Chapter 3 - Spline Adaptive Filters: Theory and Applications

Abstract

In this chapter we propose a unifying overview of a recent class of nonlinear adaptive filters, known as Spline Adaptive Filter (SAF). This family of nonlinear adaptive filters comes from the general class of block-wise architectures consisting of a cascade of a suitable number of linear blocks and flexible memoryless nonlinear functions. In particular, the nonlinear function involved in the adaptation process is based on a spline function whose shape can be modified during the learning. Specifically, B-splines and Catmull–Rom splines are used, because they allow one to impose simple constraints on control parameters. The spline control points are adaptively changed using gradient-based techniques. In addition, in this chapter we show some of the most meaningful theoretical results in terms of upper bounds on the choice of the step sizes and excess mean square error values.