Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)

Abstract

We generalize quaternion and Clifford Fourier transforms to general two-sided Clifford Fourier transforms (CFT), and study their properties (from linearity to convolution). Two general \textit{multivector square roots} $\in \cl{p,q}$ \textit{of} -1 are used to split multivector signals, and to construct the left and right CFT kernel factors. Keywords: Clifford Fourier transform, Clifford algebra, signal processing, square roots of -1 .

19 pages, 1 figure

References in corpus (3)

• Applications of Clifford's Geometric Algebra
• Directional Uncertainty Principle for Quaternion Fourier Transform
• OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions

Cited by in corpus (1)

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