In multi-dimensional signal processing the Cliiord Fourier transform (CFT or in the 2-D case: quater-nionic Fourier transform/QFT) is a consequent extension of the complex valued Fourier transform. Hence, we need a fast algorithm in order to compute the transform in practical applications. Since the CFT is based on a corresponding Cliiord algebra (CA) and CAs are not commutative in general, we ...