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Algebra |
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Authors: Eckhard Hitzer
We generalize the space-time Fourier transform (SFT) [1] to a special affine Fourier transform (SASFT, also known as offset linear canonical transform) for 16-dimensional space-time multivector Cl(3,1)-valued signals over the domain of space-time (Minkowski space) R^{3,1}. We establish how it can be computed in terms of the SFT, and introduce its properties of multivector coefficient linearity, shift and modulation, inversion, Rayleigh (Parseval) energy theorem, partial derivative identities, a directional uncertainty principle and its specialization to coordinates. All important results are proven in full detail. [1] E. Hitzer, Quaternion Fourier Transform on Quaternion Fields and Generalizations. Adv. Appl. Clifford Algebras 17(3), pp. 497-517 (2007), DOI: https://doi.org/10.1007/s00006-007-0037-8.
Comments: 18 Pages. To be published in Adv. Appl. Clifford Algebras, 2022.
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[v1] 2022-06-14 06:15:00
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