1D Cubic B-spline Interpolation via Digital Filtering. Java example

This post based on my previous post “Introduction to splines. B-spline” . In spline interpolation problem coefficients are determined such as that the function goes through the data points exactly. For splines of degree 0 and 1 the B-spline coefficients are identical to the signal samples . For higher-degree splines the procedure is more complicated. 

Traditionally, the B-spline interpolation problem has been approached using a matrix framework and setting up a system of equations, which is then solved using standard numerical techniques. But it was showed by M. Unser [1, 2, 3] that this problem could be solved using simpler digital filtering techniques.

Introduction to splines. B-spline

This is the introduction post about using splines mathematical apparatus for signal processing. The representation of signals using splines has many useful properties and introduces effective signal processing tool. 

The Spline is a smooth, piecewise-defined polynomial function. Spline has a high smoothness degree at pieces joining points, which are called knots.