General in-place calculation of discrete Fourier transforms of multidimensional sequences

The computation of the discrete Fourier transform (DFT) of real multidimensional sequences requires an extraordinary amount of computer memory. The in-place calculation of the discrete Fourier transform reduces the required memory and is thus highly desirable. The present paper relies on the conjugate property of the generalized DFT in order to define novel, advantageous algorithms for the in-place calculation of the DFT of multidimensional sequences.