized spline interpolation the first step is to determine the coefficients from the input samples. The operation is a pre-filtering. This paper offers an alternative to calculate the coefficients using the values of the second derivative for the input signal. Dealing with numerical data the problem is to estimate the derivative values in each point. Two methods are presented and used to obtain the coefficients. With a cubic B-spline function being the basis function is performed the signal reconstruction and interpolation by a factor m=2. The algorithms are implemented for some well known signals and the results are presented.