K-cyclic symmetries in multidimensional sampled signals

In this paper, K-cyclic frequency domain symmetry conditions for N-dimensional sampled signals are introduced. It is shown that these frequency domain symmetry conditions result in certain interrelationships between the sample values. A theorem is given that specifies these interrelationships. Several interesting properties of K-cyclic symmetries are discussed. Also, a systematic approach is given for finding the parameters of several commonly encountered symmetry conditions. Certain implications to multidimensional digital filtering are discussed, including L
p
optimality and the reduction in computation for design and implementation.