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OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions (1306.1650v1)
Published 7 Jun 2013 in math.RA and cs.CV
Abstract: We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f,g$. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by $f,g$, or by only one pure unit quaternion $f$, comment on their geometric meaning, and establish inverse transformations. Keywords: Clifford geometric algebra, quaternion geometry, quaternion Fourier transform, inverse Fourier transform, orthogonal planes split