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

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 .Comment: 19 pages, 1 figur

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

We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain $\R^{p,q}$ taking values in Cl(p,q), p+q=2. Keywords: algebra, Fourier transforms; Logic, set theory, and algebra, Fourier analysis, Integral transformsComment: 6 pages, 2 figure