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The equation above defines the basic structure of the 2-D DIT radix-<math>(r\times r)</math> "butterfly". (See 1-D "butterfly" in [[Cooley–Tukey FFT algorithm]])
When <math>r=2</math>, the equation can be broken into four summations, and this leads to:<ref name=Dudgeon83/>
:<math> X(k_1,k_2) = S_{00}(k_1,k_2) + S_{01}(k_1,k_2) W_N^{k_2} +S_{10}(k_1,k_2) W_N^{k_1} + S_{11}(k_1,k_2) W_N^{k_1+k_2}</math> for <math>0\leq k_1, k_2 < \frac{N}{2}</math>,
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