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 $\mathit{\text{multivector}}\mathit{\text{square}}\mathit{\text{roots}}$ $\in \text{cl}p,q$ $\mathit{\text{of}}$ -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 .