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

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

4 pages

References in corpus (2)

• Quaternion Fourier Transform on Quaternion Fields and Generalizations
• Directional Uncertainty Principle for Quaternion Fourier Transform

Cited by in corpus (5)

• Applications of Clifford's Geometric Algebra
• Quaternionic Fourier-Mellin Transform
• Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q=2
• Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)
• Heisenberg's and Hardy's Uncertainty Principles in Real Clifford Algebras