Calculation of multidimensional Hartley transforms using one-dimensional Fourier transforms

In the processing of real-valued data, a purely real transform such as the Hartley transform is more desirable than the complex Fourier transform because it avoids unnecessary complex computations. This advantage is most significant in multidimensional transformations, where a large amount of data has to be processed. A multidimensional fast Hartley transform algorithm is described that successively applies 1D Fourier transforms. Redundant operations are reduced to a minimum. Special indexing schemes (parity operators) are introduced to avoid unscrambling procedures