Ricerc@Sapienza

The performance of hypercomplex adaptive filters has been widely experimented during the last decade. Quaternion filters, especially, have been utilized in systems where the signals to be processed have some form of correlation. However, besides correlation, some resolved explanation about what particular algebra to use in a certain context has not been provided, yet. This work tries to contribute in this direction by proposing an experiment that puts filters to the test with changing the input signal geometry.

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.