Decomposition of 2D Hypercomplex Fourier transforms into pairs of complex fourier transforms

Hypercomplex 2D Fourier transforms have been proposed by several authors with applications in image processing of both grayscale and colour images. Previously published works on hypercomplex Fourier transforms have utilized direct evaluation of a Fast Fourier transform using hypercomplex arithmetic. This paper shows that such transforms may be implemented by decomposition into two independent complex Fourier transforms and may thus be implemented by building upon existing complex code. This is a significant step because it makes available to researchers using hypercomplex Fourier transforms all the investment made by others in efficient complex fft implementations, and requires substantially less effort than coding hypercomplex versions of existing code.