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We suppose the 2-D DFT is defined
:<math>X(k_1,k_2) = \sum_{n_1=0}^{N_1-1} \sum_{n_2=0}^{N_2-1} x[n_1, n_2] \cdot W_{N_1}^{k_1 n_1} W_{N_2}^{k_2 n_2}, </math>
where <math>k_1 = 0,\dots,N_1-1</math>, and <math>k_2 = 0,\dots,N_2-1</math>, and <math>x[n_1, n_2]</math> is an <math>N_1 \times N_2</math> matrix, and <math>W_N = \exp(-j 2\pi /N)</math>.
For simplicity, let us assume that <math>N_1=N_2=N</math>, and the radix-<math>(r\times r)</math> is such that <math>N/r</math> is an integer.
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