3-D planar quadrantal and diagonal symmetry-based Winograd Fourier transform algorithm

A fast algorithm for computing the discrete Fourier transform (DFT) of single planar quadrantal symmetric data is discussed. The algorithm is developed employing the techniques of the multidimensional Winograd Fourier transform algorithm (WFTA). It is found that an interesting relationship exists between the quadrantal and diagonal symmetries when the length of the data along each axis is odd. This implies that from one set of symmetry-based WFTA, the other set can be obtained, and the mapping is one-to-one. This idea is formulated, and the single planar diagonal symmetry-based WFTA is derived from single planar quadrantally symmetric WFTA.