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This report presents a derivation of the modified discrete Fourier transform, which has the property that the origin in frequency space appears in the center of the plot rather than at the edges (one dimension) or at the four corners (two dimensions), as in conventional treatments. Also included is a listing of an unusual fast Fourier transform (FFT) program for calculating the twodimensional, modified discrete Fourier transform. The program makes use of the Eklundh fast matrix transpositiondoi:10.21236/ada220567 fatcat:472uuuq26vfwvoyrvw7oh6qh2e