E. Hitzer

**OPS-QFTs: A new type of quaternion
Fourier transforms based on the orthogonal planes split with one or two
general pure quaternions**

*Numerical Analysis and Applied Mathematics ICNAAM 2011*,
AIP Conf. Proc. 1389, pp. 280--283 (2011),
doi: 10.1063/1.3636721

**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.

**AMS Subject Classification:**
15A66, 42A38

[PDF] 977 kb

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