E. Hitzer: Extending Fourier Transformations to Hamilton’s Quaternions and Clifford’s Geometric Algebras

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.

Download: PDF http://vixra.org/pdf/1310.0249v1.pdf

Source: http://vixra.org/abs/1310.0249

Leave a comment

Filed under publications

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s