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

Hitzer In memory of our dear friend Rev. Olaug Hansen. 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 multivector square roots ∈Cl(p,q) of −1 are used to split multivector signals, and to construct the left and right CFT kernel factors