Ricerc@Sapienza

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.

The degree of diffusion of hypercomplex algebras in adaptive and non-adaptive filtering research topics is growing faster and faster. The debate today concerns the usefulness and the benefits of representing multidimensional systems by means of these complicated mathematical structures and the criterions of choice between one algebra or another. This paper proposes a simple comparison between two isodimensional algebras (quaternions and tessarines) and shows by simulations how different choices may determine the system performance.