Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q=2
This work provides a theoretical extension for signal processing in Clifford algebras, but it appears incremental as it builds on existing transforms without clear practical applications.
The authors tackled the problem of generalizing the complex Fourier-Mellin transform to Clifford algebra-valued signals in a 2D domain, resulting in a non-commutative formulation for Cl(p,q) with 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 transforms