KEYNOTE LECTURE

We show how real and complex Fourier transforms are extended to W.R. Hamilton's algebra of quaternions and to W.K. Clifford's geometric algebras. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Clifford's geometric algebras are complete algebras, algebraically encoding a vector space and all its subspace elements, including Grassmannians (a vector space and all its subspaces of given dimension k). Applications include electromagnetism, and the processing of images, color images, vector field and climate data. Further developments of Clifford Fourier Transforms include operator exponential representations, and extensions to wider classes of integral transforms, like Clifford algebra versions of linear canonical transforms and wavelets.

Biography of the Speaker: Eckhard M. S. Hitzer Short Bio