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

Abstract

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 prefiltering. 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.

Some aspects of implementing a cubic spline interpolation algorithm on a DSP

“…The signal reconstruction and signal interpolation by a factor m=2 were performed and the interpolation errors were determined. Some of the results were discussed in [1] and compared with the results obtained for other input functions. For all the computations there was used the extended precision.…”

“…In some previous papers [1], [2] there were developed and implemented some new algorithms for signal interpolation. From the fast cubic spline interpolation algorithm there are preserved the coefficients expansion and the indirect B-spline filtering.…”

“…This is why the new process became a Hermite interpolation algorithm. It was determined a relation between the coefficients and the second order derivative of the function [1]. Any coefficient c(k) can be computed using:…”