Spline Functions and Stochastic Filtering

Nonlinear spline adaptive filtering

In this paper a new class of nonlinear adaptive filters, consisting of a linear combiner followed by a flexible memory-less function, is presented. The nonlinear function involved in the adaptation process is based on a spline function that can be modified during learning. The spline control points are adaptively changed using gradient-based techniques. B-splines and Catmull-Rom splines are use...

APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.

Refinement equations and spline functions

In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution of powers of a fixed number modulo 1, and show the nonexistence of a non-trivial C∞ solution of the refinement equation with non-integer dilations. Using this, we extend the results on the refinable splines with non-integer dilations and construct a counterexample...

Smoothing by Spline Functions