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 multivector square roots∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in}$$\end{document}Cl(p, q) of −1 are used to split multivector signals, and to construct the left and right CFT kernel factors.