Clifford Fourier Transform


William Kingdon Clifford created the geometric algebras in 1878. They usually contain continuous submanifolds of geometric square roots of minus one. Each element, called multivector, has a natural geometric interpretation.
The generalization of the Fourier transform to multivector valued functions in the geometric algebras is very reasonable. It helps to interpret the transform, apply it in a target oriented way to the specific underlying problem and allows a new point of view on fluid mechanics.
The geometric product of two vectors in a Clifford algebra is invertible and contains information about their orientational relation. This property can be used for the development of rotationally invariant algorithms for signal and image processing of multivariate data.


Dipl.-Math., B.Sc. Inf. Roxana Bujack
Dipl.-Math. Wieland Reich