Geometric-Algebra Adaptive Filters

The Multidimensional Isotropic Generalization of Quadrature Filters in Geometric Algebra

In signal processing, the approach of the analytic signal is a capable and often used method. For signals of finite length, quadrature filters yield a bandpass filtered approximation of the analytic signal. In the case of multidimensional signals, the quadrature filters can only be applied with respect to a preference direction. Therefore, the orientation has to be sampled, steered or orientati...

Extensors in Geometric Algebra

This paper, the third in a series of three introduces the basics of the theory of extensors that are need for the a theory of multvector and extensor fields in arbitrary manifolds, developed in a following series of five papers. Key notions such as the extension and generalization operators of a given linear operator (a (1, 1)-extensor) acting on a real vector space V are introduced and studied...

Projective Geometric Algebra

Oriented Conformal Geometric Algebra

In [12] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogenous representation of geometry could provide a multitude of benefits. This paper extends his work by applying the same approach to Conformal Geometric Algebra. Oriented Conformal Geometric Algebra allows intuitive manipulation of such concepts as half-s...

Universal Geometric Algebra

Alfred North Whitehead promoted the idea of UNIVERSAL ALGEBRA in his monumental treatise of 1897 [1]. He proposed two candidates for this lofty title, the algebra of Boole and Grassmann’s Algebra of Extension. Boolean algebra has since secured universality status in Set Theory and Symbolic Logic, although only the former is universally known and used by mathematicians. However, Whitehead’s work...