Programming the WFTA for two-dimensional data

The author introduces a two-dimensional Winograd Fourier transform algorithm (WFTA) technique and compares it with more traditional fast Fourier transform (FFT) implementations. Techniques for programming the WFTA in two dimensions are introduced. For completeness, enumerations of the Winograd small-n transposes, required when applying these techniques, are included. It is found that the WFTA implementation does save CPU time when implemented on a general-purpose computer for the following reasons: (1) the number of multiplications is far fewer than for common algorithms; (2) integer arithmetic can be used, at least for several stages of input additions, with no loss of accuracy; and (3) the fact that many operations are written out explicitly allows a programmer to save on the computation of indexes