Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q=2

Abstract

We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain ${\mathbb{R}}^{p,q}$ taking values in Cl(p,q), p+q=2. Keywords: algebra, Fourier transforms; Logic, set theory, and algebra, Fourier analysis, Integral transforms

6 pages, 2 figures

References in corpus (4)

• Biquaternion (complexified quaternion) roots of -1
• OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions
• Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)
• Square Roots of -1 in Real Clifford Algebras