A M-D FFT algorithm for symmetric signals

Symmetric signals are defined by subsets of their support which depend on the specific symmetry. Depending on the symmetry, the cardinality of these subsets may be much smaller than that of the supports. The DFT of the symmetric signals enjoys symmetries related to the input symmetry, by which the DFT is defined by subsets the same as those defining the input signal. In principle, the computation of the DFT of symmetric signal can only use the input subset sufficient for defining the signal. In practice, all known MD FFT algorithms can only take advantage of even and odd parity's symmetries, and cannot exploit general signal symmetries for reducing the computation. This work presents a new MD FFT algorithm capable of saving computation in front of general signal's symmetries.