Eckhard Hitzer, In T. Simos, G. Psihoyios and C. Tsitouras (eds.), Numerical Analysis and Applied Mathematics ICNAAM 2013, AIP Conf. Proc. 1558, pp. 529 -532 (2013). DOI: 10.1063/1.4825544.
We show how Fourier transformations can be extended to Hamilton’s algebra of quaternions. 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. Hamilton’s algebra of quaternions is only one example of the larger class of Clifford’s geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Keywords: Clifford geometric algebra, quaternion Fourier transform, Clifford Fourier transform, Clifford Fourier-Mellin transform, Mulitvector wavepackets, Spacetime Fourier transform.
AMS Subj. Class. 15A66, 42A38
Comments: 4 Pages. 2 figures.